113_1_midterm_09_A

# 113_1_midterm_09_A - X z = ln(1 αz-1 | z |> | α |(b...

This preview shows page 1. Sign up to view the full content.

EE113: Digital Signal Processing Prof. Mihaela van der Schaar Midterm Exam (Version A) Spring 2009 Name: Student ID: 1. A causal linear time-invariant system is initially relaxed and described by the diﬀerence equation y ( n ) - 5 y ( n - 1) + 6 y ( n - 2) = 2 x ( n - 1) (a) Determine the modes of the system. (b) Determine the impulse response of the system. (c) Determine the step response of the system using convolution. (d) Determine the step response of the system without using convolution. 2. (a) Consider the following complex series expansion of the natural logarithm for | t | < 1, ln(1 + t ) = X n =1 ( - 1) n +1 n t n , | t | < 1 Use the result to determine the sequence x ( n ) whose z-transform is given by
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: X ( z ) = ln(1 + αz-1 ) , | z | > | α | (b) Find the inverse z-transform of X ( z ) = z-1 1-( 1 2 ) 50 z-50 , | z | > 1 2 3. Consider the system illustrated in Figure 1. The output of an LTI system with an impulse response h ( n ) = ( 1 4 ) n u ( n +10) is multiplied by a unit step function u ( n ) to yield the output of the overall system. Answer each of the following questions, and brieﬂy justify your answers: Figure 1: The overall system (a) Is the overall system linear? (b) Is the overall system time-invariant? (c) Is the overall system causal? (d) Is the overall system BIBO stable? 1...
View Full Document

## This note was uploaded on 06/01/2010 for the course EE EE113 taught by Professor Mihaela during the Spring '10 term at UCLA.

Ask a homework question - tutors are online