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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