MIT2_017JF09_p19

# MIT2_017JF09_p19 - 19 ALIASING 19 57 Aliasing Consider...

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19 ALIASING 57 19 Aliasing Consider sampling the sinusoidal process: x ( t )=0 . 9sin(2 πf o t ). 1. When we sample the signal at frequency f s (Hz) or ω s (rad/s), the Nyquist rate of f N = f s / 2 is the maximum frequency the sampling can detect. See the ﬁgure for some examples; undersampling of 1.7 indicates that the process frequency exceeds the Nyquist rate by a factor of 1.7. What is the required sampling rate to detect f o = 20kHz? Extrapolating from the ﬁgure, is this sampling rate good enough to observe the process with reasonable ﬁdelity? The required rate is twice the process rate, or 40kHz. This rate does not give good phase or amplitude information of the 20kHz signal; about 200-400kHz would be much better, giving ﬁve to ten points per cycle. 2. Suppose that you can only sample at f s =5 . 5 kHz . What is the time step? For the time interval t = [0 0.002], plot x ( t ) sampled at a high enough rate that you can clearly see the sine wave, and overlay it with the signal

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## This note was uploaded on 11/29/2011 for the course CIVIL 1.00 taught by Professor Georgekocur during the Spring '05 term at MIT.

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MIT2_017JF09_p19 - 19 ALIASING 19 57 Aliasing Consider...

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