Discrete Convolution and the DFT
DOI link for Discrete Convolution and the DFT
Discrete Convolution and the DFT book
This chapter introduces the linear convolution of two nite sequences, which, on the one hand, allows to approximate continuous convolution using sampled function values, and on the other hand, is algebraically equivalent to the multiplication of two polynomials. It analyses the periodic convolution is also useful in computing the chirp Fourier transform, which computes a partial discrete Fourier transform (DFT) in the neighborhood of a particular frequency in order to measure it to greater accuracy. Since the chirp Fourier transform is a partial DFT, it cannot be computed by the fast Fourier trans- form. For its efficient computation, the chapter discusses the partial DFT into a partial linear convolution, which can then be converted to a cyclic convolution, because the latter can be computed via DFT and inverse DFT.