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

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

ISBN-10: 0137549202

ISBN-13: 9780137549207

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 indications and structures. Written via admired, DSP pioneers, it offers thorough remedy of the basic theorems and houses of discrete-time linear platforms, filtering, sampling, and discrete-time Fourier research. through targeting the overall and common strategies in discrete-time sign processing, it continues to be important and correct to the recent demanding situations bobbing up within the box -without proscribing itself to express applied sciences with really brief existence spans.

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This is the options guide for the second one version. comprises a number of the difficulties from the 3rd variations.

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

Sample text

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]. So and g[n] = z[n] • y"[-n) form a transform pair. (b) 00 L (z[n] •11"[-nj) e-jwn --co 00 00 = L L z[k)y"[k- n)e-i"" a=-cob-cc forn=O: 1 [ . i2e eacll sequence to be a pulse in the frequency domain: X(ei"') -+-------L---L---L------~~ w " _, Substituting into Eq. 77-1): 00 2: --= = :(n]y"(n] 2_ (' X(ei"')Y"(e'"')dw 271" = 2_ 2.. H 2 5 6">] 2 1 = 60 2.

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]. So and g[n] = z[n] • y"[-n) form a transform pair. (b) 00 L (z[n] •11"[-nj) e-jwn --co 00 00 = L L z[k)y"[k- n)e-i"" a=-cob-cc forn=O: 1 [ .

N,w) L = Aan+Nu[n + N]Aan-Nu[n- N]e-;wn n=-oo L 00 = A2 a2ne-jvln nEN 00 L = A2 (a•e-iw)n n=N = A2 (a•e-iw)N 1- a2e-Jw 0 2Ne-iwN = A•-"--':-~ 1- c2e-iw. (c) X(e-i<•+(w/2))) = L :r(n]e-j(v+w/2)n. L 2Jf J" -1f X(ei(•+(w/2H)X*(ei<•-(w/ 2 ll)ei2 •N dv ' then·. s = = = f" L -1 00 27r -· n=-oo .. ;<•-n+2N) dv -tr :r(n]:r*(k]e-;-';+» 2sin(r(k- n + 2N)) k - n + 2N 00 = " = L = L . o:(n]e-'<•+w/2)n ( [ .... J z n]:r* n- 2N)e-' ' 00 :r(n + N):r*(n- N)e-iwn +s(N,w). w/2HjeJ2•N dv. 80. , E{(w[n]- m,) 2 } = E{ w'[n]} - m!

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


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