Hilbert Transformer

Hi all,=20

I am a new member. Could you help me to answer the question that is: the fu=
nction "remezord" in Matlab uses what formula to estimate the order of filt=
ers and why the function can not be used to estimate the order of Hilber tr=
ansformer and FIR differentiator?

Thank you so much, 

On Thursday, January 3, 2013 3:11:20 PM UTC-5, Anh Tuan Phan wrote:
> Hi all,=20
>=20
>=20
>=20
> I am a new member. Could you help me to answer the question that is: the =
function "remezord" in Matlab uses what formula to estimate the order of fi=
lters and why the function can not be used to estimate the order of Hilber =
transformer and FIR differentiator?
>=20
>=20
>=20
> Thank you so much,

The order of an FIR filter is related to the order of the polynomial used t=
o approximate the desired frequency response. In the case of FIR filters th=
e polynomial is trigonometric. Common FIR filters use cosines as their basi=
s functions whereas hilbert transformers and differentiators use sines as t=
he basis functions in the trigonometric polynomial approximation. So as you=
 can guess the estimatating functions are different.=20

IHTH,
Clay 

Thank you very much. Could you tell me more details about the formula that the function "remezord" of matlab uses to estimate the order of filters?

On 1/4/13 2:30 PM, Anh Tuan Phan wrote:
> Thank you very much. Could you tell me more details about the formula that the function "remezord" of matlab uses to estimate the order of filters?

even though the MATLAB reference cites Rabiner and Gold, i thought the 
function was the same as this from O&S:

FIR length  L = (-10 log_10( d_p d_s ) - 13)/(2.324( w_s - w_p )) + 1

2 d_p is the linear ripple in the passband
2 d_s is the linear ripple in the stopband
w_s is the normalized angular frequency of the stopband edge
w_p is the normalized angular frequency of the passband edge



-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

On Jan 4, 2:30=A0pm, Anh Tuan Phan <phananhtuan...@gmail.com> wrote:
> Thank you very much. Could you tell me more details about the formula tha=
t the function "remezord" of matlab uses to estimate the order of filters?

I'm going by memory. I believe the formula used in remezord orginally
appeared in an IEEE paper. The formula is just a heuristic
approximation. Given a filter order they measured the achievable
transition width, attenuation and passband ripple. They then found an
equation that gives the approximate answers.

If you search through the literature you'll find several equations
that give the approximate filter length.

You should also note that the filter length estimate does not work
well when the frequencies are near zero or Fs/2, where Fs is your
sampling frequency.

Cheers,
Dave