Discrete Fourier Transforms: DtFT and DFT

In this chapter we investigate a big family of Fourier transforms: continuous Fourier transform (CFT), Fourier series (FS), discrete-time Fourier transform (DtFT), and discrete Fourier transform (DFT). The DFT, in its fast form (FFT), is probably one of the most frequently used orthogonal transforms in the world apart from the discrete cosine transform (DCT). We learn that DtFT originates from continuous Fourier transform, while DFT from Fourier series. We become familiar with transform features and understand their strong and weak points. We learn the fundamentals of frequency analysis of discrete-time signals by DtFT and DFT. We see the significance of special signal shaping functions called windows in spectral analysis of signals.