By Alan V. Oppenheim
For senior/graduate-level classes in Discrete-Time sign Processing.
Discrete-Time sign Processing, 3rd Edition is the definitive, authoritative textual content on DSP – perfect for people with introductory-level wisdom of indications and structures. Written by way of well-known DSP pioneers, it offers thorough therapy of the elemental theorems and houses of discrete-time linear structures, filtering, sampling, and discrete-time Fourier research. by way of concentrating on the final and common ideas in discrete-time sign processing, it is still important and correct to the hot demanding situations bobbing up within the field.
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Additional info for Discrete-Time Signal Processing (3rd Edition) (Prentice-Hall Signal Processing Series)
In t h e remaining parts of this figure we have depicted five time-shifted, scaled unit impulse sequences, where the scaling on each impulse equals the value of x[n] a t the particular time instant at which the unit sample is located. For example, ... I,,, -4-3-2-1 0 1 2 3 4 ... 3) < equals x[n] for -2 2 n 2. More generally, by including ;~dtlitionalshifted, scaled impulses, we can write that For a n y value of n only one of the terms on thc right-hand side of eq. 4) is nonzero, and the scaling on that term is precisely x[n].
For this system the difference between two successive values of the output is precisely the last input value. 39(c). Examples of noninvertible systems are corresponding outputs must also be equal up to this same time. The motion of an automobile is causal since it does not anticipate future actions of the driver. Similarly, the systems described by eqs. 63) YO) = x(t 1) are not. Note also that all memoryless systems are causal. Although causal systems are of great importance, they do not by any means constitute the only systems that are of practical significance.
Chap. -%l ? : ka ,\ I . 13. 1" this problem we explore several of the properties of even and odd sinnals. I 7 (a) Show that if x[n] is an odd signal, then [-- )' (b) f Show that if x,[n] is an odd signal and x2[n] is an even signal, then xl[n]x2[n] is an odd signal. + (d) Although parts (a)-(c) have been stated in terms of discrete-time signals, the analogous properties are also valid in continuous time. (t) are, respectively, the even and odd parts of x(t). 14. 14(a) be the even part of a signal x[n].