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DIGITAL FILTERS: DESIGN OF FIR FILTERS Lecture 23-24 احسان احمد عرساڻي

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Presentation on theme: "DIGITAL FILTERS: DESIGN OF FIR FILTERS Lecture 23-24 احسان احمد عرساڻي"— Presentation transcript:

1 DIGITAL FILTERS: DESIGN OF FIR FILTERS Lecture احسان احمد عرساڻي

2 Introduction to FIR filters These have linear phase No feedback Output is function of the present and past inputs only These are also called all-zero and non-recursive filters These do not have any poles

3 Applications Where: highly linear phase response is required Need to avoid complicated design

4 FIR Filter Design Methods Windows Frequency-sampling

5 FIR Filter Design: Windows Method Start from the desired frequency response H d ( ω ) Determine the unit (sample) pulse reponse h d (n)=F -1 {H d ( ω )} h d (n) is generally infinite in length Truncate h d (n) to a finite length M

6 Truncating h d (n) Take only M terms N=0 to N=M-1 Remove all others

7 Truncating h d (n) Take only M terms N=0 to N=M-1 Remove all others Multiplying h d (n) with a rectangular window

8 Determine H( ω ) Take Fourier transform of h(n) Therefore, compute: H d ( ω ) and W( ω ) H d ( ω ) depends on the required response h d (n)

9 Computing W( ω ) W( ω )=F{w(n)} w(n) is a rectangular pulse

10 Example A low-pass linear phase FIR filter with the frequency response H d ( ω ) is required H d (n) happens to be non-causal having infinite duration

11 The impulse response h d (n)

12 Windowing the h d (n)

13 The truncated h d (n)

14 Example A low-pass linear phase FIR filter with the frequency response H d ( ω ) is required

15 Frequency of oscilation increases with M Magnitude of oscillation doesnt increase or decrease with M Oscillations occur due to the Gibbs phenonmenon caused by the multipli- cation of the rectangular window with H d ( ω )

16 Frequency of oscilation increases with M Magnitude of oscillation doesnt increase or decrease with M Oscillations occur due to the Gibbs phenonmenon caused by the multipli-cation of the rectangular window with H d ( ω )

17 Other windows

18

19 Spectrum of Kaiser window (Cycles per sample)

20 Spectrum of Hanning window

21 Spectrum of Hamming Window (Cycles per sample)

22 Spectrum of Blackman Window (Cycles per sample)

23 Spectrum of Tukey Window (Cycles per sample)

24 Windows characteristics

25 The FIR filters response with Rectangular window M=61

26 FIR filters response with Hamming window M=61

27 FIR filters response with Blackman window M=61

28 FIR filters response with Kaiser window M=61

29 Using the FIR filter

30 Blackmans filter output


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