EASWARI ENGINEERING COLLEGE

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1 EASWARI ENGINEERING COLLEGE DEPARTMENT OF ECE QUESTION BANK Sub Code: EC1302 Subject : Digital signal Processing Faculty :S.Sridharan Degree/Branch:B.E / ECE Year/semester/Section: III / V / A& B PART-A UNIT I 1. If H(k) is the N-point DFT of a sequence h(n),prov that H(k) and H(N- K) are comlex conjugates. (Nov2008) Complex conjugate property of DFT 2. What are the differences and similarities between DIF and DIT algorithms? (Nov2008) Sl.No DIT FFT DIF FFT 1 The time domain sequence is The DFT x(k) is decimated decimated 2 Input sequence is to be given in bit reversed order. The DFT at the output is in bit reversed order. 3 First calculate 2-point DFTs and combines them Decimates the sequence step by step to 2-point sequence and 4 Suitable for calculating inverse DFT. calculate DFT. Suitable for calculating DFT. 3. Define the properties of convolution. (April 2008, Nov 2005) Commutative Law x(n)*h(n)= h(n)*x(n) Associative Law [ x(n)*h1(n)]*h2(n)= x(n)*[h1(n)*h2(n)] Distributive Law x(n)*[h1(n)]+h2(n)]= x(n)*h1(n)+x(n)*h2(n) 4. Draw the basic butterfly diagram of radix-2 FFT. (April 2005, May 2007 & April 2008) a A=a+W n b b W n -1 B=a-W n b

2 5. State and prove parseval s relation for DFT.(Nov 2007) Refer book: Digital signal processing Proakis(pgno:424) 6. What do you mean by the term bit reversal as applied to FFT Refer book: Digital signal processing by Ramesh Babu.(pgno:4.9) 7. Determine the DTFT of a sequence x(n) = a n u(n) (Nov 2006) X(K) = x(n) e j2πkn/n The given sequence x(n) = a n u(n) DTFT{x(n)} = x(n) e j2πkn/n = (a e j2πk/n ) n Where a n = 1-a n /(1-a) X(K) = (1 a N e j2πk )/ (1-ae j2πk/n ) 8. What are the advantages of FFT algorithm over direct computation of DFT? (May 2007) The complex multiplication in the FFT algorithm is reduced by (N/2) log2n times. Processing speed is very high compared to the direct computation of DFT. 9. the first five DFT coefficients of a sequence x(n) are x(0) = 20, x(1) = 5+j2, x(2) = 0, x(3)=0.2+j0.4, X(4) = 0. Determine the remaining DFT coefficients. (May 2007) By complex conjugate property x(5)=0.2-j0.4,x(6)=0,x(7)=5-j2 10. Define symmetric and Anti symmetric signals. How do you prevent aliasing while sampling a CT signal? (May 2007) A real valued signal x(n) is called symmetric if X (n) = X (-n) On the other hand, a signal x(n) is called antisymmetric X (-n) = -X (n) 11. what is the necessary and sufficient condition on the impulse response for stability? (May 2007) The necessary and sufficient condition for the impulse response is given by + h (n) < n=- 12. Define Complex Conjugate of DFT property. (May 2007) DFT If x(n) X(k) then N

3 X*(n) (X*(-k)) N = X*(N-K) 13. What is FFT? (Nov 2006) The fast Fourier transform is an algorithm is used to calculate the DFT. It is based on fundamental principal of decomposing the computation of DFT of a sequence of the length N in to successively smaller discrete Fourier Transforms. The FFT algorithm provides speed increase factor when compared with direct computation of the DFT. 14. State sampling theorem? (Nov 2006) Sampling is the process to convert analog time domain continuous signal into discrete time domain signal. But it is the process of converting only time domain not in amplitude domain. Nyquist criteria: We sample the signal based on the following condition i.e., f s 2f m Where f x = Sampling frequency F m = maximum signal frequency If these above conditions are not satisfied we will meet the following demerits after the sampling process. 1. Guard band 2. Aliasing Effect 15. What is BIBO Stability? What is necessary and sufficient condition for BIBO stability? (May 2006, Nov 2004) Any system is said to be BIBO stable of and only if every bounded input gives a bounded output. The BIBO stability depends on the impulse response of the system. The necessary and sufficient condition for BIBO stability 16. How will you perform linear convolution via circular convolution? (May 2006) Let the length of x(n) be L, length of h(n) be M. then linear convolution of x(n) and h(n) can be obtained through following steps. i. Append x(n) with M-1 zeros. Hence its length will be L+M-1 ii. Append h(n) with L-1 zeros. Hence its length will be L+M-1 iii. Perform circular convolution of above sequences. The result is linear convolution of length L+M How many multiplications and additions are required to compute N- point DFT using radix-2 FFT? In computing N-point DFT by this method the number of stages of computation will be m-times. The number r is called the radix of the FFT algorithms. In radix-2-fft, the total number of complex additions are reduced to N log 2 N and total number of complex multiplications are reduced too (N/@)log 2 N.

4 18. What is decimation-in-time algorithm? The computation of 8-point DFT using radix -2 DIT FFT, involves three stages of computation. Here N= = 2 3 therefore r=2 and m=3. The given 8 point sequence is decimated to 2 point sequences. For each 2 point sequence, the 2 point DFT is computed. From the result of 2-point DFT the 4-point DFT can be computed. From the result of 4-point DFT, the 8-point DFT can be computed. Let the given sequence be X9o),X(1),X(2), X(3), X(4), X(5), X(6), X(7) which consists of 8 samples. 19. What is decimation-in-frequency algorithm? In decimation in frequency algorithm the frequency domain sequence X(k) is decimated. In this method, the output DFT sequence X(k) is divided into smaller sequence. 20. Derive the necessary and sufficient condition for an LTI system to be BIBO stable. (April 2005) A system is BIBO stable, if for every bounded input, the output is finite. Mathematically if x(t) < And y(t) < then the system is stable. The necessary and sufficient condition for Continuous time signal is stable if and only if - h(t) 1 = h(n) dt < In discrete time system h 1 = h(n) n=- 21. Define DTFT pair? (April 2004 & May 2007) The DTFT pairs are X(k) = x(n)e -j2πkn/n X(n) = x(k)e j2πkn/n 22. What is aliasing? (Nov 2003) If we operate the sampler at f x < f m, the frequency components of the frequency spectrum will overlap with each other i.e., the lower frequency of the second frequency component will overlap with higher frequency of the first frequency component. This overlapping effect is called as Aliasing effect.

5 For avoiding overlapping of high and low frequency components, we have to use low-pass filter to cut the unwanted high frequency components. 23. Test the following systems for time variance a. y(n) = nx 2 (n) Time variance b. y(n) = a x(n) Time invariance 24. Give any two properties of DFT a)periodicity x(k+n)=x(k) b)linearity DFT{a1x1(n)+a2x2(n)}=a1x1(k)+a2x2(k). 25. Explain Linearity property of DFT DFT{x (n)}=x (k)&dft{x (n)}=x (k) For any real valued constant a &a. DFT{a x (n)+a x (n)=a X (k)+a X (k) 26. Find the DFT of the sequence. X(n)={1,1,0,0} DFT{x(n)}=X(k) = x(n)e^-j2 n k/n X(k)= x(n)e^j2 nk/4 =1+e^-j k/2+0+0 =2 cos( K/4)e^-j k/4 X(k)=- k/4 UNIT -II 1. Show that the filter with h (n) = [-1, 0, 1] is a linear phase filter. (Nov 2008,May 2007) Refer Book: Digital signal processing Ramesh Babu.(pgno:MQ17) 2. What is prewarping? (Nov 2003,2008) When bilinear transformation is applied, the discrete time frequency is related continuous time frequency as, Ω = 2tan -1 ΩT/2 This equation shows that frequency relationship is highly nonlinear. It is also called frequency warping. This effect can be nullified by applying prewarping. The specifications of equivalent analog filter are obtained by following relationship, Ω = 2/T tan ω/2 This is called prewarping relationship. 3. What are the merits and demerits of FIR filters? (Nov 2005 & April 2008) FIR filters that have ideal linear phase characteristics can be easily designed. FIR filters realized non-recursively are always stable.

6 Errors arising from quantization of signals and finite word length effects are usually less critical for FIR filter designs as these realization do not have feedback FIR filters are implemented through FFT algorithms, which greatly reduced its processing time. 4. What is the relation betweeen analog and digital frequency in impulse invariant transformation?(april 2008) ΩT= ω 5. In the design of FIR digital filters, how is Kaiser window different from other windows? (Nov 2007) It provides flexibility for the designer to select the side lobe level and N. It has the attractive property that the side lobe level can be varied continuously from the low value in the Blackman window to the high value in the rectangular window. 6. Find the digital transfer function H(z) by using impulse invariant method for the analog transfer function H(s) = 1/ (s+2). Assume T=0.1 sec. (Nov 2007) H(Z)=1/(1-e (-p1*t) z -1 ) H(Z)=1/(1-e (-0.2) z -1 ) 7. Obtain the block diagram representation of a FIR System. (Nov 2006) 8. State the condition for a digital filter to be causal and stable. (May 2007) The response of the causal system to an input does not depend on future values of that input, but depends only on the present and/or past values of the input. A filter is said to be stable, bounded-input bounded output stable, if every bounded input produces a bounded output. A bounded signal has amplitude that remains finite. 9. What is the condition satisfied by linear phase FIR filter? (Nov/Dec 2003 & May 2007)

7 Linear phase is of the form θ (ω) = k ω Here k is constant. Thus phase shift is linearly proportional to frequency. For linear phase, the impulse response should satisfy following condition. h (n) = ± h (M-1-n) 10. Find the digital transfer function H (z) by using impulse invariant method for the analog transfer function H(s) = 1/(S+2). Assume T=0.5sec. H(s) = 1/s+2 The system function of the digital filter is obtained by H (z) = 1/ (1-e -2T z -1 ) Since T=o.5 sec H (z) = 1/ (1-.067Z -1 ) 11. Compare FIR and IIR filters. (May 2007) Sl.No IIR FIR 1 H(n) is infinite duration H(n) is finite duration 2 Poles as well as zeros are These are all zero filters. present. Sometimes all pole filters are also designed. 3 These filters use feedback from These filters do not use output. They are recursive filters. feedback. They are nonrecursive. 4 Nonlinear phase response. Linear phase response for h(n) Linear phase is obtained if H(z) = ± h(m-1-n) = ±Z -1 H(Z -1 ) 5 These filters are to be designed These are inherently stable for stability filtersl 6 Number of multiplication More requirement is less. 7 More complexity of Less complexity of implementation implementation 8 Less memory is required More memory is requied 9 Design procedure is Less complicated complication 10 Design methods: 1. Bilinear Transform 2. Impulse invariance. 11 Can be used where sharp cutoff characteristics with minimum order are required Design methods: 1. Windowing 2. Frequency sampling Used where linear phase characteristic is essential. 12. Give any two properties of Butterworth filter and chebyshev filter. (Nov/Dec 2006, May/June 2006, Apr 2005 & Nov 2004)

8 a. The magnitude response of the Butterworth filter decreases monotonically as the frequency increases (Ώ) from 0 to. b. The magnitude response of the Butterworth filter closely approximates the ideal response as the order N increases. c. The poles on the Butterworth filter lies on the circle. d. The magnitude response of the chebyshev type-i filter exhibits ripple in the pass band. e. The poles of the Chebyshev type-i filter lies on an ellipse. 13. Mention any two procedures for digitizing the transfer function of an analog filter. (Nov 2006) 1. Impulse Invariant Technique 2. Bilinear Transform Technique 14. what are the parameters that can be obtained from the chebyshev filter specification? (Nov 2006 May 2007) (or) Give the equation for the order N, major, minor and axis of an ellipse in case of chebyshev filter. (Nov 2005) N cosh -1 (λ/ε) / cosh -1 (Ώ S / Ώ P ) Where λ = (10 0.1αs 1) ε = (10 0.1αp 1) 15. What are the advantages and disadvantages of bilinear transformation? Advantages: (May 2006) 1. Many to one mapping. 2. linear frequency relationship between analog and its transformed digital frequency, Disadvantage: Aliasing 16. What are the desirable and undesirable features of FIR Filters? (May2006) The width of the main lobe should be small and it should contain as much of total energy as possible. The side lobes should decease in energy rapidly as w tends to π 17. Define Hanning and Blackman window functions. (May 2006) The window function of a causal hanning window is given by W Hann (n) = cos2πn/ (M-1), 0 n M-1 0, Otherwise The window function of non-causal Hanning window I s expressed by W Hann (n) = cos2πn/ (M-1), 0 n (M-1)/2 0, Otherwise The width of the main lobe is approximately 8π/M and thee peak of the first side lobe is at -32dB. The window function of a causal Blackman window is expressed by W B (n) = cos2πn/ (M-1) cos4πn/(m-1), 0 n M-1

9 = 0, otherwise The window function of a non causal Blackman window is expressed by W B (n) = cos2πn/ (M-1) cos4πn/(m-1), 0 n (M-1)/2 = 0, otherwise The width of the main lobe is approximately 12π/M and the peak of the first side lobe is at -58dB. 18. Write the magnitude function of Butterworth filter. What is the effect of varying order of N on magnitude and phase response? (Nov 2005) H(jΏ) 2 = 1 / [ 1 + (Ώ/Ώ C ) 2N ] where N= 1,2,3,. 19. Mention the necessary and sufficient condition for linear phase characteristics in FIR filter. (Nov 2005) The necessary and sufficient conditions is that the phase function should be linear function w, which in turn requires constant phase delay (or) constant phase and group delay i.e., Q(w) α w Q(w) = - α w -π w π 20. What is impulse invariant mapping? What is its limitation? (Apr/May 2005) The philosophy of this technique is to transform an analog prototype filter into an IIR discrete time filter whose impulse response [h(n)] is a sampled version of the analog filter s impulse response, multiplied by T. This procedure involves choosing the response of the digital filter as an equi-spaced sampled version of the analog filter. 21. What is linear phase? What is the condition to be satisfied by the impulse response in order to have a linear phase? (Apr 2005 & Nov 2003) For a filter to have linear phase the phase response θ(w) α w is the angular frequency. The linear phase filter does not alter the shape of the signal. The necessary and sufficient condition for a filter to have linear phase. h(n) = ± h(n-1-n); 0 n N What is frequency warping? (Nov2004 & May 2007) The bilinear transform is a method of compressing the infinite, straight analog frequency axis to a finite one long enough to wrap around the unit circle only once. This is also sometimes called frequency warping. This introduces a distortion in the frequency. This is undone by pre-warping the critical frequencies of the analog filter (cutoff frequency, center frequency) such that when the analog filter is transformed into the digital filter, the designed digital filter will meet the desired specifications. 23. List the characteristics of FIR filters designed using window functions. (Nov 2004)

10 the Fourier transform of the window function W(e jw ) should have a small width of main lobe containing as much of the total energy as possible the fourier transform of the window function W(e jw ) should have side lobes that decrease in energy rapidly as w to π. Some of the most frequently used window functions are described in the following sections. 24. What are the limitations of impulse invariant mapping technique? (Apr2004) The impulse invariance technique is appropriate only for band limited filter like low pass filter. Impulse invariance design for high pass or band stop continuous-time filters, require additional band limiting to avoid severe aliasing distortion, if impulse designed is used. Thus this method is not preferred in the design of IIR filters other than low-pass filters. 25. Give the transform relation for converting low pass to band pass in digital domain. (Apr 2004) Low pass with cut off frequency Ώ C to band pass with lower cut-off frequency Ώ 1 and higher cut-off frequency Ώ 2 : S Ώ C ( s 2 + Ώ1 Ώ2) / s (Ώ 2 - Ώ 1 ) The system function of the high pass filter is then H(s) = H p { Ώ C ( s 2 + Ώ1 Ώ2) / s (Ώ 2 - Ώ 1 )} 26. Give the Kaiser Window function. (Apr 2004) The Kaiser Window function is given by W K (n) = I 0 (β) / I 0 (α), for n (M-1)/2 Where α is an independent variable determined by Kaiser. Β = α[ 1 (2n/M-1) 2 ] 27. Give the bilinear transformation. (Nov2003) The bilinear transformation method overcomes the effect of aliasing that is caused due to the analog frequency response containing components at or beyond the nyquist frequency. The bilinear transform is a method of compressing the infinite, straight analog frequency axis to a finite one long enough to wrap around the unit circle only once. S = (2/T) (Z-1) (Z+1) UNIT III 1. Express the fraction (-9/32) in sign magnitude, 2 s complement notations using 6 bits. (Nov 2008) Sign magnitude : s complement :

11 2. What are the various factors which degrade the performance of digital filter implementation when finite word length is used? (Nov 2008) 3. What are the three types of quantization error occurred in digital systems? ( Nov 2006 & Apr 2008) Input quantization error coefficient quantization error product quantization error 4. What is meant by limit cycle oscillations? ((May 2006,Apr 2005 May 2007, Nov 2007 & Apr 2008) In fixed point addition, overflow occurs due to excess of results bit, which are stored at the registers. Due to this overflow, oscillation will occur in the system. Thus oscillation is called as an overflow limit cycle oscillation. 5. Express the fraction(-7/32) in signed magnitude and two s complement notations using 6 bits. (Nov 2007) Sign magnitude : s complement : Express the fraction 7/8 and -7/8 in sign magnitude, 2 s complement and 1 s complement. (Nov 2006) 7/8-7/8 Sign magnitude : s complement : s complement : Define Sampling rate conversion. (May 2007) Sampling rate conversion is the process of converting a signal from one sampling rate to another, while changing the information carried by the signal as little as possible. Sample rate conversion needed because different systems use different sampling rates. 8. Convert the number 0.21 into equivalent 6-bit fixed point number. (May 2007) Why rounding is preferred to truncation in realizing digital filter?(may2007) Error introduced due to rounding operation is less compared to truncation. Similarly quantization error due to rounding is independent of arithmetic operation. And mean of rounding error is zero. Hence rounding is preferred over truncation in realizing digital filter. 10. What are the different quantization methods? (Nov 2006) amplitude quantization vector quantization

12 scalar quantization 11. What is zero padding? Does zero padding improve the frequency resolution in the spectral estimate? (Nov 2006) The process of lengthening a sequence by adding zero valued samples is called appending with zeros or zero padding. 12. List the advantages of floating point arithmetic. (Nov 2006) Large dynamic range Occurrence of overflow is very rare Higher accuracy 13. Give the expression for signal to quantization noise ratio and calculate the improvement with an increase of 2 bits to the existing bit.(nov2006,nov2005) SNR A / D = b-20log 10 (R FS /σ x ) db. With b= 2 bits increase, the signal to noise ratio will increase by 6.02 X 2 = 12dB. 14. Draw the probability density function for rounding. (Nov 2005) Shows the probability density function of error in rounding operation. 15. Compare fixed point and floating point representations. (May/Jun 2006) Fixed Point Arithmetic It covers only the dynamic range. Compared to FPA, accuracy is poor Compared to FPA it is low cost and easy to design It is preferred for real time operation system Errors occurs only for multiplication Processing speed is high Floating Point Arithmetic It covers a large range of numbers It attains its higher accuracy Hardware implementation is costlier and difficult to design It is not preferred for real time operations. Truncation and rounding errors occur both for multiplication and addition Processing speed is low Overflow is a range phenomenon Overflow is rare phenomenon 16. What is dead band? (Nov 2004)

13 In a limit cycle the amplitude of the output are confined to a range of value, which is called dead band. 17. How can overflow limit cycles be eliminated? (Nov 2004) Saturation Arithmetic Scaling 18. What is zero input limit cycle oscillation? (Apr 2004) Zero Input Limit Cycles: Zero input limit cycles are usually of lower amplitude in comparison with overflow limit cycles. If the system enters to the limit cycles oscillations, it will continue even after input attains zero range. 19. What is steady state noise power at the output of an LTI system due to the quantization at the input to L bits? (Nov 2003 &Apr 2004) The steady state noise power is basically the variance of output noise. Π σ P = σ e2.1/2π H(ω) 2 dw -π Here σ e 2 is the variance of input error signal. Σ e 2 = 2-2L R FS 2 /48 π σ v 2 = 2-2L R FS 2 /48 X ½π H (ω) 2 dw - π This equation gives steady state noise power due to quantization. 20. What is meant by finite word length effects in digital filters? (Nov 2003) The digital implementation of the filter has finite accuracy. When numbers are represented in digital form, errors are introduced due to their finite accuracy. These errors generate finite precision effects or finite word length effects. When multiplication or addition is performed in digital filter, the result is to be represented by finite word length (bits). Therefore the result is quantized so that it can be represented by finite word register. This quantization error can create noise or oscillations in the output. These effects are called finite word length effects. 21. What is round-off noise error? Rounding operation is performed only on magnitude of the number. Hence round-off noise error is independent of type of fixed point representation. If the number is represented by b u bits before quantization and b bits after quantization, then maximum round-off error will be (2 _b -2 -bu )/2. It is symmetric about zero. 22. What is meant by fixed point arithmetic? Give example?

14 In the fixed point arithmetic, the digits to the left of the decimal point represent the integer part of the number and digits to the right of the decimal point represent fractional part of the number. For example, ( ) 10 ( ) 2 are the fixed point numbers note that base of the number system is also written outside the bracket. 23. What is round off noise error? Rounding operation is performed only on magnitude of the number. Hence round-off noise error is independent of type of fixed point representation. If the number is represented by b u bits before quantization and b bits after quantization, the maximum round-off error will be (2 -b 2 -bu )/2. It is symmetric about zero. UNIT IV 1. Defione unbiased estimate and consistent estimate. ( Apr 2007,Nov 2008)) Consistency is an asymptotic property : defining consistency requires considering arbitrarily large samples. In real life, sample size will be limited by time or budget constraints. So it is natural to consider what quality should be expected from an estimator based on samples of a fixed size n. Then you would certainly hope the central region of the distribution of the estimator to be close to the true value θ 0 of the parameter. One way of expressing this idea is to consider estimators whose distribution mean is equal to θ 0 for any value of n, the true value of the parameter θ. Such an estimator is said to be unbiased., and unbiasedness translates into : 2. E[θ] n = θ 0 for any n 3. What are the disadvantages of non-parametric methods of power spectral estimation? (May 2007,Nov 2008) It requires long data sequences to obtain the necessary frequency resolution. Spectral leakage effects because of windowing The assumption of the autocorrelation estimate r xx (m) to be zero for m N. this assumption limits the frequency resolution and quality of the power spectrum estimate. Assumption that the data are periodic with period N. these assumption may not be realistic. 4. What is periodogram? ( Apr/May 2008) Periodogram is used to detect and measure hidden periodicity in the data let us take average value of periodogram estimate from equation 5. Determine the frequency resolution of the bartlett method of power spectrum estimates for a quality factor Q=15. Assume that the length of the sample sequence is (Apr 2008)

15 6. Define the terms autocorrelation sequence and power spectral density(apr 2007)If x(t) is the stationary random process, then its autocorrelation function is given as, γ xx (τ) = E[ x * (t) x(t+ τ)] Here E [] denotes the statistical average. 7. Define power spectral density and cross spectral density. (May2007) power spectral density (PSD), which describes how the power of a signal or time series is distributed with frequency. The instantaneous power (the mean or expected value of which is the average power) is then given by: The PSD is the Fourier transform of the autocorrelation function, R(τ), of the signal if the signal can be treated as a wide-sense stationary random process. The power of the signal in a given frequency band can be calculated by integrating over positive and negative frequencies, The power spectral density of a signal exists if and only if the signal is a widesense stationary process. The power spectrum G(f) is defined as Cross-spectral density "Just as the Power Spectral Density (PSD) is the Fourier transform of the autocovariance function we may define the Cross Spectral Density (CSD) as the Fourier transform of the cross-covariance function. 8. Explain deterministic and nondeterministic signals with examples. (Nov2006) Deterministic signals are functions that are completely specified in time. The nature and amplitude of such a signal at any time can be predicted. The pattern of the signal is regular and can be characterized mathematically. Examples:-

16 X(t) = αt this is a ramp whose amplitude increases linearly with time and slope is α. A non-deterministic signal is one whose occurrence is random in nature and its pattern is quite irregular. A typical example of non deterministic signal is thermal noise in an electrical circuit. 9. Explain the use of DFT in power spectrum estimate? We know that the periodogram f the signal is given as, P xx (f) = 1/N X(f) 2 = 1/N x(n) e -j2πfn n=- The fourier transform on right hand side of above equation can also be evaluated using DFT. The DFT contains N-points. It is given as, N-1 P xx (k/n) = 1/N x(n) e -j2πkn/n 2 n=0 Thus the periodogram will now be evaluated at discrete frequencies f k = k/n. the resolution of the spectrum can be increased bu increasing the length of the DFT. 10. Define autocorrelation. If x(t) is the stationary random process, then its autocorrelation function is given as, γ xx (τ) = E[ x * (t) x(t+ τ)] Here E [] denotes the statistical average. 11. List the non-parametric methods for power spectral estimation. Barlett method Welch method Blackman and Turkey method 12. What are the steps involved in Bartlett method? The N-point sequence is subdivided into K number of non overlapping segments. Each segment has the length M. i.e., X i (n) = x(n+i M), i=0, 1,.k-1 Compuite the periodogram of each segment independently i.e., M-1 P i xx(f) = 1/N x(n) e -j2πfn 2 n=0 Take average of periodograms of all the K segments to get barlett power spectrum estimate. k-1

17 P B xx(f) = 1/K P i xx(f) i=0 This equation gives the estimate of power spectrum using Bartlett method. 13. What are the steps involved in Welch method? This method makes few modifications to Bartlett method. The three steps are as follows to calculate the periodogram. The N-point sequence is subdivided into L number of segments. These segments overlap over each other. The data segment is passed through the window and then periodogram is calculated. The power density spectrum is then obtained by averaging the modified periodogram. 14. Define Blackman and turkey method? The Blackman and tukey suggested a new method in which less weight is given to end points of r xx (m), variance is very high. As per this method, the autocorrelation sequence is first passed through a window w(m). this window shapes r xx (m) in such a way that weights of end points are reduced. UNIT V 1. What are the factors that may be consideredd when selecting a DSP processor for an application? (Nov 2008) 2. State the merit and demerit of multiported memories?(may 2007,Nov 2008) 3. What is meant by pipelining? (Apr2008 & Nov 2007) A pipeline is the continuous and somewhat overlapped movement of instruction to the processor or in the arithmetic steps taken by the processor to perform an instruction. With pipelining, the computer architecture allows the next instructions to be fetched while the processor is performing arithmetic operations, holding them in a buffer close to the processor until each instruction operation can be performed. The staging of instruction fetching is continuous. The result is an increase in the number of instructions that can be performed during a given time period. 4. What is the principal features of the harvard Architecture?(Apr 2008) The Harvard architecture has two separate memories for their instructions and data.it is capable of simultaneous reading an instruction code and reading or writing a memory or peripheral.

18 5. Differentiate between von Neumann and Harvard architecture? (May 2007) Sl.No Harvard Architecture Von-Neumann Architecture 1 Separate memories for It shares same memory for program and data. 2 The speed of execution in Harvard architecture is high 3 In this architecture having a common interval address and data bus. 4 It is not suitable for DSP processors. program and data. The speed of execution is increased by pipelining It is having a separate interval address and data bus. It is normally used for Harvard architecture. 6. Give the digital signal processing application with the TMS 320 family. (Nov 2006) DSP processors should have circular buffers to support circular shift operations. The DSP processor should be able to perform multiply and accumulate operations very fast. DSP processors should have multiple pointers to support multiple operands jumps and shifts. 7. What is the advantage of Harvard architecture of TMS 320 series? (Nov 2006) It shares same memory for program and data The speed of execution is increased by pipelining It is having a separate interval address and data bus. It is normally used for Harvard architecture 35. What are the desirable features of DSP Processors? (Nov 2006) o DSP processors should have multiple registers so that data exchange from register to register is fast. o DSP operations require multiple operands simultaneously. Hence DSP processor should have multiple operand fetch capacity. o DSP processors should have circular buffers to support circular shift operations. o The DSP processor should be able to perform multiply and accumulate operations very fast.

19 o o DSP processors should have multiple pointers to support multiple operands jumps and shifts. Multi processing ability. 36. What are the different types of DSP Architecture? Von-Neumann Architecture Harvard Architecture Modified Harvard Architecture 37. Define MAC unit? The dedicated hardware unit is called MAC. It is called multiplieraccumulator. It is one of the computational unit in processor. The complete MAC operation is executed in one clock cycle. The DSP processors have a special instruction called MACD. This means multiply accumulate with data shift. 39. Mention the Addressing modes in DSP processors. Short immediate addressing Short Direct Addressing Memory-mapped Addressing Indirect Addressing 6.5 bit reversed addressing mode Circular addressing 40. State the features f TMS3205C5x series of DSP processors. Powerful 16 bit CPU TDM port 16X16 bit multiplies / Add operations can be performed in single cycle. 224KX16 bit maximum addressable external memory space. Full duplex synchronous serial port for coder / decoder interface. On-chip scan based emulation logic. Boundary scan Low power dissipation IEEE standard text access ports 41. Define Parallel logic unit? It executes logic operations on the data without affecting the contents of ACC. PLU provides bit manipulation which can be used to set, clear, test or toggle bits in data memory control or status registers. 42. Define scaling shifter?

20 The scaling shifter has a 16 bit input connected to the data bus and 32 bit output connected to the ALU. The scaling shifter produces a left shift of 0 to 16 bits on the input data. The other shifters perform numerical scaling, bit extraction, extended precision arithmetic and overflow prevention. 43. Define ARAU in TMS320C5X processor? ARAU meant Auxiliary register and auxiliary register arithmetic unit. These register are used for temporary data storage. The auxiliary register file is connected to the auxiliary register arithmetic unit. The contents of the auxiliary register can be ARAU helps to speed up the operations of CALU. 44. What are the Interrupts available in TMS320C5X processors? It has four general purpose interrupts. INT4 INT1 RS (Reset) NMI (Non Maskable interrupt) 45. What are the addressing modes available in TMS320C5X processors? Direct Indirect Immediate Register Memory mapped Circular Addressing 46. Write the syntax of assembly language syntax. The source statement can contain following four ordered fields. i.e., [Label][:] mnemonic [operand list] [; comment] The source statement follows following guidelines All the statements must begin with a label, a blank, an asterisk or a semicolon. Labels may be placed before the instruction mnemonic on the same line or on the proceeding line in the first column. Each field must be separated with blanks. If comment begins in column 1 it must have semicolon or asterisk at its beginning. In other columns, comments can begin with semicolon. PART B UNIT I 1. (a) Two finite duration sequences are given by (Nov 2008) x(n)=cos(n π/2) for n=0,1,2,3 0, elsewhere

21 h(n)=(0.5) n for n=0,1,2,3 0, elsewhere (i) Calculate the 4 point DFT X(k) Refer book: Digital signal processing by S.Salivahanan(pgno:344) (ii) Calculate the 4 point DFT H(k) (iii) If Y(k)=X(k)H(k),determine y(n),the inverse DFT of Y(k) 2. (a) Obtain an 8-point DIT FFT flow graph from first principles. (May 2007,Nov 2008) Refer book: Digital signal processing by S.Salivahanan(pgno:320) (b) Using the above flow graph compute DFT of x(n) = cosn π/4 for n=0,1,, 7(Nov 2008) 3. (a) Discuss in detail the important properties of the Discrete Fourier Transform Refer book: Digital signal processing by S.Salivahanan(pgno:308) (b) find the 4 point DFT of the sequence x(n) = Cos nπ/4 (Apr 2008) 4. Compute an 8 point DFT using DIF FFT radix 2 algorithm X(n) = {1,2,3,4,4,3,2,1}(May 2006 & Apr 2008) Refer book: Digital signal processing by S.Salivahanan(pgno:340) 5. (a) Obtain an 8-point DIF FFT flow graph from first principles. Refer book: Digital signal processing by S.Salivahanan(pgno:334) (b) Using the above flow graph compute DFT of x(n) = cosn π/4 for n=0,1,, 7(Nov 2007,April 2008) 6. Two finite duration sequences are given by X(n) = sin(n π/2 for n= and h(n) =2 n for n=0,1,2,3 find circular convolution using DFT method. (Nov 2007) 7. (a) i. calculate the DFT of the sequence x(n) = [ 1,1,-2,-2 ii. Determine the response of LTI system by radix 2 DIT FFT. iii. How do you linear Filtering by FFT using save-add method? Refer book: Digital signal processing by S.Salivahanan(pgno:371) 8. State and prove parseval s theorem for discrete time Fourier Transform. (May 2006) Refer book: Digital signal processing by S.Salivahanan(pgno:310) 9. Find the 8 point DFT of the sequence x(n) = [1,2,3,4,4,3,2,1] using decimation-intime radix -2 FFT algorithm. (May 2006) Refer book: Digital signal processing by S.Salivahanan(pgno:329) 10. i. finite duration sequence of length L is given as X (n) = 1 for o n L-1 0 for otherwise, (May2007)

22 Determine the N point DFT of the sequence for N=L. ii. Perform the circular convolution of the following two sequences. X 1 (n) = { } X 2 (n) = { } (May 2007) Refer Book: Digital signal processing Ramesh Babu.(pgno:MQ32) 11. Draw the butterfly diagram using 8 point DIT FFT for the following sequences. X(n) = { 1,0,0,0,0,0,0,0} (May2007) Refer Book: Digital signal processing Ramesh Babu.(pgno:4.36) 12. Compute the DFT of each of the following (i) x(n) = δ(n-n 0 ) (ii) y(n) = x 1 (n) x 2 (n) (May 2007) 13. A DFT program is available, how will you this to compute inverse DFT. (May 2007) 14. Two real signals of x(n) and y(n) are of length M. find the FT of x(n) and y(n) with minimum computation. (May2007) 15. Compute the DFT of the sequence,x(n)={1,0,1,0,1,0,1,0} and hence find X(2). Refer book: Digital signal processing by Ramesh Babu.(pgno:3.19) (APR 2005 CS) 16. Draw the FET flowchart for radix 2,DIT algorithm. Assume N=8.(APR 2005 CS) Refer book: Digital signal processing by nagoor kani. (pgno213) 17. Find the 8 pt DFT of the sequence (APR 2005 IT) x(n)={ 1 0<n<7 { 0 otherwise (using DIT FFT ) Refer book: Digital signal processing by Ramesh Babui.(pgno:4.26) 18. Compute the 8 pt DFT of the sequence (NOV 04 IT) x(n)={0.5,0.5,0.5,0.5,0,0,0,0} using DIT FFT Refer book: Digital signal processing by Ramesh Babu.(pgno:4.30) 19. Determine the 8 pt DFT of the sequence (APR 04 IT) x(n)={0,0,1,1,1,0,0,0} Refer book: Digital signal processing by nagoor kani.(pgno:226) 20. What is DIF algorithm. Write the similarities and differences between DIT and DIF. Refer book: Digital signal processing by nagoor kani.(pgno:219) (APR 04 IT) 21. Determine 8pt DFT of x(n)=1 for 3<n<3 using DIT-FFT algorithm. (APR 04 IT) Refer book: Digital signal processing by Ramesh Babu.(pgno:5.49) 22. Obtain the 8pt DIT FFT algorithm

23 Refer book: Digital signal processing by nagoor kani.(pgno:207) 23. Obtain the 8pt DIF FFT algorithm x(n)={2,2,2,2,1,1,1,1} (NOV 04 EC) Refer book: Digital signal processing by nagoor kani.(pgno:225) 24. Obtain the 8 pt DIF FFT algorithm x(n)={0,1,2,3,,4,5,6,7} (APR 05 EC) Referbook:Digital signal processing by nagoor kani.(pgno:224) UNIT II 1. A band reject filter of length 7 is required. It is to have lower and upper cutoff frequencies of 3 KHz and 5 KHz resp. The sampling frequency is 20Khz. Determine the filter coefficients using Hanning window. Assume the filter to be causal. (NOV 08) Refer book: Digital signal processing by Ramesh Babu.(pgno:MQ20) 2. Design a digital Butterworth filter that satisfies the following constraint using bilinear transformation. Assume T=0.1 sec. (NOV 08) 0.8 < H(e jω ) < 1, 0 < ω < 0.2π H(e jω ) < 0.2, 0.6π < ω < π Refer book: Digital signal processing by S.Salivahanan(pgno:437) 3. Determine the magnitude response of an FIR filter (M=11) and show the phase and group delays are constant H(z) = h(n) z -n (Apr 2008) 4. If the desired response of a low-pass filter is (Apr 2008) H d (e jω )= e -j3ω, -3π/4 w 3π/4 0, 3π/4 < ω < π Determine H(e jω )=for M=7 using a Hamming Window. 5. For the analog transfer function H(s) = 1/ (S+1) (S+2) determine H(z) using impulse invariant technique. Assume T=1sec. (Apr 2008) Refer book: Digital signal processing by S.Salivahanan(pgno:426) 6. Design a digital butterworth filter that satisfies the following constraint using bilinear transformation ( T = 1 Sec) 0.9 H (e jω ) 1 for 0 ω π/2 H (e jω ) 0.2 for 3π/4 ω π (Apr 2008) Refer book: Digital signal processing by S.Salivahanan(pgno:437) 7. Describe the design of FIR filters using frequency sampling technique. Refer book: Digital signal processing by Ramesh Babu. pgno: The desired frequency response of a low pass filter is given by H d (e jω )= e -j2ω, -π/4 w π/4

24 0, π/4 < ω < π determine the filter coefficients h d (n). obtain the coefficients h(n) of FIR filter using a rectangular window defined by w(n) = 1, 0 n 4 0, otherwise (Nov 2007) Refer book: Digital signal processing by S.Salivahanan(pgno:398) 9. Design a digital butterworth filter satisfying the following specifications 0.7 H (e jω ) 1 for 0 ω 0.2π H (e jω ) 0.004, for 0.6π ω π Assume T=1 sec. Apply impulse invariant transformation (Nov 2007) 10. Design an FIR filter using rectangular window. The magnitude specification is given Fig.1 [ first 10 coefficients only] (May 2007) Figure Here 11. design a digital Butterworth filter satisfying the constraints H (e jω ) 1 for 0 ω π/2 H (e jω ) 0.2 for 3π/4 ω π with T=1 sec using 1. Bilinear Transformation. 2. Impulse invariance. Realize the filter in each case using the most convenient realization form. (May 2007) Refer book: Digital signal processing by Ramesh Babu.(pgno:5.79) 12. Design a Chebyshev filter with a maximum pass band attenuation of 2.5 db; at Ώ p = 20 rad/sec and the stop band attenuation of 30 db at Ώ S = 50 rad/sec.(may 2007) Refer book: Digital signal processing by Ramesh Babu.(pgno:5.27) 13. Design an ideal Hilbert transformer having frequency response (May 2007) H (e jω ) = j for -π ω 0 = -j for 0 ω π using i) rectangular window ii) black man window For N=11 plot the frequency response in both cases. Refer book: Digital signal processing by Ramesh Babu.(pgno:6.75) 14. Realize the system given by difference equation (May 2007) y (n) = -0.1 y(n-1) y(n-2) + 0.7x(n) x(n-2) in parallel form Refer book: Digital signal processing by Ramesh Babu.(pgno:5.61) 15. An FIR filter is given by the difference equation y(n) = 2x(n) + 4/5x(n-1)+3/2x(n-2)+2/3x(n-3) determine its lattice form. (May 2007) Refer book: Digital signal processing by Ramesh Babu.(pgno:6.114)

25 16. Using a rectangular window technique design a low pass filter with pass band gain of unity, cut off frequency of 1000 Hz and working at a sampling frequency of 5 KHz. The length of the impulse response should be 7. (May 2007) Refer book: Digital signal processing by Ramesh Babu.(pgno:6.97) 17. Derive the frequency response of a linear phase FIR filter with symmetric impulse response. (NOV 04EC) Refer book: Digital signal processing by nagoor kani.(pgno:36) 9. Explain in detail about frequency sampling method of designing an FIR filter. (NOV 04 IT) Refer book: Digital signal processing by Ramesh Babu.(pgno: ) 10. What are the issues in designing FIR filter using window method. (APR 04 IT) Refer book: Digital signal processing by nagoor kani.(pgno:370) 11. (i) Mention the advantages and disadvantages of FIR and IIR filters. (APR 04IT) Refer book: Digital signal processing by Ramesh Babu.(pgno:5.59) (ii).state the merits and demerits of FIR filter. (NOV03IT) Refer book: Digital signal processing by Ramesh Babu.(pgno:5.52) 12. Using the Bilinear transform design a high pass filter, monotonic in (NOV05EC) Pass band with cutt off frequency of 1000Hz and down 10dB at 350Hz.The sampling frequency is 5000Hz Refer book: Digital signal processing Ramesh Babu.(pgno: 5.62) 13. (i) An analog filter has a transfer function. Using impulse invariant method converts to digital filter. (NOV04IT) H(s) = s 2 +7s+10 (ii) Refer book: Digital signal processing Nagoor kani.(pgno:219) Using bilinear transformation convert to z domain at T=1sec. (NOV03IT) H(s)= (s+1)(s+2) Refer Book: Digital signal processing Ramesh Babu.(pgno:5.49) 14. Using impulse invariant mapping technique converts the following Analog transfer function to digital assume T=0.1sec (NOV 04 EC) H(s) = (s+1)(s+2) Refer book: Digital signal processing Ramesh Babu.(pgno:4.26)

26 UNIT III 1. (i)consider (b+1)-bit (including sign bit) biplar ADC. Obtain an expression for signal to quantization noise ratio.state the assumptions made.(nov 2008) Refer book: Digital signal processing Proakis(pgno:753) (ii)consider the truncation of negative fraction numbers represented in (β+1) bit fixed point binary form including sign bit. Let (β-b) bits be truncated. Obtain the range of truncation errors for signed magnitude. 2 s complement and 1 s complement representations of the negative numbers. (Nov 2007,Nov 2008) Refer book: Digital signal processing by Ramesh Babu.(pgno:MQ.21) 2. (i)the coefficients fo a system defined by H(z) = 1 (1-0.3z -1 ) (1-0.65z -1 ) are represented in a number system with a sign bit and 3 data bits using signed magnitude representation and truncation. Determine the new pole locations for direct realization and for cascade realization of first order systems. (Nov 2008) Refer book: Digital signal processing by Ramesh Babu.(pgno:MQ.22) (ii)an IIIR causal filter is defined by the difference equation y(n) = x(n)- 0.96y(n).The unit sample response h(n) is computed such that the computed values are rounded to one decimal place. Show that under these stated conditions, the filter output exhibits dead band effect. What is the dead band range?(nov 2008) Refer book: Digital signal processing by Ramesh Babu.(pgno:MQ.22) 3. Discuss in detail the truncation error and Round-off error for sign magnitude and two s complement representation. (Apr 2008) Refer book: Digital signal processing by Ramesh Babu.(pgno:7.9) 4. Explain the quantization effects in converting analog signal into digital signal. (Apr 2008) Refer book: Digital signal processing Proakis(pgno:750) 5. (a) A digital system is characterized by the difference equation Y(n) = 0.9y(n- 1)+x(n) with x(n) = 0 and initial condition Y(-1) = 12. Determine the dead band of the system. Refer book: Digital signal processing by Ramesh Babu.(pgno:MQ.16) (b) what is meant by the co-eefficient quantization? Explain. (Apr 2008) Refer book: Digital signal processing by Ramesh Babu.(pgno:7.29) 6. An 8-bit ADC feeds a DSP system characterized by the following trnafer function H(z) = 1/(z+0.5) estimate the steady state quantization noise power at the output of the system. (Nov 2007) 7. The coefficients fo a system defined by

27 H(z) = 1 (1-0.4z -1 ) (1-0.55z -1 ) are represented in a number system with a sign bit and 3 data bits using signed magnitude representation and truncation. Determine the new pole locations for direct realization and for cascade realization of first order systems. (Nov 2007) Refer book: Digital signal processing by Ramesh Babu.(pgno:MQ.22) 8. An IIIR causal filter has the system function H(z) = z / (z-0.97) assume that the input signal is zero-valued and the computed oputput signal values are rounded to one decimal place. Show that under these stated conditions, the filter output exhibits dead band effect. What is the dead band range? (Nov 2007) 9. (i)the input to the system y(n) = 0.999y(n-1)+x(n) is applied to an ADC. What is the power produced by the quantization noise at the output of the filter if the input is quantized to (i) 8 bits (ii) 16 bits (May 2007) Refer book: Digital signal processing by Ramesh Babu.(pgno:MQ.27) (ii)convert the following decimal number into binary: (May 2007) a. (20.675) 10 b. (120.75) 10 Refer book: Digital signal processing by Ramesh Babu.(pgno:MQ.27) 10. consider the transfer function H(z)=H 1 (z)h 2 (z) where H 1 (z) = 1/(1-a 1 z -1 ) and H 2 (z) = 1/(1-a 2 z -1 ). find the output round off noise power. Assume a 1 = 0.5 and a 2 = 0.6 and find output round off noise power. (May 2007,Nov 2006) Refer book: Digital signal processing by Ramesh Babu.(pgno:MQ.27) 11. explain the characteristics of a limit cycle oscillation with respect to the system described by the difference equation y(n) =0.95y(n-1)+x(n). determine the dead band of the filter. (Nov2006) 12. Draw the product quantization noise model of second order IIR system.(nov 2006) 13. Expain the effect of finite word length effects. (APR 05 EC) Refer book: Digital Signal Processing by Nagoor kani (pg no 264) 14. Derive the steady state noise power at the output if an LTI system due to quantization at the input. (NOV 04 EC) Refer book: Digital Signal Processing by Nagoor kani (pg no 275&294) 15. Explain about fixed point and foating point representation. (NOV 04 EC) Refer book: Digital Signal Processing by Ramesh Babu. (pg no6.38&6.39) 16. Discuss limit cycles in digital filters. (NOV 03 EC) Refer book: Digital Signal Processing by Nagoor kani (pg no 307) 17. Draw the quantization noise model for a second order

28 system with system function. H(z) = rcos0 z -1 + r 2 z -2 (APR 05 EC) 18. Determine the steady state noise. Refer book:digital Signal Processing by Nagoor kani (pg no 276) 19. Expain coefficint quantization effects in direct form realization of IIR filter. (APR 04 EC) Refer book: Digital Signal Processing by Nagoor kani (pg no 6.130&6.131) 20. A digital sytem is characterized by the difference equation. (APR 04 EC) y(n)=0.9y(n-1)+x(n) Refer book: Digital Signal Processing by Nagoor kani (pg no 6.130) 21. For the given transfer function H(z)= H 1 (z ) H 2 (z) where H 1 (z) = 1 / (1-0.5z -1 ) & H 2 (z) = 1 / (1-0.4z -1 ). Find the output round off noise Power. Calculate the value if b=3 (NOV05EC) Refer book: Digital Signal Processing by Nagoor kani (pg no 7.59) 22. Explain the characteristics of a limit cycle oscillation with respect to the system described by the difference equation y (n) =0.95y (n-1) +x (n) Determine the dead band of the filter. (NOV05EC) Refer book: Digital Signal Processing by Nagoor kani (pg no 7.63) 23. Find the effect of co-efficient quantization on pole location of the Given second order IIR system when it is realized in direct form I and in cascade form. Assume a word length of 4 bits through truncation H(z) = 1 (NOV05EC) z z -1 Refer book: Digital Signal Processing by Nagoor kani (pg no 7.66) UNIT IV 1. (i) With suitable relations, describe briefly the periodogram method of power spectral estimation. Examine the consistency and bias of periodogram. (Nov 2008,May 2007) Refer book: Digital signal processing Proakis(pgno:902) (ii)compare the basic principles used in Barlett and Welch method in spectrum estimation (Nov 2008) 2. (i)explain how the Blackman method is used in smoothing the periodogram. Derive the mean and variance of the power spectral estimate (Nov 2008) Refer book: Digital signal processing Proakis(pgno:913)