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L05_filtering - Filtering in Continuous and Discrete Time...

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1 6.02 Spring 2008 Lecture 5 Filtering in Continuous and Discrete Time, Slide 1 Filtering in Continuous and Discrete Time Lowpass, highpass, bandpass filtering Filter response to cosine wave inputs “Real World” signals <--> MATLAB sequences Filtering based on difference equations Copyright © 2007 by M.H. Perrott & C. G. Sodini All rights reserved. 6.02 Spring 2008 Lecture 5 Filtering in Continuous and Discrete Time, Slide 2 Motivation for Filtering Filtering is used to remove undesired signals outside of the frequency band of interest Enables selection of a specific radio, TV, WLAN, cell phone, cable TV channel Undesired channels are often called interferers
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2 6.02 Spring 2008 Lecture 5 Filtering in Continuous and Discrete Time, Slide 3 Lowpass Filter Only low frequency (i.e. baseband ) portion remains 6.02 Spring 2008 Lecture 5 Filtering in Continuous and Discrete Time, Slide 4 Highpass Filter Only high frequency (i.e. RF ) portion remains
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3 6.02 Spring 2008 Lecture 5 Filtering in Continuous and Discrete Time, Slide 5 A More Formal Treatment of Filters An ideal filter would have a “brickwall” magnitude response and zero phase response Practical filters have a more gradual magnitude rolloff and a non-zero phase response Design of the filter usually focuses on getting a reasonable magnitude rolloff with a specified cutoff frequency f c (i.e., filter bandwidth ) 6.02 Spring 2008 Lecture 5 Filtering in Continuous and Discrete Time, Slide 6 Key Observations of Filter Response Input cosine wave is scaled in amplitude and phase-shifted in time Scale factor set by magnitude of H(f) at f=f o
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