TAILIEUCHUNG - DISCRETE-SIGNAL ANALYSIS AND DESIGN- P16

DISCRETE-SIGNAL ANALYSIS AND DESIGN- P16: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. | 4 Smoothing and Windowing In this chapter we consider ways to improve discrete sequences including the reduction of data contamination and the improvement of certain time and frequency properties. Smoothing and windowing are useful tools for signal waveform processing in both domains. Simplifications with limited goals will be a desirable approach. The References in this chapter can be consulted for more advanced studies. Our suggested approaches are quite useful where great sophistication is not required for the processing of many commonly occurring discrete-signal waveforms. SMOOTHING Consider Fig. 4-1a and the rectangular discrete sequence W i for i from 0 to 63 with amplitude and drawn in continuous form for visual clarity. The simple Mathcad Program shown creates this sequence. Observe that the rectangle is delayed at the beginning and terminated early pedestal would be a good name . This sequence is a particular kind of simple window that is useful in many situations because of the zero-value segments Discrete-Signal Analysis and Design By William E. Sabin Copyright 2008 John Wiley Sons Inc. 61 62 DISCRETE-SIGNAL ANALYSIS AND DESIGN Y1 i .25 W i - 1 .5 W i .25 W i 1 Y2 i .25 Y1 i - 1 .5 Y1 i .25 Y1 i 1 Y3 i .25 Y2 i - 1 .5 Y2 i .25 Y2 i 1 Y8 i .25 Y7 i - 1 .5 Y7 i .25 Y7 i 1 i 0 1. 63 W i 0 1 if i 8 0 if i 56 3 smoothings 8 smoothings a M no smoothing Figure 4-1 Smoothing operation on a discrete signal waveform a without added random noise b with added random noise. at each end that are known as guardbands that greatly reduce spillover aliasing Chapter 3 into adjacent regions. Figure 4-1 then shows how at each value of i the three-point smoothing sequence is applied to the data points W i 1 W i and W i 1 respectively to get Y i i . We then repeat the operation using the Y i i values to get the Y2 i values then the Y2 i values to get the Y3 i values and so on. We pause at Y3 to view the intermediate results and see that the edges of the .

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