The discrete-time Fourier transform (DTFT) is the (conventional) Fourier transform of a discrete-time signal. Its output is continous in frequency and periodi

2013年8月29日 · DFT and DTFT are obviously similar as they both generate the fourier spectrum of time-discrete signals. However, while the DTFT is defined to process an infinitely long signal (sum from -infinity to infinity), the DFT is defined to process a periodic signal (the periodic part being of finite length).

A DFT produces a finite number of results (frequency bins), so the complex result vector can be indexed by 0..(N-1). A DTFT produces a result over a continuous range of frequencies (more than a finite number of results) so must be specified by a real number as opposed to an integer.

As a summary, FT, FS, DTFT, DFT is exactly connected by a cube, where periodization in one domain corresponds to sampling in the other domain: Note that there are two routes to go from the Fourier transform to the DFT. Please read my write-up for more details. It is exactly inspired by this relabeling trick I discovered a while ago.

2021年2月9日 · The DFT is important because there exist efficient algorithms to compute $(3)$. This class of algorithms is called Fast Fourier Transform (FFT). The DFT can be used to approximately compute samples of the DTFT and of the CTFT. For finite length sequences, the DFT computes (exact) samples of the DTFT.

2020年12月21日 · The mathematical computation of DFT and DFS and absolutely identical. There is no different in the mathematical computation between the them. However, this does not make them equal. The DFT inherently extends the periodicity of the finite length signal. By applying the DFT, we extends the periodicity of the finite-length signal.

2020年4月1日 · Simply append zeros prior to computing the DFT. The phase result will change based on where you add the zeros (prepend vs postpend vs both) given it can potentially time shift the waveform but the amplitude result in exactly identical to samples of the DTFT.

2008年10月10日 · (2) DTFT and DTFS are different, since one is for aperiodic sequence, while the other is for periodic sequence. but the result of DTFT is continuous, and it's not fit computing by digital computer, therefore, the sequence is assumed to be periodic, and DTFS/DFT could be used to compute the discrete spectrum. also, the original aperiodic ...

We know that the DTFT for sampled signal is a series of replications of the spectrum of the original signal at frequencies spaced by the sampling frequency. Now, since DTFT is continuous and periodic, we can further breakdown DTFT at intervals and still be possible to reconstruct the DTFT and consequently the original signal.

2016年9月13日 · $\begingroup$ windowing is not an action taken by the DFT nor the DTFT. neither the DFT nor the DTFT window one's data. windowing happens when one selects a finite subset out of an infinite stream of samples (that had its origin and end billions of years from now) before either the DFT or DTFT ever sees the (truncated) data.