hw8soln

# hw8soln - ME 365 Homework Set 8 Out Due Problem No 1 An ADC...

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ME 365 Homework Set 8 Out October 20, 2011 Due October 27, 2011 Problem No. 1 An ADC board is used to sample an audio signal (20 Hz~20 kHz) continuously with a sampling frequency of 25 kHz. A low pass anti-aliasing filter with a cut-off frequency at 12.5 kHz is used before the ADC to avoid aliasing. (a) Specify the frequency band of the signal that can pass through the low pass anti-aliasing filter. (b) If the audio signal contains a 60 Hz noise from the power line. Design a notch filter to reduce the noise effect. Use the frequency response function we gave in class and make sure the two cutoff frequencies are chosen to be at 40 Hz and 80 Hz. Draw the Bode diagram of your designed filter using MATLAB and specify the stop band. Explain how to implement such a filter using a low pass and a high pass filter. (c) Design a band pass filter using the simplest form we gave in class (assume no loading). At 100 and 10000 Hz, the magnitude of the signal drops by 3dB. Draw the Bode diagram of your designed filter using MATLAB and specify the pass band. Solution: (a) 20 Hz~12500 Hz (b) τ LP =1/(2π *40Hz)=0.004 sec τ HP =1/(2π *80Hz)=0.002 sec The frequency response function of the notch filter is: 1 006 . 0 ) ( 10 8 1 004 . 0 ) ( 10 8 1 002 . 0 002 . 0 1 004 . 0 1 ) ( 2 6 2 6 j j j j j j j j G BP

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ME 365 Homework Set 8 Out October 20, 2011 Due October 27, 2011 The stop band is from 251.32 rad/s(40Hz) to 502.65 rad/s (80Hz). On the
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## This note was uploaded on 12/26/2011 for the course ME 365 taught by Professor Merkle during the Fall '07 term at Purdue.

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hw8soln - ME 365 Homework Set 8 Out Due Problem No 1 An ADC...

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