TAILIEUCHUNG - DISCRETE-SIGNAL ANALYSIS AND DESIGN- P6

DISCRETE-SIGNAL ANALYSIS AND DESIGN- P6: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 11 a N 2 N N-1 d Figure 1-1 Infinite sequence operations for wave analysis. a The segment of infinite periodic sequence from 0 to N 1. The next sequence starts at N. b The Segment of infinite sequence from 0 to N 1 is not periodic with respect to the rest of the infinite sequence. c The two-sided sequence starts at 4 or 0. d The sequence starts at 0. 12 DISCRETE-SIGNAL ANALYSIS AND DESIGN identified in both time and amplitude. If the sequence is nonrepeating random or if it is infinite in length or if it is periodic but the sequence is not chosen to be exactly one period then this segment is not one period of a truly periodic process as shown in Fig. 1-1b. However the wave analysis math assumes that the part of the wave that is selected is actually periodic within an infinite sequence similar to Fig. 1-1a. The selected sequence can then perhaps be referred to as pseudo-periodic and the analysis results are correct for that sequence. For example the entire sequence of Fig. 1-1b or any segment of it can be analyzed exactly as though the selected segment is one period of an infinite periodic wave. The results of the analysis are usually different for each different segment that is chosen. If the 0 to N 1 sequence in Fig. 1-1b is chosen the analysis results are identical to the results for 0 to N 1 in Fig. 1-1a. When selecting a segment of the data for instance experimentally acquired values it is important to be sure that the selected data contains the amount of information that is needed to get a sufficiently accurate analysis. If amplitude values change significantly between samples we must use samples that are more closely spaced. There is more about this later in this chapter. It is important to point out a fact about the time sequences x n in Fig. 1-1. Although the samples are shown as thin lines that have very little area each line does represent a definite amount of energy. The sum of these energies within a unit time interval and if there are

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