Download presentation

Presentation is loading. Please wait.

1
**Digital filters: Design of FIR filters**

احسان احمد عرساڻي Lecture 23-24

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 Hd(ω) Determine the unit (sample) pulse reponse hd(n)=F-1{Hd(ω)} hd(n) is generally infinite in length Truncate hd(n) to a finite length M

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

7
**Truncating hd(n) Take only M terms Remove all others**

N=0 to N=M-1 Remove all others Multiplying hd(n) with a rectangular window

8
**Determine H(ω) Take Fourier transform of h(n) Therefore, compute:**

Hd(ω) and W(ω) Hd(ω) depends on the required response hd(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 Hd(ω) is required Hd(n) happens to be non-causal having infinite duration

11
**The impulse response hd(n)**

12
Windowing the hd(n)

13
The truncated hd(n)

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

15
**Frequency of oscilation increases with M**

Magnitude of oscillation doesn’t increase or decrease with M Oscillations occur due to the Gibbs phenonmenon caused by the multipli- cation of the rectangular window with Hd(ω)

16
**Frequency of oscilation increases with M**

Magnitude of oscillation doesn’t increase or decrease with M Oscillations occur due to the Gibbs phenonmenon caused by the multipli-cation of the rectangular window with Hd(ω)

17
Other windows

18
Other windows

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 filter’s response with Rectangular window**

M=61

26
**FIR filter’s response with Hamming window**

27
**FIR filter’s response with Blackman window**

28
**FIR filter’s response with Kaiser window**

M=61

29
Using the FIR filter

30
**Blackman’s filter output**

Similar presentations

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google