HT - -4-3-2-1 1 2 3 4-1.5-1-0.5 0.5 1 1.5 Perfect...

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ECE 301, A Half-Time Delay Demonstration Input: Given an band-limited input x ( t ) with bandwidth W M = 2 . 5 π . Sample it with sampling period T = 2 / 5 ( ω s = 5 π ). Let x [ n ] denote the sampled discrete-time (digital) array. Goal: Design a discrete-time processing h [ n ] satisfying the following. Let y [ n ] denote the output of the discrete-time system: y [ n ] = x [ n ] * h [ n ]. Use perfect band-limited reconstruction to generate a continuous signal y ( t ). We desire that y ( t ) being the half-time delay x ( t ). That is, T = 2 5 and y ( t ) = x ( t - 1 5 ). (Note that all we can handle/manipuate is the samples x [ n ], not the original signal x ( t ).) Example: x ( t ) = sin(2 πt ) Original signal -4 -3 -2 -1 0 1 2 3 4 -1.5 -1 -0.5 0 0.5 1 1.5
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What you really have is the sampled values:
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Unformatted text preview: -4-3-2-1 1 2 3 4-1.5-1-0.5 0.5 1 1.5 Perfect reconstruction without any processing:-4-3-2-1 1 2 3 4-1.5-1-0.5 0.5 1 1.5 Introducing half-time delay by discrete time signal processing: (see lecture notes) h [ n ] = (-1) n +1 ( n-1 2 ) . (1)-4-3-2-1 1 2 3 4-1.5-1-0.5 0.5 1 1.5 Comparison to the original samples:-4-3-2-1 1 2 3 4-1.5-1-0.5 0.5 1 1.5 Half-time delay + perfect reconstruction:-4-3-2-1 1 2 3 4-1.5-1-0.5 0.5 1 1.5 Comparison to the original reconstructed curve:-4-3-2-1 1 2 3 4-1.5-1-0.5 0.5 1 1.5...
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HT - -4-3-2-1 1 2 3 4-1.5-1-0.5 0.5 1 1.5 Perfect...

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