what are the hamming, fft, ifft functions?

% Signal parameters:
f = [ 440 880 1000 2000 ];      % frequencies   
M = 256;                        % signal length 
Fs = 5000;                      % sampling rate

% Generate a signal by adding up sinusoids:
x = zeros(1,M); % pre-allocate 'accumulator'
n = 0:(M-1);    % discrete-time grid 
for fk = f; 
    x = x + sin(2*pi*n*fk/Fs); 
end
% Filter parameters:
L = 257;    % filter length 
fc = 600;   % cutoff frequency 

% Design the filter using the window method:
hsupp = (-(L-1)/2:(L-1)/2);
hideal = (2*fc/Fs)*sinc(2*fc*hsupp/Fs);
h = hamming(L)' .* hideal; % h is our filter

% Choose the next power of 2 greater than L+M-1 
Nfft = 2^nextpow2(L+M-1);
% Zero pad the signal and impulse response:
xzp = [ x zeros(1,Nfft-M) ];
hzp = [ h zeros(1,Nfft-L) ];

X = fft(xzp); % signal
H = fft(hzp); % filter
Y = X .* H;
y = ifft(Y);
relrmserr=norm(imag(y))/norm(y) % check... should be zero
y = real(y);
subplot(2,1,1), plot(x)
subplot(2,1,2), plot(y)
grid on

my low pass filter works but I don't want to use hamming, fft and ifft. Instead of these I want to use hamming, fft, ifft functions. I found some codes about them but it didn't work. Could you help me please?

[Walter Roberson]

What are the symptoms of "it didn't work"?

[Image Analyst]

I don't understand - you say you don't want to use those three functions and then you say you want to use them instead of themselves. What does all that mean? Do you want to use them or not?

[SELDA]

I'm really sorry about my bad english. for example in my filter there is fft function.But I must not use fft function.I have to use equation of fft. I wrote

w = .54 - .46*cos(2*pi*(0:L-1)'/(L-1)); instead of hamming

I wrote

N=length(x); for k=1:N X(k)=0; for n=1:N X(k)=X(k)+x(n).*exp(-1j.*2.*pi.*(n-1).*(k-1)./N); end end instead of fft

I wrote for o=1:L T(o)=0; for u=1:L T(o)=(1/L)*(T(o)+X(u).*exp(2.*pi.*j.*(o-1).*(u-1)./L)); end end instead of ifft

but these didn't work

Answer 1

[Rick Rosson]

   >> doc filter
   >> doc fdatool
   >> doc fir1