TAILIEUCHUNG - DISCRETE-SIGNAL ANALYSIS AND DESIGN- P8

DISCRETE-SIGNAL ANALYSIS AND DESIGN- P8:Electronic circuit analysis and design projects often involve time-domain and frequency-domain characteristics that are difÞcult to work with using the traditional and laborious mathematical pencil-and-paper methods of former eras. This is especially true of certain nonlinear circuits and sys- tems that engineering students and experimenters may not yet be com- fortable with. | FIRST PRINCIPLES 21 For N 2M points there are N values including 0 and N intervals to the beginning of the next sequence. For a two-sided time sequence the special midpoint term N 2 can be labeled as i. sec and also i. sec as shown in Fig. 1-4. It is important to do this time scaling correctly. Figure 1-2b shows an identical way to label frequency values and frequency intervals. Each value is a specific frequency and each interval is a frequency band . This approach helps us to keep the spectrum more clearly in mind. If amplitude values change too much within an interval we will use a higher value of N to improve frequency resolution as discussed previously. The same idea applies in the time domain. The term picket fence effect describes the situation where the selected number of integer values of frequency or time does not give enough detail. It s like watching a ball game through a picket fence. NUMBER OF SAMPLES The sampling theorem Carlson 1986 p. 351 says that a single sine wave needs more than two preferably at least three samples per cycle. A frequency of 10 000Hz requires 1 10 000-3 for each sample. A signal at 100Hz needs 1 100-3 for each sample. If both components are present in the same composite signal the minimum required total number of samples is 102 100. In other words 100 cycles of the 10 000-Hz component occupy the same time as 1 cycle of the 100-Hz component. Because the time sequence is two-sided positive time and negative time 200 samples would be a better choice. The nearest preferred value of N is 28 256 and the sequence is from 0 n N - 1. The plot of the DFT phasor spectrum X k is also two-sided with 256 positions. N 256 is a good choice for both time and frequency for this example. If a particular waveform has a well-defined time limit but insufficient nonzero data values we can improve the time resolution and therefore the frequency resolution by adding augmenting zeros to the

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