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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/...
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- Spring '05
- Signal Processing, sampling rate, Johnson/Cornell/ECE2200/Spring 09/SECTION