Filter Bank using Multirate Concept

clear all; close all; clc; %% creating a low pass prototype filter filtobj=lpfilt3; %MATLAB generated function from fdatool h=impz(filtobj.Numerator,1)'; % creating low pass filter %% choosing the number of bands cc=input('Enter Number of Bands = '); M=cc; % number of banks %% zero padding to make the number of elements of impulse response integer multiple of M if rem(length(h),M)~=0 h=[h zeros(1,M-rem(length(h),M))]; end %% downsampling and putting them into different bands for i=1:M h1=reshape(h,[M numel(h)/M]); end %% upsample and delay for i=1:M h2(i,:)=upsample(h1(i,:),M); h2(i,:)=delayseq(h2(i,:)',i-1)'; end %% taking the fourier transform of the impulse response of each bands for i=1:M h2(i,:)=fft(h2(i,:)); end %% multiplication of inverse DFT matrix and fourier transform of the impulse response in frequency domain H=M*inv(dftmtx(M))*h2; %% watch filter response for i=1:M subplot(M,4,i), stem(linspace(-pi,pi,numel(H(i,:)))/pi, fftshift(abs(H(i,:)))); % str=['Magnitude Response of Filter Bank ' num2str(i)]; % ylabel(['\mid E_{' num2str(i) '}(\omega) \mid']); % xlabel('\omega'); % title(str); end %% buiding a signal N=numel(H(1,:)); n=1:N; x=zeros(1,numel(n)); for i=0.1:0.1:2 x=x+2*i*sin(i*pi*n); end %% watcing filter output X=fft(x,length(H)); for i=1:M Y(i,:)=X.*H(i,:); end for i=1:M subplot(M,4,M+i), stem(linspace(-pi,pi,numel(Y(i,:)))/pi, fftshift(abs(Y(i,:)))); % str=['Magnitude Response of the Output from Filter Bank ' num2str(i)]; % ylabel(['\mid Y_{' num2str(i) '}(\omega) \mid']); % xlabel('\omega'); % title(str); end %% watching recontruction Y=sum(Y)/M; err=abs(Y)-abs(X); subplot(M,4,[2*M+1:3*M]), stem(linspace(-pi,pi,numel(X))/pi, fftshift(abs(X))) % ylabel('\mid X (\omega) \mid'); % xlabel('\omega'); % str=[num2str(length(H)) '-point Fourier Transform of the original signal.']; % title(str); subplot(M,4,[3*M+1:4*M]), stem(linspace(-pi,pi,numel(Y))/pi, fftshift(abs(Y))) % ylabel('\mid Y (\omega) \mid'); % xlabel('\omega'); % str=['Magnitude response of the signal recontructed from filter outputs.']; % title(str);