Design of digital filters

Digital filters Desgn

1. Design of Digital Filters Naila Bibi BEE (Electronics) 2014 Batch

2. Content

3. What are Digital filters? In signal processing, a  digital filter  is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal.

4. Why digital filters? Digital filters are used for two general purposes Separation of signals that have been combined. Restoration of signals that have been distorted in some way

5. One of the reasons why we design a filter is to remove disturbances. Filter SIGNAL NOISE

6. We discriminate between signal and noise in terms of the frequency spectrum.

7. Example Imagine that you have a project for measuring the infant ECG from the body surface of a mother •The raw signal recordings will likely be corrupted by the breathing and heartbeat (ECG) of the mother •A filter might be used to separate the infant ECG from these combined signals so that they can be individually analyzed

8. Types of Digital filters

9. Comparative analysis of digital Filters Finite Impulse Response Implemented non-recursively No Feedback Always stable Simple to implement Linear phase response in pass-band More filter coefficients More memory More processing power Infinite Impulse Response Implement recursively With Feedback Stability not guaranteed Difficult to implement Non-linear phase response in pass-band less filter coefficients than FIR Less memory Less processing power

10. The ability to have an exactly linear phase response is the one of the most important of FIR filters A general FIR filter does not have a linear phase response but this property is satisfied when, four linear phase filter types,

11. FIR Fillers Output is function of the present input and the past inputs Output does not depend on the previous outputs L+1 is said to be the filter length

12. IIR Filters Output is the function of the present input, the past inputs and also the past outputs

13. FIR Design Methods 1. Windowing 2. Frequency Sampling 3. Computer Aided Design

14. Window Design Method Also known as Fourier transform method Create an ideal specification of the filter in frequency-domain Take Inverse Fourier Transform to get the time-domain impulse response of the filter

15. Steps… 1 . Note the specification i) Pass Band frequency ii) Pass Band ripple iii) Stop Band frequency iv) Stop Band attenuation Find the ideal impulse response; approximate where ever necessary Truncate the ideal impulse response to finite number of samples Choose a suitable window function to ‘smoothen out’ the ideal impulse response 5. Multiply the ideal-truncated impulse response with the window function 6. The result is the approximated impulse response of the filter, you ideally wanted to design

16. Example, Pass band Stop band we need to design a low pass filter. Pass band cut off at – Wc to Wc.

17. Take the I-DTFT to get the time-domain impulse response of the filter

18. -∞ < n < ∞ (1)

19. There are two ‘major’ problems with it The filter has infinite number of coefficients It has to be a non-causal system (system requires future values)

20. The solution to first problem is to truncate (cut) the impulse response, to a number of coefficients can be implemented with out too much trouble N=41 Truncate to N terms

21. The solution to second problem is to add a delay to the impulse response, so that all coefficients t0 The left of n=0, can be move on the positive time axis. Move the (N-1)/2 Terms to the right N=41 (N-1)/2 = 20

22. So, the impulse response with the delay of (N-1)/2 samples is given as,

23. But… With truncation of impulse response, ripples occur In the pass band and stop band Due to I.R. suddenly becoming zero Going from infinite no. of coefficients to a finite no. Known as Gibb’s effect Can be mitigated by multiplying I.R. by a suitable window function

24. Window Functions

25. The filter coefficients can be calculated as n=0,1,2,…..,20 Where, h[0] = h[1] = h[2] = h[3] = h[4] = h[5] = h[6] = h[7] = h[8] = h[9] = h[10] = h[11] = h[12] = h[13] = h[14] = h[15] = h[16] = h[17] = h[18] = h[19] = h[20] = 0.000000 -0.015933 0.010394 0.011006 -0.018921 0.000000 0.021624 -0.014392 -0.015591 0.027521 0.000000 -0.033637 0.023387 0.026728 -0.050455 0.000000 0.075683 -0.062366 -0.093549 0.302731 0.600000

26. IIR filter Design From Analog Filters By approximation of Derivatives By impulse variance Bilinear transformation

27. Applications 1 . Noise suppression (a) imaging devices (medical, etc) (b) bio-signals (heart, brain) (c) signals stored on analog media (tapes)

28. Applications continue.. 2. Enhancement of selected frequency ranges (a) equalizers for audio systems (increasing the bass) (b) Edge enhancement in images

29. Applications continue.. 3. Simulation/Modeling (a) Simulating communication channels (b) Modeling human auditory system

30. Applications continue.. 4. Removal or attenuation of selected frequencies (a) Removing the DC component of a signal Removing interferences at a specic frequency, for example those caused by power supplies

31. Conclusion Digital Filters Have a linear phase response in the band of interest. Can work for low frequency signals Digital filters is not affected by environmental effects (heat), There frequency can be easily adjusted (since it is a program),

32. Thank you 