# Phase response of a digital filter

Discussion in 'General Electronics Chat' started by curiousmind666, Aug 28, 2010.

1. ### curiousmind666 Thread Starter New Member

Aug 28, 2010
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Can anyone please tell me why the phase response value of a digital filter always lies between the values (-)pi and (+) pi ?
Also, I would like to know what is it meant by "limit cycle oscillations" in the context of "finite word-length effect" in DSP.

2. ### Papabravo Expert

Feb 24, 2006
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In the same way that higher frequencies are aliased into the baseband based on the relationship between the frequency and the sample rate, phase responses outside the range are indistinguishable from those inside the range.

A limit cycle occurs in a continuous non-linear system when there is no stable state. It is graphically demonstrated in a phase-plane plot. In the context of DSP, the finite word length implies that if a stable state requires an input or output to assume a value "in-between" two digital words, then the system will oscillate or hunt around the stable state without ever being able to reach it.

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3. ### curiousmind666 Thread Starter New Member

Aug 28, 2010
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Thank you Papabravo, for your interest in my post. But, can u please give me an analytical explanation to the above two problems, or just suggest me a good reference? Thanks in advance

4. ### Papabravo Expert

Feb 24, 2006
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I don't know what you mean by an analytical explanation.

http://www.dspguide.com/

5. ### curiousmind666 Thread Starter New Member

Aug 28, 2010
3
0
Thanks again, Parabavo. By the way, by analytical explanation I just meant a mathematical way of explanation. Anyway, I am going to check the book you referred to me. Thanks a lot, friend.

6. ### Papabravo Expert

Feb 24, 2006
11,789
2,497
For a periodic function:

f(x) = f(x+2π)

this also implies that

f(x+ε) = f(x+ε+2π)

and that says that points on a periodic function separated by 2π are indistinguishable. The same argument can be made for the interval [-π, π] as for the interval [0, 2π]