Editing Discrete Fourier transform (section)

===Data compression===
The field of digital signal processing relies heavily on operations in the frequency domain (i.e. on the Fourier transform). For example, several [[lossy compression|lossy]] image and sound compression methods employ the discrete Fourier transform: the signal is cut into short segments, each is transformed, and then the Fourier coefficients of high frequencies, which are assumed to be unnoticeable, are discarded. The decompressor computes the inverse transform based on this reduced number of Fourier coefficients. (Compression applications often use a specialized form of the DFT, the [[discrete cosine transform]] or sometimes the [[modified discrete cosine transform]].)
Some relatively recent compression algorithms, however, use [[wavelet transform]]s, which give a more uniform compromise between time and frequency domain than obtained by chopping data into segments and transforming each segment.  In the case of [[JPEG2000]], this avoids the spurious image features that appear when images are highly compressed with the original [[JPEG]].