- 14th February 2005, 15:51 #1

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## Zeros in FIR filter

Hello all,

On the diagram, there are three types of Zeros:

1) Just on the unit circle ? what is it

2) inside the unit circle ?= attenuation band

3) outside the unit circle ?= bypass band

Am I right? And what are they for? And are they all the denser the better?

And for example, I have a FIR low-pass filter (bandwidth is 1000Hz), how can I get the bandwidth from the Zero/Pole Diagram?

Thanks,

davy

- 14th February 2005, 15:51

- 14th February 2005, 16:07 #2

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## Re: Zeros in FIR filter

zero on the unit circle means your system (filter) will cancel out any signal with that frequency completly . because the transfer function of filter at that frequency is zero.

the zeros outside the unit circle are non minimum phase zeros and inside the unit circle are minimum phase zeros. the difference between outside and inside is in the phase rather than magnitude (if we use a linear gain for compensation).

if you have pole-zero map to calculate magnitude at any point you should multiply the magnitude of vectors from that point to all zeros and divide it by the magnitude of vectors from that point to all poles. for the phase you should add the phase of zero's vector and subtract the phase of pole's vectors.

- 14th February 2005, 16:07

- 14th February 2005, 16:49 #3

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## Re: Zeros in FIR filter

Approximate bandwidth = angular distance between the zeros.

The system takes lesser time to transport energy than the maximum phase and this makes minimum phase systems desirable.

brmadhukar

- 14th February 2005, 16:49

- 14th February 2005, 16:52 #4
## Re: Zeros in FIR filter

You may find these links useful for some digital filter information.

http://ccrma.stanford.edu/~jos/filters/

http://www.eeglossary.com/filters.htm

- 15th February 2005, 10:14 #5

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## Re: Zeros in FIR filter

Poles on the unit circle---the systme will be marginally stable e.g. resonator.An impulse given to the system will result into a continuously oscillating system.

pole inside the unit cirle will result into a stable system whereas pole outside the circle will result into an unstable system.By the way FIR filters only have poles only on origin.

zeros on the unit circle e.g. comb filter the frequency will be attenuated at that frequency.zeros inside and outside will depend on the placement of poles also and effect the frequency response of the filter.

More the number of zeros greater will be the order and more computations, but closer to the ideal frequency response.