By Steven W. Smith

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**Extra resources for The science and engineer's guide to digital signal processing**

**Example text**

Second, it is often desirable to recalculate the mean and standard deviation as new samples are acquired and added to the signal. We will call this type of calculation: running statistics. While the method of Eqs. 2-1 and 2-2 can be used for running statistics, it requires that all of the samples be involved in each new calculation. This is a very inefficient use of computational power and memory. A solution to these problems can be found by manipulating Eqs. 2-1 and 2-2 to provide another equation for calculating the standard deviation: EQUATION 2-3 Calculation of the standard deviation using running statistics.

Take each number generated by this equation, multiply it by the desired standard deviation, and add the desired mean. Chapter 2- Statistics, Probability and Noise 31 12 11 pdf a. 5, Ú = 1/û12 10 9 8 7 6 5 4 3 2 1 0 0 16 32 48 64 80 Sample number 96 112 128 127 12 11 pdf b. 0, Ú = 1/û6 10 9 8 7 6 5 4 3 2 1 0 0 16 32 48 64 80 Sample number 96 112 128 127 12 11 pdf c. X = RND+RND+ ... 0, Ú = 1 10 9 8 7 6 5 4 3 2 1 0 0 16 32 48 64 80 Sample number 96 112 128 127 FIGURE 2-10 Converting a uniform distribution to a Gaussian distribution.

In (d), the frequency of the analog sine wave is greater than the Nyquist frequency (one-half of the sampling rate). This results in aliasing, where the frequency of the sampled data is different from the frequency of the continuous signal. Since aliasing has corrupted the information, the original signal cannot be reconstructed from the samples. Two terms are widely used when discussing the sampling theorem: the Nyquist frequency and the Nyquist rate. Unfortunately, their meaning is not standardized.