QUESTION BANK DEPARTMENT: ECE SEMESTER: V SUBJECT CODE / Name: EC2301 DIGITAL COMMUNICATION UNIT 2 BASEBAND FORMATTING TECHNIQUES 1. Why prefilterring done before sampling [AUC NOV/DEC 2010] The signal must be limited to some highest frequency W Hz before sampling. Then the signal is sampled at the frequency of fs=2w of higher. Hence the single should be prefiltered at higher that W Hz.If the signal is not prefiltered, then frequency component higher that W Hz will generate aliasing in the sampled signal spectrum 2. Define quantization noise power [AUC NOV/DEC 2010] Quantisation noise power is the noise power due to quantisation noise. Let the quantisation noise has the pdf of f (Є).Then Quantisation noise power is given as, E[Є] 2 = Є 2 f (Є)d Є 3. State sampling theorem. [AUC APR/MAY 2011] [AUC APR/MAY 2012] A band limited signal of finite energy, which has no frequency components higher than W Hz, may be completely recovered from the knowledge of its samples taken at the rate of 2W samples per second 4. What is quantization error [AUC APR/MAY 2011] Because of quantization inherent error are introduces in the signal. The error is called quantizationє=xq(nts)-x(nts) xq(nts)- quantised value of the signal x(nts)- value of the sample before quantization 5. Compare uniform and non uniform quantization [AUC NOV/DEC 2011] S.NO UNIFORM QUANTIZATION NON QUANTIZATION 1. The quantization step size remains The quantization step size varies with same throughout the dynamic range the amplitude of the input signal EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 1
of the signal 2. SNR ratio varies with input signal amplitude SNR ratio can be maintained constant 6. What is meant by temporal waveform coding The singal which varying with time can be digitzed by periodic time sampling and amplitude quantization.this process is called temporal waveform coding.dm,adm,dpcm are example of temporal waveform coding [AUC NOV/DEC 2011] 7. What is meant by quantization [AUC APR/MAY 2012] The conversion of analog sample of the signal into digital form is called quantizing process 8. Differentiate the principle of temporal waveform coding and model based coding TEMPORAL WAVEFORM CODING The signal which varying with time can be digitized by periodic time sampling and amplitude quantization. This process is called temporal waveform coding.dm,adm,dpcm are example of temporal waveform coding MODEL BASED CODING The signal is characterised in various parameter. This parameter represent the model of the signal.lpc is an example model based coding [AUC NOV/DEC 2012] 9. What is meant by DPSK? In DPSK, the input sequence is modified. Let input sequence be d(t) and output sequence be b(t). Sequence b(t) changes level at the beginning of each interval in which d(t)=1 and it does not changes level when d(t)=0. When b(t) changes level, phase of the carrier is changed. And as stated above, b(t) changes t=its level only when d(t) =1. This means phase of the carrier is changed only if d(t)=1. Hence the technique is called Differential PSK. PART B 1. Explain in detail the various sources coding techniques for speech signal and compare their performance[auc NOV/DEC 2010] [AUC APR/MAY 2011] There are several analog source coding techniques Most of the coding techniques are applied speech and image coding Three type of analog source encoding Temporal Waveform coding :design to represent digitally the time-domain characteristic of the signal EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 2
Spectral waveform coding: signal waveform is sub divided into different frequency band and either the time waveform in each band or its spectral characteristics are encoded. Model-based coding: Based on the mathematical model of source. Temporal Waveform Coding Most common used methods: Pulse-code modulation (PCM) Differential pulse-code modulation (DPCM) Delta modulation(dm) Pulse-code modulation (PCM) Let s have continuous source function x (t ) and each sample taken from x (t ) is xn at sampling rate f s 2W, where W is the highest frequency in x (t ).In PCM, each sample is quantized to one of 2R amplitude level, where number of binary digits used to represent each sample. The bit rate will be Rfs [bit/s] PULSE-CODE MODULATION (PCM) The quantized value will be n and x Assume that a uniform quantizer is used, then PDF of quantization error is Δ is step size and obtained Δ = 2 R Encoding methods for Speech signal SPECTRAL WAVEFORM CODING Filter the source output signal into a number of frequency subband and separately encode the signal in each subband. Each subband can be encoded in time-domain waveform or EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 3
Each subband can be encoded in frequency-domain waveform Source signal (such as speech or image) is divided into small number of subbands and each subband is coded in timewaveform More bits are used for the lower-frequency band signal and fever band used for higherfrequency band Subband Coding Filter design is important in achieving good performance Quadrature-mirror filters (QMFs) used most used in practice SUBBAND CODING Let s assume that Speech signal bandwidth is 3200Hz. Example: The first pair of QMFs divides the spectrum into two Low: 0-1600Hz, and High: 1600-3200Hz. The Low band split into two using another pair of QMFs Low: 0-800Hz, and High: 800-1600Hz. The Low band split into two again using another pair of QMFs Low: 0-400Hz, and High: 400-800Hz. We need 3 pairs of QMS and we have signal in the frequency band 0-400,400-800,800-1600,and 1600-3200 ADAPTIVE TRANSFORM CODING (ATC) The source signal is sampled and subdivided into frames of Nf samples. The data in each frame is transformed into the spectral domain for coding At the decoder side, each frame of spectral samples is transformed back into the time domain and signal is synthesized from the time domain samples For efficiency, more bit is assigned to more important spectral coefficients and less bit is assigned to less important coefficients For transform from time to frequency domain, DFT or Discrete cosine transform (DCT) can be used MODEL-BASED SOURCE CODING The Source is modeled as a linear system that results in the observed source output. Instead of transmitted samples of the source, the parameters of the linear system are transmitted with an appropriate excitation table. If the parameters are sufficient small, provides large compression Linear predictive coding (LPC) EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 4
Let s have sampled sequence xn, n=0,1,,n-1 and assume that is generated by discrete time filter that gives transfer function Speech signal band limits 200-3200Hz. Sampling frequency 8000samples/s for all encoder except DM If the input is a white noise sequence or an impulse, we may estimate (predict) of xn by weighted linear combination The filter coefficients {ak } canbe selected to minimize the mean square error 2. State the Nyquist sampling theorem. Demonstrate its validity for an analog signal x(t) having a Fourier transform X(f) which is zero outside the internal[-fm<f<fm] [AUC NOV/DEC 2010] Explain a non uniform qunaisation process EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 5
3. Write noted on temporal waveform coding(8) [AUC APR/MAY 2011] [AUC APR/MAY 2011] Temporal Waveform coding :design to represent digitally the time-domain characteristic of the signal Temporal Waveform Coding Most common used methods: Pulse-code modulation (PCM) Differential pulse-code modulation (DPCM) Delta modulation(dm) Pulse-code modulation (PCM) Let s have continuous source function x (t ) and each sample taken from x (t ) is xn at sampling rate f s 2W, where W is the highest frequency in x (t ). In PCM, each sample is quantized to one of 2R amplitude level, where number of binary digits used to represent each sample.the bit rate will be Rfs [bit/s] PULSE-CODE MODULATION (PCM) The quantized value will be n and x EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 6
Assume that a uniform quantizer is used, then PDF of quantization error is Assume that a uniform quantizer is used, then PDF of quantization error is Encoding methods for Speech signal EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 7
EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 8
DIFFERENTIAL PULSE CODE MODULATION EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 9
EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 10
Delta modulation [AUC APR/MAY 2012] EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 11
4. Explain natural sampling and flat top sampling ii) with neat block diagram PCM modulation and demodulation system[auc APR/MAY 2012] EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 12
A message signal may originate from a digital or analog source. If the message signal is analog in nature, then it has to be converted into digital form before it can transmitted by digital means. The process by which the continuous-time signal is converted into a discrete time signal is called Sampling. Statement:- If a band limited signal g(t) contains no frequency components for f > W, then it is completely described by instantaneous values g(kts) uniformly spaced in time with period Ts 1/2W. If the sampling rate, fs is equal to the Nyquist rate or greater (fs 2W), the signal g(t) can be exactly reconstructed. Pulse Code Modulation: Pulse code Modulation: The pulse code modulator technique samples the input signal x(t) at a sampling frequency. This sampled variable amplitude pulse is then digitalized by the analog to digital converter. Figure. shows the PCM generator. n the PCgenerator, the signal is first passed through sampler which is sampled at a rate of (fs) where: The output of the sampler x(nts) which is discrete in time is fed to a qlevel quantizer. The quantizer compares the input x(nts) with it's fixed levels. It assigns any one of the digital level to x(nts) that results in minimum distortion or error. The error is called quantization error, thus the output of the quantizer is a digital level called q(nts). The quantized EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 13
signal level q(nts) is binary encode. The encoder converts the input signal to v digits binary word.the receiver starts by reshaping the received pulses, removes the noise and then converts the binary bits to analog. The received samples are then filtered by a low pass filter; the cut off frequency is at fc. fc= fm It is impossible to reconstruct the original signal x(t) because of the permanent quantization error introduced during quantization at the transmitter. The quantization error can be reduced by the increasing quantization levels. This corresponds to the increase of bits persample(more information). But increasing bits (v) increases the signaling rate and requires a large transmission bandwidth. The choice of the parameter for the number of quantization levels must be acceptable with the quantization noise (quantization error) Signaling Rate in PCM Let the quantizer use 'v' number of binary digits to represent each level. Then the number of levels that can be represented by v digits will be : q=2v The number of bits per second is given by : (Number of bits per second)=(number of bits per samples)x(number of samples per second) = v (bits per sample) x fs (samples per second) The number of bits per second is also called signaling rate of PCM and is Signaling rate= v fs Quantization Noise in PCM System Errors are introduced in the signal because of the quantization process. This error is called "quantization error". ε= xq (nts)- x(nts) Let an input signal x(nts) have an amplitude in the range of xmax to - xmax The total amplitude range is : Total amplitude = xmax-(- xmax)=2 xmax If the amplitude range is divided into 'q' levels of quantizer, then the step EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 14
size 'Δ'. Δ= q/2 X max If the minimum and maximum values are equal to 1, xmax,=1, - xmax=-1, Δ= q/2 Signal to Quantization Noise ratio in PCM The signal to quantization noise ratio is given as: The number of quantization value is equal to: q=2v Let the normalized signal power is equal to P then the signal to quantization noise will be given by: Advantages of PCM 1. Effect of noise is reduced. 2. PCM permits the use of pulse regeneration. 3. Multiplexing of various PCM signals is possible. 5. Explain the noise in delta modulation system.how to overcome the effects in delta modulation ii) [AUC APR/MAY 2012] In delta modulation (DM), an incoming message signal is oversampled (i.e., at a rate much higher than the Nyquist rate) to purposely increase the correlation between adjacent samples of the signal. In its basic form, DM provides a staircase approximation to the oversampled version of the message signal. In DM, the difference between the input signal and its approximation is quantized into only two levels namely, ± Δ, corresponding to positive and negative differences. Thus, the modulated signal in DM carries information not about the signal samples but about the difference between EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 15
successive samples. Therefore, DM carries the information about the derivative of m(t), hence, the name delta modulation. Notice that the staircase approximation remains within ± Δ of the input signal provided the input signal does not change too rapidly from sample to sample. Delta modulation (DM) is implemented by applying a sampled version of the incoming message signal to a transmitter that consists of a comparator, quantizer, and accumulator connected together as shown in Figure 2 (a). The comparator computes the difference between its two inputs. The quantizer consists of a hard limiter with an input output characteristic that is a scaled version of the signum function. The accumulator operates on the quantizer output so as to produce an approximation to the message signal. We denote the input signal by m(t) and its staircase approximation by mq(t). The basic principle of delta modulation may then be formalized in the following set of three discrete-time relations: where Ts is the sampling period. e(nts) is an error signal representing the difference between the present sample value m(nts) of the input signal and the latest approximation to it mq(nts Ts). eq(nts) is the quantized version of e(nts); and sgn[.] is the signum function, EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 16
assuming the value +1 or 1. The quantizer output eq(nts) is finally encoded to produce the desired DM data. DM system (a) Transmitter (b) Receiver To reconstruct the original signal, the received signal at the demodulator is passed through an accumulator similar to the one in the modulator. A lowpass filter after the accumulator will smooth the reconstructed signal Quantization Errors Delta modulation is subject to two types of quantization error: (1) slope overload distortion and (2) granular noise. We first discuss the cause of slope overload distortion and then granular noise. the digital equivalent of integration in the sense that it represents the accumulation of positive and negative increments of magnitude Δ. Also, denoting the quantization error by q(nts), as shown by ' EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 17
the input to the quantizer is Thus, except for the delayed quantization error q(nts Ts), the quantizer input is a first backward difference of the input signal, which may be viewed as a digital approximation to the derivative of the input signal or, equivalently, as the inverse of the digital integration process. If we now consider the maximum slope of the original message signal m(t), it is clear that in order for the sequence of quantized samples {mq(nts)} to increase as fast as the sequence of input samples {m(nts)} in a region of maximum slope of m(t), we require that the condition be satisfied. Otherwise, we find that the step size Δ is too small for the staircase approximation mq(t) to follow a steep segment of the original message signal m(t), with the result that mq(t) falls behind m(t), as illustrated in Fig.3. This condition is called slope overload. Correspondingly, the resulting quantization error is called slope-overload distortion (noise). Note that since the maximum slope of the staircase approximation mq(t) is fixed by the step size Δ, increases and decreases in mq(t) tend to occur along straight lines, as illustrated in the front end of Fig. 3. For this reason, a delta modulator using a fixed value for the step size Δ is often referred to as a linear delta modulator In contrast to slope-overload distortion, granular noise occurs when the step size Δ is too large relative to the local slope characteristic of the original message signal m(t). This second situation causes the staircase approximation mq(t) to hunt around a relatively flat segment of m(t), which is illustrated in the back end. Granular noise in delta modulation is analogous of quantization noise in a PCM system. EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 18
6. Explain a DPCM system.derive the expression for slope overload noise of the system.show that SNR of DPCM is better than that of PCM [AUC NOV/DEC2012] Differential Pulse-Code Modulation (DPCM) DPCM is a combination between DM and PCM techniques. In DPCM scheme shown in Figure 4, the input signal to the quantizer is defined by e( nts) =m (nts) m (nts) the difference between the input sample m(nts) and a prediction of it, denoted by m nts which is produced by using a prediction filter. The difference signal e(nts) is called the prediction error, since it is the amount by which the prediction filter fails to predict the incoming message signal exactly. By encoding the quantizer output in Figure 4(a), we obtain a variation of PCM, which is known as differential pulse-code modulation (DPCM). It is this encoded signal that is used for transmission. The quantizer output may be expressed as eq nts =e (nts) +q (nts) where q(nts) is the quantization error. According to Figure the quantizer output eq(nts) is added to the predicted value m nts to produce the prediction-filter input: the sum term m (nts) + e (nts) is equal to the sampled message signal m(nts). EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 19
which represents a quantized version of the message sample m(nts). That is, irrespective of the properties of the prediction filter, the quantized signal mq(nts) at the prediction filter input differs from the sampled message signal m(nts) by the quantization error q(nts). The receiver for reconstructing the quantized version of the message signal is shown in Fig. 4(b). It consists of a decoder to reconstruct the quantized error signal. The quantized version of the original input is reconstructed from the decoder output using the same prediction filter in the transmitter of Fig.4(a). From the foregoing analysis we thus observe that DPCM includes DM as a special case. In particular, comparing the DPCM system with the DM system, we see that they are basically similar, except for two important differences The use of a one-bit (two-level) quantizer in the DM system. Replacement of the prediction filter in the DPCM by a single delay element (i.e., first order prediction filter). In other words, DM is the 1-bit version of DPCM. Note, however, that unlike a PCM system, the transmitters of both the DPCM and DM involve the use of feedback. We may finally make the following two statements: 1. DPCM, like DM, is subject to slope-overload distortion whenever the input signal changes too rapidly for the prediction filter to track it. 2. Like PCM, DPCM suffers from quantization noise. 7. Explain subband coding II) Compare the performance of various speech coding methods Draw the block diagram of adaptive sub band coding scheme for speech signal and explain [AUC NOV/DEC2012] SPECTRAL WAVEFORM CODING Filter the source output signal into a number of frequency subband and separately encode the signal in each subband. Each subband can be encoded in time-domain waveform or Each subband can be encoded in frequency-domain waveform Source signal (such as speech or image) is divided into small number of subbands and each subband is coded in timewaveform More bits are used for the lower-frequency band signal and fever EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 20
band used for higher-frequency band Subband Coding Filter design is important in achieving good performance Quadrature-mirror filters (QMFs) used most used in practice SUBBAND CODING Let s assume that Speech signal bandwidth is 3200Hz. Example: The first pair of QMFs divides the spectrum into two Low: 0-1600Hz, and High: 1600-3200Hz. The Low band split into two using another pair of QMFs Low: 0-800Hz, and High: 800-1600Hz. The Low band split into two again using another pair of QMFs Low: 0-400Hz, and High: 400-800Hz. We need 3 pairs of QMS and we have signal in the frequency band 0-400,400-800,800-1600,and 1600-3200 Adaptive Transform Coding (ATC) The source signal is sampled and subdivided into frames of Nf samples. The data in each frame is transformed into the spectral domain for coding At the decoder side, each frame of spectral samples is transformed back into the time domain and signal is synthesized from the time domain samples For efficiency, more bit is assigned to more important spectral coefficients and less bit is assigned to less important coefficients For transform from time to frequency domain, DFT or Discrete cosine transform (DCT) can be used PERFORMANCE OF VARIOUS SPEECH CODING METHODS Encoding methods for Speech signal Speech signal band limits 200-3200Hz. Sampling frequency 8000samples/s for all encoder except DM EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 21
EC2301 DIGITAL COMMUNICATION V Sem ECE R.Vanitha Asst.Prof./ECE Page 22