SP 2005 CH 3 DT Signals

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

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Unformatted text preview: EE 3120 Chapter 3 Time Domain Analysis of Discrete-Time Signals 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 x n x Mn = [ ] d x n This may be a way to compress the digital signal, requires less data storage. 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 x n L n L L x n = = 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 EE 3120 Linear Systems Analysis [ ] 1 f n = is a two sided sequence, the discrete counterpart of the constant function [ ] 1 n = Impulse sequence Kronecker delta sequence n n = if i is a fixed integer ; [ ] n i- [ ] n shifts to n i = [ ] 1 n i- = n i = n i n n Chapter 3 Elementary discrete-time signals and their manipulation EE 3120 Linear Systems Analysis [ ] [ ] [ ] i f n f i n i =- =- Impulse Sequence Could be samples of an analog signal [ 2] 4 f- = [ 1] f- = [0] 2 f = [1] f = [2] 5 f = - [3] 1 f = [ ] 4 [ 2] 2 [ ] 5 [ 2]...
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SP 2005 CH 3 DT Signals - EE 3120 Chapter 3 Time Domain...

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