Discrete-Time Signal Processing: Solutions Manual (2nd by Alan V. Oppenheim, Ronald W. Schafer, John R. Buck

By Alan V. Oppenheim, Ronald W. Schafer, John R. Buck

For senior/graduate-level classes in Discrete-Time sign Processing. THE definitive, authoritative textual content on DSP - excellent for people with an introductory-level wisdom of signs and structures. Written by means of famous, DSP pioneers, it presents thorough therapy of the elemental theorems and homes of discrete-time linear platforms, filtering, sampling, and discrete-time Fourier research. by way of targeting the final and common strategies in discrete-time sign processing, it continues to be very important and proper to the recent demanding situations bobbing up within the box -without restricting itself to precise applied sciences with particularly brief existence spans.

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This is the suggestions handbook for the second one version. comprises the various difficulties from the 3rd versions.

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Extra info for Discrete-Time Signal Processing: Solutions Manual (2nd Edition)

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Then: w,[n] = O[n + 2] 1112[n] = 6[n- 2]. 69. (a) The overall system is not guarameed to he an LTI system. A simple counterexample is: = y,[n] z[n] 112[n] = z[n] y[n] = y,[n]1f2[n] = z 2 (n] which is not a. linear system, therefore the system is not LTI. (ei"') Y(ei"') = H 1 (ei"')X(ei"') = H2(ei"')X(ei"') = Y,(ei"') • Y2(ei"'). Using the above relationships, we get: Y(ei"') = { 11DSpeCified 2. 70. 6.. ~ lwl ~ ... = V(z(n]) = z(n]- z(n- 1]. r2[n- 1) = a(:r1 (n)- :r1 [n- 1)) + b(:r2[n)- :r2[n- 1)) = V(cu1[n)) + V(az2[n)).

OCl n:&[nje·jwn b:r,[n]e·iwn 2. 75. The output of an LTI system is obtained by the convolution sum, 00 y[n] = L 1=-oo z[kjh[n - kj. Taking the Fourier transform, Y(eiw) = = 1: 1: 00 = (1: ~f;oo z[k)h[n- k)) e-i~ 00 Cf;oo·h[n- kje-iwn) z[kje-i"> (_too h{n- k}e-iw(n->)) z[kj 00 Hence, 2. 76. _, (' d8 (' dw X (ei 1 )W(e'(w-B>)e->w• (21r) '-· L. 2... f' d8 X(ei1 )w[n]ei'• 21f )_ .. z[n]w[n] 2. 77. (a) The Fourier transform of y•[-n] is Y"(e'"), and X(ei")Y(e'") forms a transform pair with z[n] • y[n].

T... b $lwl $ .. t... 3.. 3.. 58. Note that X(dw) is real, and Y(eiw) is given by: Y(eiw) = { -jX(~) +jX(e'w) w[n] = z[n] + jy[n], therefore: O

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