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When the DFT is used for [[Frequency spectrum#Spectrum analysis|spectral analysis]], the {''x<sub>n</sub>''} sequence usually represents a finite set of uniformly spaced time-samples of some signal ''x''(''t'') where ''t'' represents time. The conversion from continuous time to samples (discrete-time) changes the underlying [[continuous Fourier transform|Fourier transform]] of ''x''(''t'') into a [[discrete-time Fourier transform]] (DTFT), which generally entails a type of distortion called [[aliasing]]. Choice of an appropriate sample-rate (see ''[[Nyquist rate]]'') is the key to minimizing that distortion. Similarly, the conversion from a very long (or infinite) sequence to a manageable size entails a type of distortion called ''[[Spectral leakage|leakage]]'', which is manifested as a loss of detail (aka resolution) in the DTFT. Choice of an appropriate sub-sequence length is the primary key to minimizing that effect. When the available data (and time to process it) is more than the amount needed to attain the desired frequency resolution, a standard technique is to perform multiple DFTs, for example to create a [[spectrogram]]. If the desired result is a power spectrum and noise or randomness is present in the data, averaging the magnitude components of the multiple DFTs is a useful procedure to reduce the [[variance]] of the spectrum (also called a [[periodogram]] in this context); two examples of such techniques are the [[Welch method]] and the [[Bartlett method]]; the general subject of estimating the power spectrum of a noisy signal is called [[spectral estimation]].
A final source of distortion (or perhaps ''illusion'') is the DFT itself, because it is just a discrete sampling of the DTFT, which is a function of a continuous frequency ___domain. That can be mitigated by increasing the resolution of the DFT. That procedure is illustrated at
*The procedure is sometimes referred to as ''zero-padding'', which is a particular implementation used in conjunction with the [[fast Fourier transform]] (FFT) algorithm. The inefficiency of performing multiplications and additions with zero-valued "samples" is more than offset by the inherent efficiency of the FFT.
*As already noted, leakage imposes a limit on the inherent resolution of the DTFT. So there is a practical limit to the benefit that can be obtained from a fine-grained DFT.
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