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Report on this topic Design filtering Content included... Abstract Introduction Principles Code design Result and discussion Conclusion Reference

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Advance Math

Report on this topic Designfiltering

Content included...

Abstract

Introduction

Principles

Code design

Result anddiscussion

Conclusion

Reference

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3.8 Ratings (411 Votes)
Abstract Filter design is the process of designing a signal processing filter that satisfies a set of requirements some of which are contradictory The purpose is to find a realization of the filter that meets each of the requirements to a sufficient degree to make it useful The filter design process can be described as an optimization problem where each requirement contributes to an error function which should be minimized Certain parts of the design process can be automated but normally an experienced electrical engineer is needed to get a good result Introduction Typical requirements which are considered in the design process are The filter should have a specific frequency response The filter should have a specific phase shift or group delay The filter should have a specific impulse response The filter should be causal The filter should be stable The filter should be localized pulse or step inputs should result in finite time outputs The computational complexity of the filter should be low The filter should be implemented in particular hardware or software An allpass filter passes through all frequencies unchanged but changes the phase of the signal Filters of this type can be used to equalize the group delay of recursive filters This filter is also used in phaser effects A Hilbert transformer is a specific allpass filter that passes sinusoids with unchanged amplitude but shifts each sinusoid phase by 90 A fractional delay filter is an allpass that has a specified and constant group or phase delay for all frequencies The impulse response Edit There is a direct correspondence between the filters frequency function and its impulse response the former is the Fourier transform of the latter That means that any requirement on the frequency function is a requirement on the impulse response and vice versa However in certain applications it may be the filters impulse response that is explicit and the design process then aims at producing as close an approximation as possible to the requested impulse response given all other requirements In some cases it may even be relevant to consider a frequency function    See Answer
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