Homework_5

Homework_5 - 1 EE113 Homework 5 Problem 6.7 Evaluate the...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 EE113 Homework 5 Problem 6.7 Evaluate the convolution sum n−1 1 3 u(−n + 2) ⋆ · u(n − 2) using both the analytical and graphical methods. Compare your results. Problem 6.9 Evaluate n−1 1 2 1 3 · u(n) ⋆ n · u(n − 2) − u(n + 1) using the distributivity property of the convolution sum. Problem 6.23 Consider two possibly complex-valued sequences x(n) and h(n). Their cross-correlation is the sequence rxh (n) whose samples are defined as follows: ∞ rxh (n) = x(k )h∗ (k − n) k=−∞ (a) Verify that rxh (n) = x(n) ⋆ h (−n). ∗ (b) Use the graphical method to evaluate the correlation of the two sequences: x(n) = {−2, 1, −1, 2} and h(n) = {0, 1, 2} Problem 6.31 A causal LTI system is described by the difference equation y (n) = 1 y (n − 1) + x(n − 1) 4 Find its impulse response sequence. Find also the response to the input sequence shown in Fig. 6.18 using the convolution sum method. Problem 7.9 Determine the solution of each of the following homogeneous equations with initial conditions: (a) y (n) + 9y (n − 2) = 0, y (0) = 0, y (−1)=1. (b) y (n) + 9y (n − 2) = 0, y (0) = 0, y (−1)=j. September 28, 2011 DRAFT 2 Problem 7.11 Find the impulse-response sequences of the following causal LTI systems: (a) y (n) + y (n − 1) − 5y (n − 2) = x(n). (b) y (n) = −4y (n − 2) + x(n − 1). (c) y (n) − 4y (n − 2) = 2x(n). Problem 7.19 Consider the relaxed and causal system 5 1 y (n) + y (n − 1) − y (n − 2) = x(n − 2) 6 6 (a) Is the system BIBO stable? (b) Find its impulse-response sequence. (c) Find its response to x(n) = ( 1 )n u(n − 2). 2 Problem 7.31 Find the solution y (n) of the so-called Fibonacci difference equation y (n) − y (n − 1) − y (n − 2) = 0 with y (−1) = 0 and y (0) = 1. September 28, 2011 DRAFT ...
View Full Document

This note was uploaded on 01/24/2012 for the course EE 113 taught by Professor Walker during the Fall '08 term at UCLA.

Page1 / 2

Homework_5 - 1 EE113 Homework 5 Problem 6.7 Evaluate the...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online