The implementation of CTA given in the chapter uses a convolution operation. For large values of M and N a FFT-based approach is efficient. For this, two issues must be carefully considered. First, the size L of the FFT must be L ≥ (M +N) and second, the negative time values of the impulse response must be properly mapped to the positive side before taking its DFT. Modify the CTA function and write a new function ctafft that uses the fft function.