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We first show that by using without-replacement sampling guarantees that the randomly sampled population will exactly match the marginal data. We then compare the statistical properties of populations sampled using pseudo- and quasirandom numbers showing that the quasirandom sampling technique provides far better degeneracy, achieving solutions closer to the maximal entropy solution that IPF converges to.

## The great advantage of sampling synthesis is .

### Anything is possible at some price.

Two terms are widely used when discussing the sampling theorem: the and the . Unfortunately, their meaning is notstandardized. To understand this, consider an analog signal composed offrequencies between DC and 3 kHz. To properly digitize this signal it must besampled at 6,000 samples/sec (6 kHz) or higher. Suppose we choose to sampleat 8,000 samples/sec (8 kHz), allowing frequencies between DC and 4 kHz tobe properly represented. In this situation their are four important frequencies:(1) the highest frequency in the signal, 3 kHz; (2) twice this frequency, 6 kHz;(3) the sampling rate, 8 kHz; and (4) one-half the sampling rate, 4 kHz. Whichof these four is the and which is the ? It dependswho you ask! All of the possible combinations are used. Fortunately, mostauthors are careful to define how they are using the terms. In this book, they areboth used to mean .

### The two major drawbacks of sampling synthesis are

Figure 3-4 shows how frequencies are changed during aliasing. The key pointto remember is that a digital signal contain frequencies above one-halfthe sampling rate (i.e., the Nyquist frequency/rate). When the frequency of thecontinuous wave is below the Nyquist rate, the frequency of the sampled datais a match. However, when the continuous signal's frequency is above theNyquist rate, aliasing the frequency into something that berepresented in the sampled data. As shown by the zigzagging line in Fig. 3-4,every continuous frequency above the Nyquist rate has a corresponding digitalfrequency between zero and one-half the sampling rate. It there happens to bea sinusoid already at this lower frequency, the aliased signal will add to it,resulting in a loss of information. Aliasing is a double curse; information canbe lost about the higher the lower frequency. Suppose you are given adigital signal containing a frequency of 0.2 of the sampling rate. If this signalwere obtained by proper sampling, the original analog signal have had afrequency of 0.2. If aliasing took place during sampling, the digital frequencyof 0.2 could have come from any one of an infinite number of frequencies in theanalog signal: 0.2, 0.8, 1.2, 1.8, 2.2, … .

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