# presec3_answers - Johnson/Cornell/ECE2200/Spring 09 SECTION...

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Johnson/Cornell/ECE2200/Spring 09/ SECTION 3 1 1. Let x ( t ) = 7sin(11 πt ) . In each of the following parts, the discrete- time signal x [ n ] is obtained by sampling x ( t ) at a rate f s , and the resultant x [ n ] can be written as x [ n ] = A cos( ω o n + φ ) For each part below, determine the values A,φ,ω o . In addition, state whether or not the signal has been over-sampled or under- sampled. Solution (a) Sampling frequency is f s = 10 samples per second. A = 7, φ =- . 5 π and ω o = 1 . 1 π Now since ω o > π , the signal is under-sampled (b) Sampling frequency is f s = 5 samples per second A = 7, φ =- . 5 π and ω o = 2 . 2 π Since ω o > π , the signal is under-sampled . (c) Sampling frequency is f s = 15 samples per second A = 7, φ =- . 5 π and ω o = 11 π 15 Since ω o < π , the signal is over-sampled . 2. Suppose that a discrete time signal x [ n ] is given by the formula x [ n ] = 2 . 2cos(0 . 3 πn- π 3 ) and that it was obtained by sampling a continuous time signal x ( t ) = A cos(2 πf o t + φ ) at a sampling rate of f s = 6000 samples/sec. Determine three different continuous- time signals that could have produced x [ n ] . All these continuous time signals must have a frequency of less than 8kHz. Solution The possible discrete time frequencies are = 0 . 3 π, 1 . 7 π, 2 . 3 π . Thus the signal can be written as x ( t ) = A cos(2 π 900 t- π/ 3) or x ( t ) = A cos(2 π 5100 t + π/ 3) or x ( t ) = A cos(2 π 6900 t- π/ 3) . Johnson/Cornell/ECE2200/Spring 09/...
View Full Document

{[ snackBarMessage ]}