JANUARY 9, DIGITAL SIGNAL PROCESSING Analytical Principles of DSP and Digital Filter Design PRESENTED TO JAGJIT SEHRA

Transcription

1 JANUARY 9, 2017 DIGITAL SIGNAL PROCESSING Analytical Principles of DSP and Digital Filter Design PRESENTED TO JAGJIT SEHRA BY ZEESHAN MUSTAFA LATIF ANSARI BEng (Hons) Electronics Engineering ID: s

2 Contents Page Numbers Introduction 3 Background 3 Part a Analytical Problems 7 Question 1, Part (i) 7 Question 1, Part (ii) 8 Question 1, Part (iii) 10 Question 1, Part (iv) 13 Proof of results obtained in Q1 (ii) by using a suitable m-file 13 Proof of results obtained in Q1 (iii) by using a suitable m-file 20 Question 2, Part (i) 22 Question 2, Part (ii) 23 Question 2, Part (iii) 24 Question 3, Part (i) 26 Question 3, Part (ii) 27 Question 3, Part (iii) 28 Part b Digital Filter Design using MATLAB and SPTOOL 29 Question 4, Part (i) 29 Question 4, Part (ii) 32 Designing LOW-PASS FIR Filter for Noisy Signal 33 Designing LOW-PASS IIR Filter for Noisy Signal 35 Question 4, Part (iii) 36 Conclusion 39 References 40 Bibliography 41 ID: s Page 2

3 Analytical Principles of DSP and Digital Filter Design Introduction The world of science and engineering is filled with signals DSP refers to various techniques for improving the accuracy and reliability of digital communications Signal processing is the science of understanding the formation of information conveyed as a function of time, space or any other variable Analysing this information requires the acquisition, storage, transmission and transformation of signals Signals can be classified as continuous or analogue, such as speech or discrete, in the form of digital information Basically DSP works by clarifying, or standardizing, the levels or states of a digital signal It is the process of analysing or modifying a signal to optimize or improve its efficiency or performance (Sehra, 2017) As per the title states the assessment is undertaken to analyse and observe the functionalities and complex behaviours of FIR and IIR filters using Matlab software In order to complete this assignment, detailed fundamental knowledge of DSP was acquired including its mathematical techniques for solving equations to design the digital filters Based on the knowledge and skills acquired in Signals and Systems and further in this (DSP) module work was initiated with solving and verifying the equations given in assessment brief Following which the required data and results obtained were implemented into Matlab to analyse, observe and design the digital filters Lastly, theoretical values and results calculated were compared with the values and results which were obtained in Matlab by using suitable program code and relevant software skills Assessment is comprised of two parts; Part A being the Analytical problems had to be solved using various mathematical techniques, learnt throughout the module, then they were plotted and analysed in Matlab Part B being the Digital Filter Design using MATLAB and SPTOOL involved designing and filtering the signals This involved the design of a noisy guitar signal and development of code (m-file) to reduce or totally remove the un-wanted noise from it to produce a clean signal which was also verified by listening both the signals This section also specifies the design requirement if a real-time system was to be employed It ends with discussion on two current DSP developments kits (available in UK) for audio processing Background In the world of communications circuits it is true whether the signals are analogue or digital they always contain some level of noise Noise is said to be the eternal bane of communications engineers who are always striving to find new ways to improve signal-to-noise ratio For this assessment it s important to explain the difference ID: s Page 3

4 between continuous-time, discrete-time and digital signals so that further work can be started (WhatIscom, 2017) A continuous signal or a continuous-time signal is a varying quantity (a signal) whose domain, which is often time, is a continuum (eg, a connected interval of the reals) That is, the function's domain is an uncountable set The function itself need not be continuous On the other hand, a discrete time signal has a countable domain, like the natural numbers A signal of continuous amplitude and time is known as a continuous-time signal or an analogue signal This (a signal) will have some value at every instant of time The electrical signals derived in proportion with the physical quantities such as temperature, pressure, sound etc are generally continuous signals Other examples of continuous signals are sine wave, cosine wave, triangular wave etc Figure 1 shows a typical continuous time signal, function ( ) for the word signal This is a mathematical representation of the signal as a function of time, t, which is refered to as the independent variable Figure 1 continuous time signal, taken from DSP Moodle Discrete-time signals can be considered, as digital signals, where the value of the signal is known at discrete time intervals All that is known about the signal is a sequence of values Both the amplitudes and time can be quantized In other words, the digital value can only take a specified value with a specific range This will depend on the quality of the conversion process of the A/D A digital signal refers to an electrical signal that is converted into a pattern of bits Unlike an analogue signal, which is a continuous signal that contains time-varying quantities, a digital signal has a discrete value at each sampling point Digital signals are discrete time signals generated by digital modulation, computers, CDs, DVDs, and other digital electronic devices (Sehra, 2017) Difference between analogue and digital signal processing The basic difference between analogue and digital signal processing is that analogue signal is a continuous signal which represents physical measurements while digital signals are discrete time signals generated by digital modulation Analog ID: s Page 4

5 waves are smooth and continuous while digital waves are stepping, square and discrete We can have a model of a system, in the context of signal processing Consider the block diagrams shown in figure 2 Figure 2 a) Analogue recording system b) Digital recording system, taken from DSP Moodle Discrete-time signals can be considered, as digital signals, where the value of the signal is known at discrete time intervals All that is known about the signal is a sequence of values Both the amplitudes and time can be quantized In other words, the digital value can only take a specified value with a specific range This will depend on the quality of the conversion process of the A/D Figure 3 shows simply the process of A/D and D/A Figure 3 A/D process, taken from DSP Moodle It should be pointed out that in order to process analogue signals they must be processed first, that is consider a physical quantity, such as sound signal, it must be first captured using some form of transducer or sensor before it can be processed It must be conditioned, to remove any un-wanted signal information, through filtering Once this is complete the analogue to digital process can be done, and the signal can be manipulated, before it is re-converted back to an analogue form, using an anti-aliasing filter, sometimes referred as a low pass filter, to remove the stair case effect of the DAC Figure 4 below shows a block diagram of an ideal system for processing continuous time signal (Sehra, 2017) ID: s Page 5

6 Figure 4 Block diagram for processing continuous time signal, Taken from DSP Moodle The Advantages of DSP 1 It s cost effective Many development kits are available at low cost as well as of industrial standard 2 DSP systems can be designed and tested in a simulation using software tools, which in many cases can guarantee accuracy of systems 3 Complex processing of information which is difficult or sometimes impossible in the analogue domain can be accomplished by digital signal processing Examples are adaptive filtering, where the digital filter can vary or adapt its performance to the characteristics of the signal; another is speech analysis and processing 4 It s reliable and compact 5 DSP systems will work the same, performance can be enhanced depending on the evolution of the hardware/software 6 Multi-processing of information is achieved by DSP Disadvantages of DSP 1 DSP is software driven process, up-dates to systems can only be done by reprogramming for example software driven radio 2 System performance can be reduced Due to an analogue to digital conversion, there are bandwidth requirements, which can lead to loss or quality of information 3 For real-time applications, it requires a good understanding of mathematical techniques to fully implement systems to chip (Sehra, 2017) Applications of DSP Real time applications of DSP are Audio and multimedia, speech processing and recognition, image and video processing, Telecommunications, Computer systems and military systems ID: s Page 6

7 Part a - Analytical Problems Causal systems are those that can be implemented in real hardware also called realisable systems A Function can be a linear but it cannot necessarily be a linear system To be a linear system it must be conforming to homogeneity and superposition Homogeneity is when the input is multiplied by a constant; the output is also multiplied by the same constant Superposition is when the input sequences of two functions are added, their outputs also are added A time invariant system is a system whose output does not depend explicitly on time, it s independent of time (Sehra, 2016) Question 1, Part (i): A causal Linear Time Invariant (LTI) System is given by the function H (Z) below: ( ) ( ) ( ) ( ) ( ) ( ) Determining the Ideal Nyquist Rate of the above input signal (F ): For Ω 40π As Ω 2πf 40π 2πf 20 Hz For Ω 80π As Ω 2πf 80π 2πf 40 Hz ID: s Page 7

8 Nyquist frequency is twice the maximum component frequency of the function being sampled So Nyquist rate 2 x Hz In other words, in order to retain data it is always sampled at twice the highest frequency ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) + 9cos (πn) As found above 0, and π Question 1, Part (ii): Transfer Function Y (Z) [ ] H (Z) ( )( ) where is Unit delay ( ( )) ( ) ( ) So frequency response ( ) [ ] which is Gain of System H ( ) Where Euler s Method θ ± j i θ ID: s Page 8

9 As cosө jsinө When ω 0 Using Euler s Method H (0) ( ) ( ( )( )) ( ( )( )) ( ( )) ( ( )) H ( ) 588 approximately 6 When ω Using Euler s Method H ( ) ( ( ) ( )) ( ( )( ) ( )( )) ( ) ( ) Here, the identity used is j ( ) Here, the identity used is j Then we use the complex number j a + jb which is the magnitude formula in order to get rid of Therefore, H ( ) j 3394 H ( ) 3394 Then in order to find the phase, the formula Ө is applied, hence; ID: s Page 9

10 Ө When ω π Using Euler s Method H (ω) ( ) ( ( ) ( ) ( ) ( )) ( ) ( ) H ( ) 4 ( ) ( ) 4 To determine the ( ) output, all the values of Gain and Phase angles are applied to the original equation given below:- [ ] H ( ) [ ] [ ] 10 + ( ) ( ) Calculated Gains are multiplied to the Gains of the system and then Phase differences are found by subtracting the found phases from the relevant system phases as shown below: [ ] 6 x x 5cos( ) + 4x9( ) [ ] cos( ) + 36( ) For ω 0 and ω π, there are no phase angles so there is no phase difference Question 1, Part (iii): To design the filters, first we need poles and zeroes:- H (Z) ( )( ) 1 0 ID: s Page 10

11 Z Also Z Filter (given below) is designed in Matlab using the poles and zeroes calculated above Figure 5Filter designed, Captured from Matlab ID: s Page 11

12 Figure 5 above represents the design of the filter that was constructed using the utility of the Matlab software (Filter Design and Analysis tool) To start with, a new filter is created using the SPTOOL utility by clicking on the command button New in the Filters column (section) as shown below in Figure 6 Figure 6 Creating Filter, Captured from Matlab After this, for the filter to be designed two poles (represented by x in the figure above) are placed at magnitude of -033 Hz (-1/3 Hz) and at 05 Hz (1/2 Hz) which were calculated above Zero was placed at the origin as shown by a hole in the figure given above Then the analysis parameters were changed to magnitude as can be seen in the figures below For this to happen Analysis panel is clicked and then the Analysis Parameters is selected Magnitude Display is also changed to Magnitude Db for more precise results The gain was taken from the system which was 4 Figure 7 Designing Filter, Captured from Matlab ID: s Page 12

13 Sampling frequency was also changed to 40Hz which was done by clicking the Analysis panel and selecting the option Sampling Frequency Figure 8 Designing Filter, Captured from Matlab All the steps given above were followed to design the filter given in figure Question 1, Part (iv): Proof of results obtained in Q1 (ii) by using a suitable m-file: Signal v v1+v2+v3 Figure 9 (m-file) Matlab code, Captured from Matlab ID: s Page 13

14 To obtain the plot for ( ) ( ) ( ) code given in figure 9 above is developed based on the calculations obtained in part (ii) Plots for individual signals v1 and v2 are also plotted to observe the changes in the signals before and after they were filtered Using the code given above, the graph plotted is shown below: ( ) ( ) ( ) Figure 10 Signal v for x(t), Captured from Matlab Code for plotting signal v1 5*cos(40*pi*t) before it was filtered is given below, following which the plot is also given: ID: s Page 14

15 Figure 11 (m-file) Matlab code and Plot for signal v1, Captured from Matlab Code for plotting signal v2 9*cos(80*pi*t) before it was filtered is given below, following which the plot is also given: Figure 12 (m-file) Matlab code and Plot for signal v2, Captured from Matlab ID: s Page 15

16 Signal v3, m-file code and Plot below shows DC values: Figure 13 Signal v3 - the dc value, Captured from Matlab The signals above were filtered in order to observe the calculated theoretical values with the values represented by the plots of filtered signals To begin with SPTOOL utility was opened, then by clicking on the File tab and then selecting Import another window will be opened Figure 14 Filtering a signal, Captured from Matlab Importation of content was done using the new opened window given below where different signals and frequencies were then selected from the Workspace contents panel ID: s Page 16

17 After pressing OK the content is imported into SPTOOL which follows another window given below: In order to filter the signal, the signal was clicked along with the filter that it would be applied to Then after pressing the Apply button another window Apply Filter opened from where Algorithm named Direct-Form II Transposed was used and pressed OK ID: s Page 17

18 Filtered Signal 1 Figure 15 Filtered Input Signal v1, Captured from Matlab The figure 15 above represents function y[n] 1697cos( ) Figure shows that the results were justified since it s a cosine wave with amplitude of 169 exactly and that was also calculated previously Filtered Signal 2 Figure 16, Filtered input signal v2, Captured from Matlab ID: s Page 18

19 The figure above represents function y[n] 36( ) Figure shows that the results were justified since it s a cosine wave with amplitude of sharp 36 and that is exactly what was also calculated previously Signal value for DC Figure 17 Filtered signal v3 - value of DC, Captured from Matlab Figure 17 above shows filtered value of DC which is 60 as theoretically calculated previously Filtered Output Signal: [ ] cos( ) + 36( ) Figure 18 Filtered output signal v, Captured from Matlab ID: s Page 19

20 The output signal given above represents function [ ] cos( ) + 36( ) It adds up all the signals correctly which was verified by summing the amplitudes together Amplification factor calculated was whereas figure shows and ; both are approximately equal to the original calculated value The slight difference occurs due to the rounding of the numbers which was done in calculating theoretical values Proof of results obtained in Q1 (iii) by using a suitable m-file: After manually working out the poles and zeroes, MatLab code given below in figure 19 is derived using the Frequency response which will do this calculation itself: Figure 19 (m-file) MatLab code for Pole-Zero Map, Captured from Matlab On running the code, pole-zero maps produced in MatLab are given below: ID: s Page 20

21 Figure 20 Pole-Zero Map, Captured from Matlab Pole-zero map given above shows the Pole at Figure above shows Pole at 05 Figure 21 Pole-Zero Map, Captured from Matlab ID: s Page 21

22 Question 2, Part (i): The structure of the FIR filter: [ ] [ [ ] - [ ]] is a difference equation, structure is drawn below: x[n] - 05 y[n] x[n-1] x[n-2] z z FIR Filters and their advantages/disadvantages FIR filters are a type of digital filter with finite impulse response They are also known as non-recursive digital filters because they do not have feedback although recursive algorithms can still be used for FIR filter realization The main advantage of FIR systems is that they are always stable and they can design to yield a linear phase response In order to make linear phase, FIR filter is very simple to make So to do it just linear phase filter delay need to be added but care must be taken not to mislead its phase FIR filters are very easy to run by winding a signal instruction; they can be schemed on DSP micro processing FIR filters are suitable to make low rating for sampling which is called decimations and also make more rating for sampling which is called interpolations They also can be implemented using coefficient of less than 10 magnitude (Guru, 2017) FIR filters offer several advantages over IIR filters: They can easily be designed to be "linear phase" (and usually are) Put simply, linear-phase filters delay the input signal, but don t distort its phase They are simple to implement On most DSP microprocessors, the FIR calculation can be done by looping a single instruction They are suited to multi-rate applications By multi-rate, we mean either "decimation" (reducing the sampling rate), "interpolation" (increasing the sampling rate), or both Whether decimating or interpolating, the use of FIR filters allows some of the calculations to be omitted, thus providing an important computational efficiency In contrast, if IIR filters are used, each ID: s Page 22

23 output must be individually calculated, even if that output is discarded (so the feedback will be incorporated into the filter) They have desirable numeric properties In practice, all DSP filters must be implemented using "finite-precision" arithmetic, that is, a limited number of bits The use of finite-precision arithmetic in IIR filters can cause significant problems due to the use of feedback, but FIR filters have no feedback, so they can usually be implemented by using fewer bits, and the designer has fewer practical problems to solve related to non-ideal arithmetic They can be implemented using fractional arithmetic Unlike IIR filters, it is always possible to implement a FIR filter using coefficients with magnitude of less than 10 (The overall gain of the FIR filter can be adjusted at its output, if desired) This is an important consideration when using fixed-point DSP's, because it makes the implementation much simpler Completely constant group delay throughout the frequency spectrum Complete stability at all frequencies regardless of the size of the filter Can be implemented with fast convolution Relatively insensitive to quantization (Guru, 2017) Disadvantages of FIR Filters In comparing the FIR filters with IIR filters, the FIR filters have less disadvantages but there are some such as they need more memory, to get the applied filter response characteristic similarly to implement to FIR filter some responses are not usual For a given filter specification they require larger degree with respect to IIR filters This is a drawback for FIR The frequency response is not as easily defined as it is with IIR filters The number of states required to meet a frequency specification may be far larger than that required for IIR filters FIR filters sometimes have the disadvantage that they require more memory and/or calculation to achieve a given filter response characteristic Also, certain responses are not practical to implement with FIR filters (Guru, 2017) Question 2, Part (ii): [ ] [ [ ] [ ]] is a difference equation Difference equation can be converted to Transfer Function by taking the Z transform ID: s Page 23

24 Delay in sample time in Frequency Domain becomes the power as shown below:- ( ) [ ] Y (Z) [ ( ) ( ) ] Y (Z) X (Z) X ( ) Y (Z) X ( ) ( ) Transfer Function: - H (Z) So H (Z) ( ) ( ) ( ) Transfer Function H (Z) can now be exchanged with Frequency Response H( ), therefore, is substituted with So ( ) H ( ) is frequency response where represents magnitude and is phase Question 2, Part (iii): As H (Z) ( ), this transfer function is used to find poles and zeroes Highest power of Z is 2 so multiply by ( ) Pole: Z 0 Zero: Z 1, -1 The value of Z that leads denominator to 0 is Pole The value of Z that leads numerator to 0 is Zero Frequency response H (ω) was found out to be:- H (ω) Now to find the type of filter, let s take 3 values of ω as ω 0, ω and ω π ID: s Page 24

25 When ω 0 then:- H ( ) H ( ( ) ) ( ( ) ( )) 0 When ω then:- H ( ( ) ) ( ( ) ( )) ( ) When ω π then:- ( ) 1 H ( ) ( ( ) ( )) ( ) 0 Figure 22, Band Pass Filter Plot So, as shown in the graph above:- When ω 0; H ( ) 0 When ω ; H ( ) 1 When ω π; H ( ) 0 ID: s Page 25

26 Values obtained and the graph drawn proves that it s a Band Pass Filter Question 3, Part (i): [ ] [ ] + [ ] + [ ] Equation above represents IIR (Infinite Impulse Response) Filter which is proven by the structure given below, it has feedback [ ] [ ] + [ ] x[n] + + y[n] z z x[n-1] y[n-1] IIR Filters IIR filters are one of two primary types of digital filters used in Digital Signal Processing (DSP) applications (the other type being FIR) "IIR" means "Infinite Impulse Response The impulse response is "infinite" because there is feedback in the filter; if you put in an impulse (a single "1" sample followed by many "0" samples), an infinite number of non-zero values will come out theoretically (Guru, 2017) Advantages of IIR Filter The advantage of IIR filters over FIR filters is that IIR filters usually require fewer coefficients to execute similar filtering operations, that IIR filters work faster, and require less memory space IIR filters can achieve a given filtering characteristic using less memory and calculations than a similar FIR filter (National, 2017) ID: s Page 26

27 Disadvantages of IIR Filters They are more susceptible to problems of finite-length arithmetic, such as noise generated by calculations, and limit cycles (This is a direct consequence of feedback: when the output isn't computed perfectly and is fed back, the imperfection can compound They are harder (slower) to implement using fixed-point arithmetic They don't offer the computational advantages of FIR filters for multi-rate (decimation and interpolation) applications (Hero, 2017) Question 3, Part (ii): To determine the transfer function H(z) for IIR filter firstly the y[n] will be converted into y[z] and then the terms of y(z) and x(z) will be separated as shown below: [ ] [ ] + [ ] + [ ] Conversion of y[n] into y[z] [ ] ( ) + ( )+ ( ) Now collecting like terms ( ) ( ) ( ) + ( ) Simplifying it (taking the common term out) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) As Transfer Function H ( ) ( ) ( ) So ( ) Now to get frequency response ( ) is exchanged with ( ) and is substituted with Therefore, ( ) ID: s Page 27

28 Transfer Function ( ) Question 3, Part (iii): The transfer function determined above is used to find poles and zeroes of H(Z) Rule states that the value of Z that leads denominator to 0 is Pole and the value of Z that leads numerator to 0 is zero So Z Zero: Z And 1 2Z Pole: Z The result shows then that ; The values of Z are less than 1 and greater than - 1 so it is proved that poles and zeroes are in the unit circle which makes the filter stable ID: s Page 28

29 Part b - Digital Filter Design using MATLAB and SPTOOL This section involves plotting the spectrums of two guitar signals, where one signal is noisy and the other one is clean, then designing the filter, using a suitable m-file, to reduce or totally remove the noise from noisy signal and finally comparing the filtered signal with noisy and clean signals to see the amount of noise reduced or totally removed Additionally if a real-time system was employed a statement will need to be made to specify the requirements of the design To finish it, two current DSP development kits (available in UK) for audio processing will be discussed Question 4, Part (i): Clean Guitar Signal Plot Figure 23 Clean Guitar Signal, Captured from Matlab ID: s Page 29

30 Spectrum view of clean guitar signal Figure 24 Spectrum view of clean guitar signal, Captured from Matlab To draw the above spectrum Parameters were changed to FFT (Fast Fourier Transform) for the Method and NffI value was set to as it s the length of the signal Then using the Options panel (shown below in Figure 25) the Magnitude Scale and the Frequency Scale were set to Linear Frequency Range was also changed to [-Fs/2, Fs/2] Figure 25, Captured from Matlab ID: s Page 30

31 Noisy Guitar Signal Plot Noise Spectrum view of Noisy Guitar Signal Figure 26 Noisy Guitar Signal, Captured from Matlab F 4300Hz F 7400Hz Figure 27 Spectrum view of noisy guitar signal, capture from Matlab ID: s Page 31

32 The spectrum view IN Figure 23 shows that noise occur at frequencies between 4300Hz to 7400 Hz approximately Matlab (m-file) codes used to draw plots of clean and noisy guitar signals: Figure 28 m-file Matlab code, Captured from Matlab Question 4, Part (ii): Noisy Guitar signal Figure 29 Noisy guitar signal, Captured from Matlab ID: s Page 32

33 Designing LOW-PASS FIR Filter for Noisy signal: Figure 30 Design of low-pass filter, Captured from Matlab As shown in the figure 30 above, the Filter is chosen as Lowpass because of its property to allow very low frequencies to pass through until its cutt-off frequenc It also blocks any other higher frequencies that come in contact with it Specifications for this filter were selected from six different panels given below: Response Type: Lowpass Design Method: FIR and Equiripple Filter Order: Minimum order Options: Density Factor chosen to be 20 Frequency Specifications: Units as Hz, Fs as as given in assessment brief, Fpass (the range for which the frequency is allowed to pass into the filter) chosen was 2000 and Fstop (the range of higher frequencies which are not allowed to pass) was chosen to be 4000 Magnitude Specifications: Units as Db, Apass (being passband ripple) was chosen as 1 and Astop (being stopband attenuation) was chosen as 100 Following this the noisy signal was applied into the filter to remove the noise ID: s Page 33

34 Filtered (Low-pass FIR) Signal Figure 31 Filter Signal, Captures from Matlab The signal above represents the noisy signal after it was filtered using the low-pass FIR filter As it can be seen the noise is completely removed and quality of sound (as it was listened) is clean (without any noise) It can be observed that the noise from 0 seconds to 15 seconds is totally removed; it s finally a clean signal FFT Spectrum of Filtered Signal Noise is removed Figure 32 Spectrum of Filtered Signal, Captured from Matlab ID: s Page 34

35 Spectrum view after filtering the noisy signal shows that the noise between 4300 Hz to 7400 Hz is totally eliminated Designing LOW-PASS IIR Filter for Noisy signal: Figure 33 Low-pass IIR Filter Design, Captured from Matlab Filter shown above represents the Low-pass IIR filter design which was designed in order to compare with Low-pass FIR filter design Specifications for this filter were selected from six different panels given below: Response Type: Lowpass Design Method: IIR and Butterworth Filter Order: Minimum order Options: passband Frequency Specifications: Units as Hz, Fs as as given in assessment brief, Fpass (the range for which the frequency is allowed to pass into the filter) chosen was 2500 and Fstop (the range of higher frequencies which are not allowed to pass) was chosen to be 4400 Magnitude Specifications: Units as Db, Apass (being passband ripple) was chosen as 05 and Astop (being stopband attenuation) was chosen as 80 Following this the noisy signal was applied to the filter to remove the noise ID: s Page 35

36 Filtered (Low-pass IIR) Signal Figure 34 Low-pass IIR Filtered Signal, Captured from Matlab Results show that IIR filter is quite decent as it provided very good sound quality when listened When comparing IIR filter with FIR filter they both produce almost the same results, especially while listening, very identical sounds were heard One thing that can be noticed after listening to both signals for a couple of times is that FIR has little better quality over IIR Question 4, Part (iii): Real-Time DSP Real-Time DSP can be defined as a system which uses predefined commands and algorithms to process a signal placed into the input of that system and which computes an outcome at the output of that system in real time The Real-Time DSP kits are normally expensive and they are in an essence, provisional to their application and quality They are available in different sizes, therefore different prices They offer features of eliminating and cancelling noise in smart devices As an example of daily life use of Real-Time DSP, they cancel the noises out in the microphone of a smartphone providing the user the ability to speak without any noise getting in his way DSP system on a Chip (SOCs) operation is used to eliminate the noise which disregards all the noise coming in the microphone Apart from that, Real-Time DSP is also applied on Electro Cardiograms (ECGs) However, Real- Time DSP systems have a lot of limitations regarding their memory, their ID: s Page 36

37 consumption of power, the speed that they require in order to process and also the input bandwidth (Sen M Kuo, 2001) The design considerations needed if a real-time DSP system were employed are as follows:- 1 Processor data bus The width of the processor data bus should be fully utilized unless its usage does not require that It should be connected with the fastest RAM chips that its interface can support Some factors that can affect its efficiency are size and layout of board, power usage, cross talk and reflection etc and these factors should be decided in the beginning of the design phase 2 Shared/Multi Ported RAM In case that multi-processor is being used in the design, their access to shared resources should be reduced RAM is a common resource in multiprocessor designs and it is designed in two ways One is Shared RAM and the other is Dual Ported RAM In case of shared RAM, arbitration logic should be used to control excess usage of processors One will access shared RAM while others are frozen by external READY delayed cycles In DPRAM the arbitration logic is embedded in such a way that no requester s cycle is delayed unless they share the same location It means that both sides can share DPRAM access in parallel without going in wait states 3 Internal RAM usage The size of the internal memory available in most DSPs being used today is not enough for the applications running, so the designer should place the most critical codes like interrupt routines or signal processing algorithms in the internal RAM and less critical codes like configuration or management performance in the external RAM 4 H/W Interrupts There are a number of details that should be kept in mind while designing with H/W interrupts eg what should be the maximum tolerable interrupt latency and the maximum interrupt service routine execution time, is there an interrupt controller for priority resolving or will it be implemented in S/W, is it needed to nest interrupts according to their priority, how frequent the signal be generated and will it be edge or level sensed, how to recover a missed interrupt, what should be maximum tolerable interrupt latency etc 5 Multi Bus Processors For best performance of multi bus processors, the connected devices to the buses should be organized carefully If a slow device is connected to a bus with high speed SDRAMs then when the DMA transfers data from/to this slow ID: s Page 37

38 device, the core will be blocked In order to avoid this problem it should be connected to the other bus In the same way data structures should be organized so as to minimize resource conflict between multi units in the processor 6 Slow Device Interface Slow devices like Flash EPROM should be designed in such a way so as to pipeline the operations eg when the processor wants to program Flash EPROM according to its FSM (Finite State Machine), a good design does not wait for the EPROM to acknowledge the operation, It should do other jobs during this process and check it periodically or be invoked by an interrupt generated based on EPROM condition signals 7 Maximum Cache Utilization As caches are too small for the whole code and data to fit in so they should be designed to minimize the cache misses as much as possible For maximum cache utilization, keep these points in mind The designer should use loops as much as possible for temporal locality, use arrays instead of separate variables for utilizing spatial locality, disable interrupts around loops if appropriate for functionality, divide the loops because the smaller the loop, the better it will fit into cache and achieve high cache hit rate 8 Maximum DMA Utilization Most processors have DMA engines inside as separate units ranging from 1 to 64 DMA channels These DMA engines should be used as much as possible because they have three distinct advantages These advantages are that highly complex DMA engines can organize data in different formats which are useful in serving multi-channel TDMs for speech codecs, moving bulk of data between memory or peripheral in the background and Read/Write data to/from peripheral on synchronous or asynchronous events in the background while core is busy with other tasks 9 Maximum Register Utilization Most of the code execution is carried out through registers So when writing the code in C language, use stack variables instead of accessing directly to variables or structures in RAM, By this method the RAM variables are read only once and then referenced as stack variables so this way there are no more memory accesses This way the compiler function is optimized In short the processor specifications, all the interfaces, communication paths with other cards and processors, function specific chipsets on the card, H/W limitations, and loopholes in the system and specific requirements of the H/W must be taken into consideration for designing real-time DSP system architecture (Serhat KOC, 2017) ID: s Page 38

39 Real-Time DSP Development Kits The first example of Real-Time DSP development kit is the one that is developed by a company named Texas Instruments The primary kit that is going to be described is the TMS320C6748 It is considered to be a robust-low cost kit based on c6748 processor (Texas Instruments, 2012) The salient features that it provides are: It provides software and development kit for digital signal processing advance/improvement regarding audio, biometric applications and more It has a feature of face and fingerprint recognition through embedded analytics which is provided by fast development of apps It has a processor which requires low-power consumption It has a variety of performance, power, peripheral and price due to its scalable platform It provides downloadable and duplicable schematics It has 128-MByte DDR2 SDRAM and 128-MByte NAND Flash memory Also, it has Micro SD/MMC slot and plenty of USB and SD connectors Lastly, it provides the benefit of having a decent amount of peripheral interfaces (Texas, 2017) The second example of Real-Time DSP development kit is Stratix V Edition which is manufactured by Altera This kit provides everything needed to create a FPGA design The kit consists of all necessary software and hardware requirements As per the Altera this kit is compliant of RoHS Stratix V Edition offers to the user the ability of developing and testing PCI Express designs at data rates up to Gen3 This can be done by using the PCIe short card form factor compliant development board It also provides the ability of developing and testing subsystems for DDR3 or QDR II memories In addition, the the user can utilise the high speed mezzanine card (HSMC) connectors in order to interface to more than 35 different HSMCs provided by the Altera partners Lastly, it supports protocols such as Serial RapidlO, 10 Gbps Ethernet, SONET, CPRI, OBSAI and others (Intel, 2017) Conclusion At the end, it can be said that this report developed significant amount of knowledge and skills required for Digital Signal Processing Based on the knowledge and skills gained in the previous module (Signals and Systems) and current module (DSP) this assessment was carried out by solving mathematical problems, following which mathematical techniques were used to implement the calculated theoretical values and then the m-file code was developed into Matlab software to design filters and then to filter noise from the noisy guitar signals Theoretical values and results calculated were compared and analysed with the results and plots were obtained in Matlab (by using suitable program code and relevant software skills) Advantages ID: s Page 39

40 and disadvantages of DSP, FIR and IIR filters were also found out Lastly, design requirements were also specified if a real-time system was to be employed which ended with discussion on two current DSP developments kits (available in UK) for audio processing Conclusion is made preceding findings, problem faced if any, objectives met (by answering questions), thorough knowledge and essential skills developed Although, it was not an easy assessment but hard work and dedication provided very good practice in DSP for a prospective electronic engineer References [1] Sehra, J (2017) Birmingham City University - Sign In [online] Moodlebcuacuk Available at: [Accessed 24 Dec 2016] [2] WhatIscom (2017) What is digital signal processing (DSP)? - Definition from WhatIscom [online] Available at: [Accessed 23 Dec 2016] [3 5] Sehra, J (2017) Birmingham City University - Sign In [online] Moodlebcuacuk Available at: [Accessed 24 Dec 2016] [6] Sehra, J (2016) Birmingham City University - Sign In [online] Moodlebcuacuk Available at: [Accessed 2 Jan 2017] [7 9] Guru, D (2017) FIR Filter FAQ [online] Dspgurucom Available at: [Accessed 20 Dec 2016] [10] Guru, D (2017) IIR Filter Basics dspgurucom [online] Dspgurucom Available at: [Accessed 27 Dec 2016] [11] National, I (2017) IIR Filters and FIR Filters - DIAdem 2012 Help - National Instruments [online] Zonenicom Available at: 01/genmaths/genmaths/calc_filterfir_iir/ [Accessed 22 Dec 2016] [12] Hero, C (2017) In contrast since IIR filters use feedback every input - MARKETING [online] Courseherocom Available at: [Accessed 21 Dec 2016] [13] Kuo, M S (2001) Introduction to Real-Time Digital Signal Processing In: John Wiley and Sons Real-Time Digital Signal processing West Sussex: John Wiley and Sons p1315 [14] Serhat KOC, I (2017) Design considerations for Real-Time with DSP and RISK architecture [online] Eurasip Available at: [Accessed 2 Jan 2017] ID: s Page 40

41 [15] Texas, I (2017) TMS320C6748 DSP Development Kit [online] Texas Instruments Available at: [Accessed 3 Jan 2017] [16] Intel, F (2017) DSP Development Kit, Stratix V Edition [online] Alteracom Available at: [Accessed 4 Jan 2017] Bibliography [1] Rafael Esquivel, (2013) ECE Designing Filters Using MATLab [video] Available at: [Accessed 20 Dec 2016] [2] David Dorran, (2013) filtering in matlab using 'built-in' filter design techniques [video] Available at: XyZeS [Accessed 18 Dec 2016] ID: s Page 41