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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