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By Soha Hassoun; Tsutomu Sasao

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In this simulation, the spacing between adjacent sets of sample sequences are varied between 7 and 19. The DFT of the cross-correlation function is shown by the right side of Fig. 18(0). This corresponds to Eq. 27). The cross-power spectrum is a function made from a real even function and an imaginary odd function. They are shown separately in the right side of the figure only in the positive frequency region. Residual power ratio is also shown at the right corner of each correlation function (impulse responses).

18(0) shows the case when the cross-correlation function is calculated in the time domain. 9 %. The next three results are obtained using Eq. 30) in a similar manner to those discussed in Sects. 10. The residual power ratios of Fig. 9 %, respectively. The last method (3), that avoids the circular correlation problem, gives much smaller errors than the other methods. The cross-correlation between the input and output becomes the impulse response of the system only when the auto-correlation function of the input sequence is equal to one at m (lag) = 0 and 0 elsewhere.

In the programs associated with the figures, the student can choose various conditions and numbers. By trying various cases, the student will learn more that is not discussed in this chapter. 12 Exercise 1. What is the standard deviation of a sine function with amplitude 1? 2. Why is Eq. 4) equal to two when x(n) and y(n) are completely uncorrelated? 3. Why is Eq. 4) equal to four when x(n) and y(n) have the same magnitudes but their signs are opposite? 52 2 Correlation 4.

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