## 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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