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DFT/FFT Signal Spectral Estimation and FIR and IIR Filters Design Using MATLAB

OBJECTIVE

1. To review the use of the FFT algorithm

2. To learn how to compute the signal spectrum using the window functions for the digital signals.

3. To learn how to design FIR (finite impulse response) filters with the given specifications

4. To learn how to design IIR (infinite impulse response) filters with the given specifications

PROCEDURE:

PART A: Spectral Estimation of the Sum of Sinusoids

1.Create a program to generate the sum of sinusoids by using: for the 240 samples using a sampling rate of 8000 Hz. Each sinusoid is defined below:

2. Write a program to compute and plot the amplitude spectrum of the signal with the number of data points you have determined based on FFT and each of the following windows

a. Rectangular window (no window)

b. Triangular window

c. Hamming window

What is the frequency resolution ?_______________________

Which window method has the most spectral leakage ?______________________

Which window method has the smallest spectral leakage ? ____________________

Part B FIR Filter Design

Use the window method to design the following filters

1. Design a lowpass FIR filter with the following specifications:

Pass band: 0 – 800 Hz

Stop band: 1200 – 4000 Hz

Pass band ripple: 0.05 dB

Stop band attenuation: 50 dB

Sampling rate =8000 samples per second

Print the lowpass FIR filter coefficients and plot the frequency responses using MATLAB.

MATLAB>>freqz(bLP,1,512,8000); % sampling rate=8000 Hz

Label and print your graph.

What are the filter gains at 800 Hz and 1200 Hz based on the plot of the magnitude frequency response?

2. Design a bandpass FIR filter with the following specifications:

Sampling rate =8000 samples per second

Passband: 1200 - 1600 Hz

Lower stopband 0 - 800 Hz

Upper stopband 2000 – 4000 Hz

Passband ripple: 1 dB

Stopband attenuation: 46 dB

Print the bandpass FIR filter coefficients and plot the frequency responses using MATLAB.

MATLAB>>freqz(bBP,1,512,8000); % sampling rate=8000 Hz

Label and print your graph.

What are the filter gains at 800 Hz, 1200 Hz, 1600 Hz, and 2000 Hz based on the plot of the magnitude response?

Part C: IIR Filter Design

1. Design highpass IIR filter with the following specifications:

Butterworth type

Lower stop band: 0 - 600 Hz

Pass band 2000 – 4000 Hz

Pass band ripple: 3 dB

Stop band attenuation: 22 dB

Sampling rate =8000 Hz

Determine the prototype filter order: ________________

Sampling rate =8000 samples per second

Bilinear z-transform design method

Print the lowpass IIR filter coefficients and plot the frequency responses using MATLAB.

MATLAB>>freqz(bHP,aLP,512,8000); axis([0 4000 –40 1]); % sampling rate=8000 Hz

Label and print your graph.

What are the filter gains at 200 Hz and 2000 Hz based on the plot of the magnitude frequency response?

2. Design a bandpass IIR filter with the following specifications:

Chebyshev type

Lower stop band: 0 - 600 Hz

Pass band 1100 – 1300 Hz

Upper stop band 1800 – 4000 Hz

Pass band ripple: 1 dB

Stop band attenuation: 20 dB

Sampling rate =8000 Hz

Determine the prototype filter order: ________________

Bilinear z-transform design method

Print the bandpass IIR filter coefficients and plot the frequyency 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 at 600 Hz, 1100 Hz, 1300 Hz and 1800 Hz based on the plot of the magnitude frequency response?

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