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# Lecture 5: Ideal and Practical Filters

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Schedule :: Fourier Series Formulas :: Nonperiodic Functions :: Useful Functions :: Simple Functions :: Fourier Transforms :: Properties :: System Analysis :: Signal Distortion :: Filters :: Parseval's Formulas

The ideal low-pass filter allows all signals below some cutoff of rad/sec to pass through undistorted, while completely cutting off all other frequencies. This is sometimes said to be the ideal "brick wall'' filter. If is strictly bandlimited to rad/sec, then the output is simply delayed:

The ideal filter has

The impulse response of the filter is then

Plot . Observe that it is noncausal , and hence physically nonrealizable. We cannot build an ideal lowpass filter, or an ideal bandpass either, for that matter. We could get pretty close, but creating a system with a large , so that most of the sinc function would be included. One approach to determine the effect of this truncation of the impulse response

is to use the properties of F.T.

The effect is to smear the response by the convolution.

Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 31). Lecture 5: Ideal and Practical Filters. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/5_9node9.html. This work is licensed under a Creative Commons License