EE 230 Lecture 39 Spring 2010

# EE 230 Lecture 39 Spring 2010 - EE 230 Lecture 39 Data...

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EE 230 Lecture 39 Data Converters Time and Amplitude Quantization

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Time Quantization How often must a signal be sampled so that enough information about the original signal is available in the samples so that the samples can be used to represent the original signal ? The Sampling Theorem An exact reconstruction of a continuous-time signal from its samples can be obtained if the signal is band limited and the sampling frequency is greater than twice the signal bandwidth. This is a key theorem and many existing communication standards and communication systems depend heavily on this property This theorem often provides a lower bound for clock frequency of ADCs The theorem says nothing about how to reconstruct the signal Review from Last Time:
Time Quantization The Sampling Theorem An exact reconstruction of a continuous-time signal from its samples can be obtained if the signal is band limited and the sampling frequency is greater than twice the signal bandwidth. Alternatively An exact reconstruction of a continuous-time signal from its samples can be obtained if the signal is band limited and the sampling frequency exceeds the Nyquist Rate. Review from Last Time:

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Time Quantization The Sampling Theorem An exact reconstruction of a continuous-time signal from its samples can be obtained if the signal is band limited and the sampling frequency exceeds the Nyquist Rate. Practically, signals are often sampled at frequency that is just a little bit higher than the Nyquist rate though there are some applications where the sampling is done at a much higher frequency (maybe with minimal benefit) The theorem as stated only indicates sufficient information is available in the samples if the criteria are met to reconstruct the original continuous-time signal, nothing is said about how this can be practically accomplished. Review from Last Time:
Time Quantization What happens if the requirements for the sampling theorem are not met? Aliasing will occur if signals are sampled with a clock of frequency less than the Nyquist Rate for the signal. If aliasing occurs, what is the aliasing frequency ? This calculation is not difficult but a general expression will not be derived at this time. If can be shown that if f is a frequency above the Nyquist rate, then the aliased frequency will be given by the expression () ( ) 1 k k ALIASED SAMP SAMP SAMP -1+ -1 kk - 1 k f= - 1 f - 1 + f f o r f < f < f 24 2 2 k + ⎡⎤ + ⎢⎥ ⎣⎦ where k is an integer greater than 1 and where f SAMP is the sampling frequency Review from Last Time:

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Time Quantization What happens if the requirements for the sampling theorem are not met?
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## This note was uploaded on 02/01/2012 for the course EE 230 taught by Professor Mina during the Fall '08 term at Iowa State.

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EE 230 Lecture 39 Spring 2010 - EE 230 Lecture 39 Data...

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