Question

I have generated the coefficients using FFTW, now I want to reconstruct the original data, but using only the first numCoefs coefficients rather than all of them. At the moment I’m using the below code, which is very slow:

for ( unsigned int i = 0; i < length; ++i )
{
    double sum = 0;
    for ( unsigned int j = 0; j < numCoefs; ++j )
    {
        sum += ( coefs[j][0] * cos( j * omega * i ) ) + ( coefs[j][1] * sin( j * omega * i ) );
    }
    data[i] = sum;
}

Is there a faster way?

Answer 1

A much simpler solution would be to zero the unwanted coefficients and then do an IFFT with FFTW. This will be a lot more efficient than doing an IDFT as above.

Note that you may get some artefacts in the time domain when you do this kind of thing – you’re effectively multiplying by a step function in the frequency domain, which is equivalent to convolution with a sinc function in the time domain. To reduce the resulting “ringing” in the time domain you should use a window function to smooth out the transition between non-zero and zero coeffs.