Real-Time Digital Signal Processing from MATLAB® to C with the TMS320C6x DSPs, Second Edition, 2nd Edition

152 CHAPTER 8. THE FAST FO URIER TRANSFORM

is the length of the data.

2

The FFT of the convolution sum is

Y [k]=H[k]X[k].

Again notice that the convolution operation in the discrete-time domain has been converted

into a multiplication operation in the discrete-frequency domain.

We might expect that to calculate the digital filter’s output back in the time domain,

we can use the IFFT and calculate

y[k] = IFFT{Y [k]}

= IFFT{H[k]X[k]}

= IFFT{FFT{h[n]}FFT{x[n]}}.

Using this approach we would take the FFT of our filter’s impulse response, h[n], and

multiply the result by the FFT of the input signal, x[n]. We would then take the inverse

FFT of the product. As w