Filtering spectrum using FIR filters

If i have signal values x[T] and filter coefficients b[i], i can perform filtering using convolution.

Suppose i have spectrum of x (after FFT) and i need to perform filtering using filters coefficients, how can i perform this? I heard that in frequency domain it will be multiplying, rather than convolution (time domain). But i can't find an equation to use it. I have 614000 values in y = fft(x[T]) vector and 119 filter coefficients (generated using fdatool), i can't multiply them directly ... Thanks.

Answer 1

[Wayne King]

You can do the following:

Let B be your vector of FIR coefficients and x your signal. I'll just present an example with a white noise vector and use a 10-point moving average filter.

   x = randn(1000,1);
   B = 1/10*ones(10,1);
   xdft = fft(x);
   H = freqz(B,1,length(x),'whole');
   Y = xdft.*H;
   y = ifft(Y,'symmetric');

Now compare the output y above to

   yconv = filter(B,1,x);
   plot(y,'b'); hold on;
   plot(yconv,'r')