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Unformatted text preview: Brief Review of Sampling This material is assumed from ECE101. Sampling is used, for example, in A/D Conversion, although here we ignore the effects of quantization . Discretize a continuous time signal for CDs, computers, etc. Define the continuous time impulse train as: p ( t ) = X k =- ( t- kT ) x ( t ) is the continuous time signal we wish to sample Let y ( t ) = x s ( t ) = x ( t ) p ( t ) be the sampled signal. Then, x s ( t ) = y ( t ) = X k =- x ( t ) ( t- kT ) = X k =- x ( kT ) ( t- kT ) X s ( ) = Y ( ) = 1 2 X ( ) * P ( ) by the multiplication property of the continuous time Fourier Transform. X ( ) is the Fourier Transform of x ( t ). Now find the Fourier Transform of p ( t ), the infinite impulse train: 1 P ( ) = F [ X k =- ( t- kT )] Use the Fourier Transform of periodic signals since the impulse train is a periodic signal (with = s ) F [ X k a k e jk s t ] = X k 2 a k ( - k s ) Find a k for the periodic impulse train:...
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This note was uploaded on 09/10/2010 for the course ECE 107 taught by Professor Fullterton during the Spring '07 term at UCSD.
- Spring '07