Download e-book for kindle: Schaum's Outline of Digital Signal Processing by Monson Hayes

By Monson Hayes

ISBN-10: 0070273898

ISBN-13: 9780070273894

Reflecting the swift advances in microelectronics and machine expertise, this strong research advisor is perfect as a complement to any path in this topic or for self sufficient research by way of electric engineering majors and training engineers. Readers will find out how electronic sign processing recommendations come into play in a variety of fields and should delight in this thorough, but concise insurance. the various illustrative issues of targeted strategies and the supplementary self-tests velocity comprehension and reduction remembering.

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13 A linear system is one that is both homogeneous and additive. (a) Give an example of a system that is homogeneous but not additive. (b) Give an example of a system that is additive but not homogeneous. There are many different systems that are either homogeneous or additive but not both. One example of a system that is homogeneous but not additive is the following: ~ ( n= ) x(n - I)x(n) x(n + I) Specifically, note that if x(n) is multiplied by a complex constant c, the output will be ~ ( n= ) cx(n-l)cx(n) cx(n + I) =c x(n-I)x(n) x(n + 1) which is c times the response to x(n).

By definition, x ( n ) = x , ( n ) x,(n). Therefore, + Note that x,(n)x,(n) is the product of an even sequence and an odd sequence and, therefore, the product is odd. Because the sum for all n of an odd sequence is equal to zero, Thus, the power in x ( n ) is m m which says that the power in x ( n ) is equal to the sum of the powers in its even and odd parts. , evaluate the sum) This is a direct application of the geometric series With the substitution of -n for n we have Therefore, it follows from the geometric series that SIGNALS AND SYSTEMS [CHAP.

27 Derive a closed-form expression for the convolution of x ( n ) and h ( n ) where I N-6 x(n) = (6) u(n) h ( n ) = ( f ) " u ( n - 3) Because both sequences are infinite In length. it is easier to evaluate the convolution sum directly: Note that because x ( n ) = 0 for n < 0 and h ( n ) = 0 for n < 3 , y ( n ) will be equal to zero for n < 3. Substituting x ( n ) and h ( n ) into the convolution sum, we have Due to the step u ( k ) , the lower limit on the sum may be changed to k = 0, and because u ( n - k - 3) is zero for k > n - 3 , the upper limit may be changed to k = n - 3 .

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Schaum's Outline of Digital Signal Processing by Monson Hayes

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