Wednesday, June 6, 2012

IIR Filter Design Using MATLAB


IIR Filter Design Using MATLAB

OBJECTIVES
To learn how to design IIR (infinite impulse response) filter with the given frequency specifications.
a. Bilinear transformation method
b. Pole-zero placement method
PROCEDURE:
Part A: Bilinear Transformation Method
1. Design lowpass IIR filter with the following specifications:
Filter order = 2, Butterworth type
Cut-off frequency=800 Hz
Sampling rate =8000 Hz
Design using the bilinear z-transform design method
Print the lowpass IIR filter coefficients and plot the frequency responses using MATLAB.
MATLAB>>freqz(bLP,aLP,512,8000); axis([0 4000 –40 1]); % sampling rate=8000 Hz
Label and print your graph.
What are the filter gains for stopband at the cut-off frequency and 2000 Hz, and passband at 50 Hz based on the plot of the magnitude frequency response?
2. Design a bandpass IIR filter with the following specifications:
Filter order =2, Butterworth type
Lower cut-off frequency=1000 Hz, upper cut-off frequency=1400 Hz,

Sampling rate =8000 Hz

Design using the bilinear z-transform design method
Print the band ass IIR filter coefficients and plot the frequency responses using MATLAB.
MATLAB>>freqz(bBP,aBP,512,8000); axis([0 4000 –40 1]); % sampling rate=8000 Hz
Label and print your graph.
What are the filter gains for the stopband at cut-off frequencies, at 500 Hz and 2500 Hz, and passband at 1200 Hz based on the plot of the magnitude frequency response?
3. Design a highpass IIR filter with the following specifications:
Filter order= 4, Chebyshev type
Ripple on the passband =1 dB
Cut-off frequency=1500 Hz
Sampling rate =8000 Hz
Design using the bilinear z-transform design method
Print the highpass IIR filter coefficients and plot the frequency responses using MATLAB.
MATLAB>>freqz(bHP,aHP,512,8000); axis([0 4000 –40 1]);% sampling rate=8000 Hz
Label and print your graph.
What are the filter gains for the stopband at the cut-off frequency and 500 Hz, and passband at 3000 Hz based on the plot of the magnitude frequency response?
Part B: Pole-zero Placement Method
1. Design lowpass IIR filter with the following specifications:
Filte
To learn how to design IIR (infinite impulse response) filter with the given frequency specifications.
a. Bilinear transformation method
b. Pole-zero placement method
4. Design lowpass IIR filter with the following specifications:
Filter order = 2, Butterworth type
Cut-off frequency=800 Hz
Sampling rate =8000 Hz
Design using the bilinear z-transform design method
Print the lowpass IIR filter coefficients and plot the frequency responses using MATLAB.
MATLAB>>freqz(bLP,aLP,512,8000); axis([0 4000 –40 1]); % sampling rate=8000 Hz
Label and print your graph.
What are the filter gains for stopband at the cut-off frequency and 2000 Hz, and passband at 50 Hz based on the plot of the magnitude frequency response?
5. Design a bandpass IIR filter with the following specifications:
Filter order =2, Butterworth type
Lower cut-off frequency=1000 Hz, upper cut-off frequency=1400 Hz,

Sampling rate =8000 Hz

Design using the bilinear z-transform design method
Print the band ass IIR filter coefficients and plot the frequency responses using MATLAB.
MATLAB>>freqz(bBP,aBP,512,8000); axis([0 4000 –40 1]); % sampling rate=8000 Hz
Label and print your graph.
What are the filter gains for the stopband at cut-off frequencies, at 500 Hz and 2500 Hz, and passband at 1200 Hz based on the plot of the magnitude frequency response?
6. Design a highpass IIR filter with the following specifications:
Filter order= 4, Chebyshev type
Ripple on the passband =1 dB
Cut-off frequency=1500 Hz
Sampling rate =8000 Hz
Design using the bilinear z-transform design method
Print the highpass IIR filter coefficients and plot the frequency responses using MATLAB.
MATLAB>>freqz(bHP,aHP,512,8000); axis([0 4000 –40 1]);% sampling rate=8000 Hz
Label and print your graph.
What are the filter gains for the stopband at the cut-off frequency and 500 Hz, and passband at 3000 Hz based on the plot of the magnitude frequency response?
. Design lowpass IIR filter with the following specifications:
Filter order = 1
3dB cut-off frequency=120 Hz
Sampling rate =8000 Hz
Design using the pole-zero placement method
Print the lowpass IIR filter coefficients and plot the frequency responses using MATLAB.
MATLAB>freqz(bLP,aLP,512,8000); axis([0 4000 –40 1]); % sampling rate=8000 Hz
Label and print your graph.
What are the filter gains for the stopband at the cut-off frequency and 2000 Hz, and passband at 100 Hz based on the plot of the magnitude frequency response?
2. Design a bandpass IIR filter with the following specifications:
Filter order =2
3dB lower cut-
r order = 1
3dB cut-off frequency=120 Hz
Sampling rate =8000 Hz
Design using the pole-zero placement method
Print the lowpass IIR filter coefficients and plot the frequency responses using MATLAB.
MATLAB>freqz(bLP,aLP,512,8000); axis([0 4000 –40 1]); % sampling rate=8000 Hz
Label and print your graph.
What are the filter gains for the stopband at the cut-off frequency and 2000 Hz, and passband at 100 Hz based on the plot of the magnitude frequency response?
2. Design a bandpass IIR filter with the following specifications:
Filter order =2
3dB lower cut-off frequency=1200 Hz, 3dB upper cut-off frequency=1400 Hz,

Sampling rate =8000 samples per second

Design using the pole-zero placement method
Hint: Using the following MATLAB code to compute the unit gain scale factor:
-----------------------------------------------------------------------------------------------
f0=
Bw=
r=1-(Bw/fs)*pi
theta=(f0/fs)*2*pi
K=(1-r)*sqrt(1-2*r*cos(2*theta)+r*r)/(2*abs(sin(theta)))
---------------------------------------------------------------------------------------------
Print the bandpass IIR filter coefficients and plot the frequency responses using MATLAB.
MATLAB>>freqz(bBP,aBP,512,8000 axis([0 4000 –40 1]); % sampling rate=8000 Hz
Label and print your graph.
What are the filter gains for the stopband at cut-off frequencies, at 500 Hz and 2500 Hz, and passband at 1200 Hz based on the plot of the magnitude frequency response?

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