By M. L. Balinski, Eli Hellerman

ISBN-10: 0444110097

ISBN-13: 9780444110091

ISBN-10: 3642007651

ISBN-13: 9783642007651

ISBN-10: 364200766X

ISBN-13: 9783642007668

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24. Illustration of the Sixth Identity. 23(b). 25. 26. Although the intermediate sequences v1[r] and v2[r] are different, the two realizations of 2/3-sampling rate conversion produce the same output sequence y[m]. The invariance of the output sequence to the interchange of the sampling rate alteration devices in 2/3-convertor described above, demonstrates the equivalence existing for the relatively prime factors L and M. The same equivalence is not true when L and M contain a common integer factor.

11(a) plots the spectrum of the original signal. Figs. 11(b-d) plot the spectra of the up-sampled signals for L = 2, L = 3 and L = 4, respectively. In each case, the up-sampling compresses the original spectrum by L, and causes the additional L-1 images of the original spectrum. DECIMATION AND INTERPOLATION Sampling rate conversion systems are used to change the sampling rate of a signal. The process of sampling rate decrease is called decimation, and the process of sampling rate increase is called interpolation.

B) Down-sampled (compressed) sequence 26 Basics of Multirate Systems  x[m / L], m = 0, ± L, ±2 L, . 5. The box with an up pointed arrow followed with the factor L is used to symbolize the up-sampling operation. The up-sampling operation increases the sampling rate FT of the original signal x(nT). e, FT’ =LFT. 6 shows the time dimension of the sampling rate conversion with an up-sampler. As in the case of a down-sampler, the sampling periods (or sampling frequencies) can be omitted in representing the up-sampling operation.

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Computational practice in mathematical programming by M. L. Balinski, Eli Hellerman

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