pcshw1 - . ±ind the average power in the signal x(t), 1 T...

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

View Full Document Right Arrow Icon
THE STATE UNIVERSITY OF NEW JERSEY RUTGERS College of Engineering Department of Electrical and Computer Engineering 332:322 Principles of Communications Systems Spring 2003 Problem Set 1 1. Derive the convolution intergal from Frst principles (as outlined in class) given by y ( t ) = R -∞ x ( τ ) h ( t - τ ) , where h ( t ) is the impulse response of a LTI system, x ( t ) the input and y ( t ) the output. 2. ±or each of the systems described by the input output relationships below, determine which of the following properties apply to the system: Memoryless(M), causal(C), linear(L), time- invariant(TI), stable(S). Justify your answers. (a) y ( t ) = sin( t + 1) x ( t ) (b) y [ n ] = x [2 - n ] + 1 3. Consider a continuous time system with the following input x ( t ) and impulse response h ( t ) , x ( t ) = 1 0 < t < 2 - 1 2 < t < 4 0 otherwise and h ( t ) = exp ( - 2 t ) u ( t ) (a) Compute the output of the system y ( t ) = x ( t ) * h ( t ) (b) Is the system stable? Is the system causal? 4. A signal x ( t ) is periodic with period T = 10 - 3 . The ±ourier series coeffecients for x(t) are given by a k = ( 1 2 j ) k k > 0 0 k = 0 ( 1 - 2 j ) - k otherwise
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . ±ind the average power in the signal x(t), 1 T R T | x ( t ) | 2 . Hint:Use Parseval’s relationship! 5. Let x ( t ) = exp (-at ) u ( t ) ,where u(t) is the unit step function. ±ind the ±ourier transform of the following signals. (a) x ( t ) (b) y ( t ) = x ( t + 5) (c) z ( t ) = x ( t ) sin(2 π 40 t ) 1 6. Evaluate the Fourier transform of the damped sinusoidal wave g ( t ) = exp(-t ) sin(2 πf c t ) u ( t ) , where u ( t ) is the unit step function. 7. Show that the overall system function H ( s ) for the feedback system in FIGURE 7 is given by H ( s ) = F ( s ) 1-F ( s ) G ( s ) . + F(s) G(s) 8. A signal x ( t ) of ±nite energy is applied to a sqaure-law device whose output is de±ned by y ( t ) = x 2 ( t ) . The spectrum of x ( t ) is limited to the frequency interval-W ≤ f ≤ W . Hence show that the spectrum of y ( t ) is limited to-2 W ≤ f ≤ 2 W . 2...
View Full Document

This note was uploaded on 04/03/2008 for the course ECE ECE332 taught by Professor Rose during the Spring '08 term at Rutgers.

Page1 / 2

pcshw1 - . ±ind the average power in the signal x(t), 1 T...

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