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ELEC212 Chapter 4 Sampling of Continuous-Time Signals part 2

# ELEC212 Chapter 4 Sampling of Continuous-Time Signals part...

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1 The Hong Kong University of Science and Technology Department of Electronic and Computer Engineering Prof. Matthew R. McKay ELEC 212 Chapter 4: Sampling of Continuous-Time Signals (Part II) 2 09-10 Fall ELEC 212 Sampling of CT Signals (Part II) Changing Sampling Rate using Discrete-Time Processing ± Discrete-time signal x [ n ] is obtained by extracting the information from a continuous-time signal x c ( t ) every T seconds: ± Often necessary to change the sampling rate of a discrete-time signal, such that ± Approach 1: Reconstruct x c ( t ) from x [ n ] , then resample x c ( t ) with period T' to obtain x' [ n ] ± Problems in practice due to non-ideal analog reconstruction filters, ADC and DAC ± Approach 2: Changing the sampling rate using only discrete-time operations 3 09-10 Fall ELEC 212 Sampling of CT Signals (Part II) Sampling Rate Reduction by an Integer Factor π 2 −∞ = = r c j T k T j X T e X ω 2 1 ) ( ] [ nM x M copies of the periodic DTFT , frequency-scaled by M and shifted by integer multiples of . (original sequence) (down-sampled sequence) ) ( j e X −∞ = = r c j T k T j X T e X 2 1 ) ( −∞ = = r c j d MT r MT j X MT e X 2 1 ) ( 4 09-10 Fall ELEC 212 Sampling of CT Signals (Part II) Sampling Rate Reduction by an Integer Factor (Time Normalization) Exact reconstruction possible in both cases! Note: Sampling here is 2x the Nyquist rate.

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5 09-10 Fall ELEC 212 Sampling of CT Signals (Part II) Sampling Rate Reduction by an Integer Factor Exact reconstruction not possible due to aliasing! Question: How do we avoid aliasing due to downsampling … ? 6 09-10 Fall ELEC 212 Sampling of CT Signals (Part II) Sampling Rate Reduction by an Integer Factor ± Aliasing due to downsampling can be avoided with prefiltering (ie. reduce the BW before downsampling) Note the LPF cutoff frequency No Aliasing!
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ELEC212 Chapter 4 Sampling of Continuous-Time Signals part...

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