By Paolo Prandoni
Taking a unique, much less classical method of the topic, the authors have written this ebook with the conviction that sign processing might be enjoyable. Their therapy is much less interested in the math and extra at the conceptual elements, permitting scholars to consider the topic at the next conceptual point, hence development the rules for extra complex themes and supporting scholars remedy real-world difficulties. The final bankruptcy pulls jointly the person subject matters into an in-depth examine the improvement of an end-to-end conversation approach. Richly illustrated with examples and workouts in each one bankruptcy, the e-book deals a clean method of the educating of sign processing to upper-level undergraduates.
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Extra info for Signal Processing for Communications (Communication and Information Sciences)
Example text
B) If x [n] is finite-support and N is smaller than the size of the support then the copies in the sum do overlap; for each n, the value of y˜ [n] is be the sum of at most a finite number of terms. (c) If x [n] has infinite support, then each value of y˜ [n] is be the sum of an infinite number of terms. Existence of y˜ [n] depends on the properties of x [n]. Prandoni and M. 8 Periodization of a simple finite-support signal (support length L = 19); original signal (top panel) and periodized versions with N = 35 > L, N = 19 = L, N = 15 < L respectively.
While historically justifiable, that approach is no longer tenable today for three fundamental reasons: first, the pervasiveness of digital storage for data (from CDs to DVDs to flash drives) implies that most devices today are designed for discretetime signals to start with; second, the trend in signal processing devices is to move the analog-to-digital and digital-to-analog converters at the very beginning and the very end of the processing chain so that even “classically analog” operations such as modulation and demodulation are now done in discrete-time; third, the availability of numerical packages like Matlab provides a testbed for signal processing experiments (both academically and just for fun) which is far more accessible and widespread than an electronics lab (not to mention affordable).
In fact, the proper generalization of N to an infinite number of dimensions is in the form of a particular vector space called Hilbert space; the structure of this kind of vector space imposes a set of constraints on its elements so that divergence problems, such as the one we just mentioned, no longer bother us. When we embed infinite sequences into a Hilbert space, these constraints translate to the condition that the corresponding signals have finite energy – which is a mild and reasonable requirement.