| Z. Wang and B.R. Hunt, "The Discrete W Transform," Applied Mathematics and Computation, vol. 16, pp. 19--48, 1985. |
....1. We will need the following properties Tm (Tn ) Tmn ; 16) U 2n 1 = 2Un 1 Tn ; 17) U 2n = VnWn : 18) 3. DISCRETE TRIGONOMETRIC TRANSFORMS There are 16 discrete trigonometric transforms (DTTs) 8 types of discrete cosine transforms (DCTs) and 8 types of discrete sine transforms (DSTs) [7]. Each of the transforms is given by an (n n) matrix M , n 1, which multiplies to a signal vector s from the left, s 7 M s. As examples, we will use the symbol DCT 2 to refer to a DCT of type 2, DST 7n to refer to a DST of type 7 and size n. Table 2 gives the definitions of the 16 DTTs, by ....
Z. Wang and B.R. Hunt, "The Discrete W Transform," Applied Mathematics and Computation, vol. 16, pp. 19--48, 1985.
.... Because of their wide spread applications in digital signal processing, particular effort has been spent on the discrete Fourier transform (DFT) and the different types of trigonometric transforms, i.e. discrete cosine and sine transforms (DCTs and DSTs) as classified by Wang and Hunt [1]. Important algorithms for the DFT include the fast Fourier transform (FFT) found by Cooley and Tukey (first discovered by Gauss [2] 3] Rader s algorithm for prime size [4] Winograd s algorithms [5] as well as [6] 8] An overview on FFT algorithms can be found in [9] or [10] Important ....
Z. Wang and B. R. Hunt, "The discrete W Transform," Appl. Math. Comput., vol. 16, pp. 19--48, 1985.
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