Download presentation

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

OK

Digital Kommunikationselektronik TNE027 Lecture 5 1 Fourier Transforms Discrete Fourier Transform (DFT) Algorithms Fast Fourier Transform (FFT) Algorithms.

Digital Kommunikationselektronik TNE027 Lecture 5 1 Fourier Transforms Discrete Fourier Transform (DFT) Algorithms Fast Fourier Transform (FFT) Algorithms.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google