TAILIEUCHUNG - DISCRETE-SIGNAL ANALYSIS AND DESIGN- P27

DISCRETE-SIGNAL ANALYSIS AND DESIGN- P27: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. | 116 DISCRETE-SIGNAL ANALYSIS AND DESIGN VL k PL k VL k 2 GB k G k watts. If G k GB k 0 the imaginary power vars PL k jB k x VL k 2. The real part of the power PL k is converted to radio or sound waves or heat dissipation of some kind and the imaginary part is cycled back and forth between energy storage elements lumped components or standing waves transmission lines of some kind. This energy cycling always involves slightly lossy storage elements that dissipate a little of the real power. Example 7-1 The Use of Eq. 7-2 Figure 7-2 is an example of the use of Eq. 7-2 . The x n input signal voltage waveform in part a is a complex time sequence of cosine and sine waves. This figure uses steps of in the n values for better visual resolution and this is the only place where x n is plotted. The two plots in part a are I n real and Q n imaginary sequences that we have looked at previously. Parts b and c are the DFT of part a that show the two-sided phasor frequency X k voltage values. The DFT uses k steps of to avoid spectral leakage between k integers Chapter 3 . If a dc voltage is present it shows up at k 0 see Fig. 1-2 . In this example there is no dc but it will be considered later. The integer values are sufficient for a correct evaluation if there are enough of them to satisfy the requirements for adequate sampling. In part d the two-sided phasors are organized into two groups. One group collects phasor pairs that have even symmetry about N 2 and are added coherently Chapter 1 . These are the cosine or j cosine terms. The other pairs that have odd symmetry about N 2 are the sine or the j sine terms and are subtracted coherently. This procedure accounts for all phasor pairs in any signal regardless of its even and odd components and the results agree with Fig. 2-2. Plots f and g need only the positive frequencies. Note also that the frequency plots are not functions of time like x n so each observation at frequency k is a steady-state measurement and we can .

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