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# Why Can Discrete-Time FIR Digital Filters be a Linear Phase?

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Why can discrete-time FIR digital filters be made exactly linear phase, whereas IIR digital filters cannot?

I only require a sentence describing why - not any derivations of formulas etc!!!.

I know what makes a filter exactly linear phase (impulse response must be symmetrical), but i don't know why IIR filters cannot be made linear? Is it to do with their feedback and past outputs???

Please just a statement not any matematical derivations!

https://brainmass.com/engineering/electrical-engineering/discrete-time-fir-digital-filters-linear-phase-18025

## SOLUTION This solution is FREE courtesy of BrainMass!

Linear Phase" refers to the condition where the phase response of the filter is a linear (straight-line) function of frequency (excluding phase wraps at +/- 180 degrees). This results in the delay through the filter being the same at all frequencies. Therefore, the filter does not cause "phase distortion" or "delay distortion". The lack of phase/delay distortion can be a critical advantage of FIR filters over IIR and analog filters in certain systems, for example, in digital data modems

A FIR filter has linear phase if its impulse response satisfies either one of the following two symmetry conditions:

h[n] = h [N-1-n] , 0<=n<=N-1

or

h[n] = - h [N-1-n] , 0<=n<=N-1

The FIR filter is called symmetric if it satisfies the former condition and antisymmetric in the latter.

There is no real way to get linear phase IIR responses in real-time because of the feedback, as you have mentioned.

However there are lot of techniques that can be used to achieve close-linear phase in IIRs

with truncated_ IIR filters (these happen to have pole-zero cancellation so their impulse response is actually finite in length but they're implemented with an IIR filter and a delay line) you can get phase linear response if by passing the signal through the forward truncated IIR and then backwards or time-reversed (in segments, using overlap-add) through an identical truncated IIR.

Hope this helped.

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