 The World's Most Interesting FIR Filter Equation: Why FIR Filters Can Be Linear Phase

This article discusses a little-known filter characteristic that enables real- and complex-coefficient tapped-delay line FIR filters to exhibit linear phase behavior. That is, this article answers the question: What is the constraint on real- and complex-valued FIR filters that guarantee linear phase behavior in the frequency domain? wenkaixu
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4 years ago
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Sorry, you need javascript enabled to post any comments. synaps
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Hello
4 years ago
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Sorry, you need javascript enabled to post any comments. josef_sepp
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My students will be amazed by this possibility !!!
4 years ago
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Sorry, you need javascript enabled to post any comments. DirkDoesDSP
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Hi Rick,

Interesting paper. One thing missing. Equation (2) is not the only equation for a real-coefficient FIR filter with linear phase. As you point out, equation (4) with beta=0 gives equation (2) for real coefficients. (2) gives even-symmetric coefficients. However equation (4) with beta = pi/2 can give an equation for linear phase odd-symmetric real-coefficient filters.
4 years ago
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Sorry, you need javascript enabled to post any comments. DirkDoesDSP
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Another attempt at getting a post to show up.

Hi Rick,

Interesting paper.

Equation (2) is a symmetric real coefficient linear filter. Another real coefficient linear filter is an antisymmetric real coefficient filter, which doesn't satify equation (2). This falls out from equation (4) if you use beta=pi/2.

Dirk
4 years ago
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Sorry, you need javascript enabled to post any comments. DirkDoesDSP
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Please substitute "linear-phase filter" for "linear filter" in my comment.
4 years ago
0 kakash
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Sorry, you need javascript enabled to post any comments. kakash
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