DSP digital bandpass filter

A digital bandpass filter has the following specifications:

Passband frequency edge: 0.2pi and 0.6pi rad/sample

Passband ripple: < 1dB

Stopband frequency edge: 0.1pi and 0.8pi rad/sample

Stopband attenuation: > 40dB

Using the windowing method, what is the lowest-order FIR filter that will meet the desired specifications? Give the numerator coefficient B.

Answer 1

[Dimitris Kalogiros]

%BANDPASSFILTER Returns a discrete-time filter object.

% MATLAB Code
% Generated by MATLAB(R) 9.4 and Signal Processing Toolbox 8.0.
% Generated on: 09-Oct-2018 22:23:40

% Equiripple Bandpass filter designed using the FIRPM function.

% All frequency values are normalized to 1.

Fstop1 = 0.1;             % First Stopband Frequency
Fpass1 = 0.2;             % First Passband Frequency
Fpass2 = 0.6;             % Second Passband Frequency
Fstop2 = 0.8;             % Second Stopband Frequency
Dstop1 = 0.01;            % First Stopband Attenuation
Dpass  = 0.057501127785;  % Passband Ripple
Dstop2 = 0.01;            % Second Stopband Attenuation
dens   = 20;              % Density Factor

% Calculate the order from the parameters using FIRPMORD.
[N, Fo, Ao, W] = firpmord([Fstop1 Fpass1 Fpass2 Fstop2], [0 1 0], ...
                          [Dstop1 Dpass Dstop2]);

% Calculate the coefficients using the FIRPM function.
b  = firpm(N, Fo, Ao, W, {dens});
Hd = dfilt.dffir(b);

% taps of this filter: Hd.Numerator
figure; stem(Hd.Numerator, '-b^'); grid on; zoom on; title('taps');

% frequency response
figure; freqz(Hd);