I came across the following problem in FIR design using window and
convolution techniques .
Project a FIR filter using a Hamming window to achieve the following
specifications:
Passband 0,3-3,4 kHz
Stopband 0-0,2 e 4-8 kHz
Stopband atenuation > 25 dB
Sampling frequency 32 kHz
Since the transition band is different , in order to solve the
problem it is necessary to build a low pass filter, then a highpass
filter and apply convolution to their coeficient, with this
procedure it is possible to find a bandpass filter. Performing these
steps, I found a correct magnitude plot but a weird phase plot.
Below I present the matlab code. I would appreciate if someone
running it could realize what is wrong .
In spite of the phase found is linear as required by FIR filters, it
is inverse from what it should be, besides , it is all over the band
up to Fs/2, usually the phase is linear just in the passband, that's
why I think there is something wrong.
It is an academic problem I have to build a code and I am not
allowed to use fir1 comand, neither remez , fir2 or any other , I
Know that I can solve this problem using fir1 command, but that is
not the point, the solution must be given through convolutioning the
two filter coefficients, so , I must find out what is wrong with the
matlab code wich follows:
Thanks, Claudio
%general data
Ap= 3;
As= 25;
Fs2000;
% taking the smaller ripple
dp=(10^(Ap/20))-1; ds^(-As/20);
d=min(dp,ds);
As= -20*log10(d);
%Lowpass:
fp 400;
fs= 4000;
% normalizing frequencies
fpn=fp/Fs;
fsn=fs/Fs;
wcn=2*pi*fpn;
% Filter order to Hamming window
Nl(3.3/(fsn-fpn));
% Hamming window
wd=hamming(N-1);
% Ideal filter
na=1:(N-1)/2;
hd=2*fpn*sin(na.*wcn)./(na.*wcn);
hdn=[fliplr(hd) 2*fpn hd];
%windowing
hn=hdn.*wd';
% Highpass
fp100;
fs1 0;
% normalizing frequencies
fpn1=fp1/Fs;
fsn1=fs1/Fs;
wcn1=2*pi*fpn1;
% Filter order to Hamming window
N1l(3.3/(fpn1-fsn1));
% Hamming window
wd1=hamming(N1);
% Ideal filter
na1=1:(N1-1)/2;
hd1=-2*fpn1*sin(na1.*wcn1)./(na1.*wcn1);
hdn1=[fliplr(hd1) 1-2*fpn1 hd1];
%windowing
hn1=hdn1.*wd1';
% bandpass filter coeficients
H=conv(hn1,hn);
%Plotting frequency response
freqz(H,1,512,Fs);