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- W991365525 abstract "This chapter discusses frequency-domain representation of discrete-time signals. The frequency-domain (Fourier) representation not only provides an alternative view of discrete-time signals but also provides a way to compute certain time-domain operations, like convolution and correlation, more efficiently. When a discrete-time signal or sequence is non-periodic or aperiodic, one cannot use the discrete Fourier series to represent it. Instead, the discrete Fourier transform (DFT) has to be used for representing the signal in the frequency domain. The DFT is the discrete-time equivalent of the (continuous-time) Fourier transforms. As with the discrete Fourier series, the DFT produces a set of coefficients that are sampled values of the frequency spectrum at regular intervals. The number of samples obtained depends on the number of samples in the time sequence. The inverse discrete Fourier transform (IDFT) converts the sequence of discrete Fourier coefficients back to the time sequence. Convolution in the time domain becomes a point-by-point multiplication in the frequency domain. Thus, a convolution operation can be performed by first performing the DFT of each time sequence, obtaining the product of the DFTs, and then inverse transforming the result back to a time sequence. This is called circular convolution, which is somewhat different from the linear convolution." @default.
- W991365525 created "2016-06-24" @default.
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- W991365525 date "2003-01-01" @default.
- W991365525 modified "2023-10-17" @default.
- W991365525 title "Frequency-domain representation of discrete-time signals" @default.
- W991365525 doi "https://doi.org/10.1016/b978-075065798-3/50004-7" @default.
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