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A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression .
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Help ... Discrete cosine transform; Discrete Fourier transform;
The sine-only expansion for equally spaced points, corresponding to odd symmetry, was solved by Joseph Louis Lagrange in 1762, for which the solution is a discrete sine transform. The full cosine and sine interpolating polynomial, which gives rise to the DFT, was solved by Carl Friedrich Gauss in unpublished work around 1805, at which point he ...
Another coordinate-remapping approach was suggested for integrals of the form (), in which case one can use the transformation = [(+ ) /] to transform the integral into the form () where () = ( [(+) /]) /, at which point one can proceed identically to Clenshaw–Curtis quadrature for f as above. [12]
By applying Euler's formula (= + ), it can be shown (for real-valued functions) that the Fourier transform's real component is the cosine transform (representing the even component of the original function) and the Fourier transform's imaginary component is the negative of the sine transform (representing the odd component of the ...
Discrete sine and cosine transforms: When the input sequence has odd or even symmetry around the origin, the DTFT reduces to a discrete sine transform (DST) or discrete cosine transform (DCT). Regressive discrete Fourier series, in which the period is determined by the data rather than fixed in advance.
Map the powers of the spectrum obtained above onto the mel scale, using triangular overlapping windows or alternatively, cosine overlapping windows. Take the logs of the powers at each of the mel frequencies. Take the discrete cosine transform of the list of mel log powers, as if it were a signal. The MFCCs are the amplitudes of the resulting ...
The modified discrete cosine transform (MDCT) is a transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset, where subsequent blocks are overlapped so that the last half of one block coincides with the first half of the next block.