Design a lowpass FIR filter with the following specifications: Number of filter

Question

Design a lowpass FIR filter with the following specifications:
Number of filter taps=31 taps
Cut-off frequency=800 Hz
Sampling rate =8000 Hz
Fourier transform method.
Print the low pass FIR filter coefficients and plot the frequency responses using MATLAB.
MATLAB>>freqz(bLP,1,512,8000); % sampling rate=8000 Hz

Explanation / Answer

OBJECTIVES To learn how to design FIR (finite impulse response) filters with the given frequency specifications. a. Fourier Transform Method and Window method b. Optimal Design Method PROCEDURE: Part A Fourier Transform and Window Method 1. Design a lowpass FIR filter with the following specifications: Number of filter taps=31 taps Cut-off frequency=800 Hz Sampling rate =8000 Hz Fourier transform method. Print the low pass 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 for the stopband at 2000 Hz and passband at 200 Hz based on the plot of the magnitude frequency response? 2. Design a bandpass FIR filter with the following specifications: Number of filter taps=31 taps, Lower cut-off frequency=1000 Hz, upper cut-off frequency=1400 Hz, Sampling rate =8000 Hz Hanning window 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 for the stopband at 500 Hz and 2500 Hz, and passband at 1200 Hz based on the plot of the magnitude response? 3. Design a highpass FIR filter with the following specifications: Number of filter taps=31 taps, Cut-off frequency=1500 Hz Sampling rate =8000 Hz Design using the Hamming window Print the highpass FIR filter coefficients and plot the frequency responses using MATLAB. MATLAB>>freqz(bHP,1,512,8000); % sampling rate=8000 Hz Label and print your graph. What are the filter gains for the stopband at 1000 Hz and cut-off frequency, and passband at 3000 Hz based on the plot of the magnitude response? Instructor Verification ______________________ Part B: Optimal Design Method Use Packs-McClellan algorithm (Remez exchange algorithm provided by MATLAB) to design the following FIR filters 1. Design a lowpass FIR filter with the following specifications: Number of filter taps= determined on your trials Sampling rate =8000 Hz Passband: 0 - 1200 Hz Stopband 1500 - 4000 Hz Passband ripple: 1 dB Stopband attenuation: 40 dB 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 for the stopband at 3000 Hz and passband at 200 Hz based on the plot of the magnitude response? 2. Design a bandpass FIR filter with the following specifications: Number of filter taps= determined on your trials Sampling rate =8000 Hz Passband: 1200 - 1600 Hz Lower stopband 0 - 800 Hz Upper stopband 2000 - 4000 Hz Passband ripple: 1 dB Stopband attenuation: 40 dB Print the band pass 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 for the stopband at 500 Hz and 2500 Hz, and passband at 1400 Hz based on the plot of the magnitude frequency response? Instructor Verification ______________________ Organize and submit your design, plots and program lists.

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