hw3_sol

# hw3_sol - MEEN 364 Fall 2004 Homework Set 3 Due 5:00 PM...

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MEEN 364 Homework Set 3 Fall 2004 September 16, 2004 Homework Set 3– Due September 23, 2004 @ 5:00 PM Note: Clearly label all the plots. Credit will not be given for unlabelled plots. 1. a) i) Signal sampled for 1 second. 0 10 20 30 40 50 60 70 80 90 100 0 50 100 150 200 250 300 350 frequency (Hz) magnitude Original signal sampled at 200 Hz for 1 second It can be seen that there are three frequency components at 10 Hz, 70 Hz and 80 Hz respectively. Note that the magnitude of the 70 Hz component is 3 times that of the 10 Hz and 80 Hz components. ii) Signal sampled for 10 seconds. 0 10 20 30 40 50 60 70 80 90 100 0 500 1000 1500 2000 2500 3000 frequency (Hz) magnitude Original signal sampled at 200 Hz for 10 second 1

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MEEN 364 Homework Set 3 Fall 2004 September 16, 2004 iii) Signal sampled at 200 Hz for 100 seconds. 0 10 20 30 40 50 60 70 80 90 100 0 0.5 1 1.5 2 2.5 3 x 10 4 frequency (Hz) magnitude Original signal sampled at 200 Hz for 100 second The frequency resolution can be defined as [sample/s] [1/s]= [sample] sampling frequency Frequency resolution total sample . Therefore, the more samples we have, the higher frequency resolution we can get. In other words, the length of time (T) for which we are prepared to sample the signal determines the reconstruction from the original signal. In our case, signal sampled at 200 Hz for 100 s has the highest frequency resolution. This phenomenon can be seen that as the number of data points increase, the side lobes in the magnitude plot decrease considerably. b) Signal downsampled by a factor of 2. 0 5 10 15 20 25 30 35 40 45 50 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 frequency (Hz) magnitude Signal downsampled by a factor of 2 2
MEEN 364 Homework Set 3 Fall 2004 September 16, 2004 After downsampling, the sampling frequency becomes 100 Hz and it is less than twice the highest signal frequency (80 Hz). Therefore we got aliasing.

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