FIR Filter Design Using MATLAB

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?

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?