By Proakis, Manolakis.
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Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book Digital Signal Processing, Fourth Edition, by John G. Proakis and Dimitris G. Manolakis. ISBN 0-13-187374-1. ∞ = n=−∞ [s(n) + γ1 s(n − k1 ) + γ2 s(n − k2 )] ∗ [s(n − l) + γ1 s(n − l − k1 ) + γ2 s(n − l − k2 )] = (1 + γ12 + γ22 )γss (l) + γ1 [γss (l + k1 ) + γss (l − k1 )] +γ2 [γss (l + k2 ) + γss (l − k2 )] +γ1 γ2 [γss (l + k1 − k2 ) + γss (l + k2 − k1 )] (b) γxx (l) has peaks at l = 0, ±k1 , ±k2 and ±(k1 + k2 ).
All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book Digital Signal Processing, Fourth Edition, by John G. Proakis and Dimitris G. Manolakis. ISBN 0-13-187374-1. 47 (a) x(n) = y(n) = y(0) = y(1) = y(2) = y(n) = 1, 0, 0, . . ↑ 1 y(n − 1) + x(n) + x(n − 1) 2 x(0) = 1, 3 1 y(0) + x(1) + x(0) = 2 2 1 3 y(1) + x(2) + x(1) = .
2 4 8 16 32 (b) y(n) = 21 y(n − 1) + x(n) + x(n − 1) (c) As in part(a), we obtain 5 13 29 61 1, , , , , . . , Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. For the exclusive use of adopters of the book Digital Signal Processing, Fourth Edition, by John G. Proakis and Dimitris G. Manolakis. ISBN 0-13-187374-1.