ABSTRACT
The discrepancies between the discrete Fourier transform (DFT) and the continuous-time Fourier transform arise because DFT requires sampling and truncation. The motivation for transforming a signal from one domain to another is that the characteristics of a signal are visible directly and can be easily extracted from such a representation. The transformation of a signal into the z-plane is called z-transform. The z-transform is a more generalized transformation when compared to the discrete-time Fourier transform and is applicable to broader classes of signals. Since fast Fourier transform (FFT) computes the DFT faster, we can use the FFT algorithm to compute the linear convolution. It has been shown earlier that the input to the Decimation-in-Frequency FFT (DIF-FFT) is in bit-reversed order, while the output is in natural order. However, in the case of DIF-FFT, it is just the reverse, that is, the input will be in natural order while the output will be in bit-reversed order.
