SP 2005 CH 3 DT Signals

SP 2005 CH 3 DT Signals - EE 3120 Chapter 3 Time Domain...

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EE 3120 Chapter 3 Time Domain Analysis of Discrete-Time Signals
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Time-Domain Analysis of Discrete-Time Systems Two different types of sampling rate alterations: Decimation and Interpolation x [ n ] Original sequence x [ n ] is decimated (sampled) every M = 3 samples creating 1 2 3 4 5 1 2 3 4 5 Decimation : Sampling the samples [] [ ] d xn x M n = [] d x n This may be a way to compress the digital signal, requires less data storage.
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Interpolation : Filling in the gaps, a way to decompress data The original signal x [ n ] can be reproduced in 2 steps: Step 1: Samples of are expanded to their original location (we must know the original decimation rate. [ ] 0, , 2 ,. .. [] 0 otherwise e xnL n L L xn =±± = Step 2: An interpolation algorithm can be executed to “fill in the gaps” Obviously this algorithm is poor, but others can be more accurate. Or maybe decimating by 3 is too severe. That is up to the engineer to decide. For our case L = 3 d x n d x n
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EE 3120 Linear Systems Analysis [] 1 fn = is a two sided sequence, the discrete counterpart of the constant function 0 [] 1 n ∂= Impulse sequence Æ Kronecker delta sequence 0 0 n n = if i is a fixed integer ; ni ∂− n shifts to = 0 1 ∂−= = n n Chapter 3 Elementary discrete-time signals and their manipulation
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EE 3120 Linear Systems Analysis [] [][ ] i fn fi n i =−∞ =∂ Impulse Sequence Æ Could be samples of an analog signal [2 ] 4 f −= [1 ] 0 f [0] 2 f = [1] 0 f = [2] 5 f = − [3] 1 f = [] 4[ 2 ] 2[] 5[ 2 ] [ 3 ] n n n n + +∂ + −∞ to n is fixed, i ranges from e.g. n = 10
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SP 2005 CH 3 DT Signals - EE 3120 Chapter 3 Time Domain...

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