Final answer:
The continuous Fourier transform (CFT) and the Fourier transform of an equivalent discrete signal (DFT) are two different mathematical representations of a signal in the frequency domain.
Step-by-step explanation:
The continuous Fourier transform (CFT) and the Fourier transform of an equivalent discrete signal (DFT) are two different mathematical representations of a signal in the frequency domain. The CFT is used to analyze continuous-time signals, while the DFT is used to analyze discrete-time signals.
Both the CFT and DFT decompose a signal into its constituent frequencies, but the CFT operates on the entire continuous signal, while the DFT operates on a finite sequence of discrete samples.
The CFT uses an integral over time to transform a continuous function into its frequency spectrum, whereas the DFT uses a finite sum of complex exponentials to transform a sequence of discrete samples into its frequency spectrum.