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DISCRETE-SIGNAL ANALYSIS AND DESIGN- P12

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DISCRETE-SIGNAL ANALYSIS AND DESIGN- P12: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. | SINE COSINE AND e 41 To get the one-sided spectrum we combine k 1 with k N 1 and so on from 1 k N 2 1 . For k 1 to 5 using the Mathcad X-Y Trace tool we get 0.3173 0.1571 0.1030 0.0754 and 0.0585. The Trace tool is a very useful asset. REFERENCES Seely S. 1956 Radio Electronics McGraw-Hill New York. Also Google Child-Langmuir. Terman F.E. 1943 Radio Engineer s Handbook McGraw-Hill New York. Zwillinger D. ed. 1996 CRC Standard Mathematical Tables and Formulae 30th ed. CRC Press Boca Raton FL. 3 Spectral Leakage and Aliasing SPECTRAL LEAKAGE The topics in the title of this chapter are concerned with major difficulties that are encountered in discrete signal waveform analysis and design. We will discuss how they occur and how we can deal with them. The discussion still involves eternal steady-state discrete signals. Figure 3-1a shows the leaky spectrum of a complex phasor using the DFT Eq. 1-2 at k 7.0 Hz kHz MHz or just 7.0 whose input signal frequency k may be different than 7.0 by the very small fractional offset e shown on the diagram. For e values of 10-15 to 10-6 the spectrum is essentially a pure tone for most practical purposes. The dots in Fig. 3-1a represent the maximum spectrum attenuation at integer values of k for each of the offsets indicated. A signal at 7.0 with the offset indicated produces these outputs at the other exact integer k values. Figure 3-1b repeats the example with k 15.0 and the discrete spectrum Discrete-Signal Analysis and Design By William E. Sabin Copyright 2008 John Wiley Sons Inc. .