# Minimum Phase Filter from Attenuation Data 1.0

OS : Windows / Linux / Mac OS / BSD / Solaris

Script Licensing : Freeware

Created : Sep 8, 2007

Downloads : 2

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## MINPHASEFIT Minimum Phase Transfer Function Fit from ...

MINPHASEFIT Minimum Phase Transfer function Fit from Attenuation Data.

[N, D, K]=MINPHASEFIT(Wk, Ak, NP) finds the filter transfer function K*N(s)/D(s) of minimum order that fits the attenuation data in Ak and Wk.

Ak is a vector of attenuations in dB and Wk is a vector of radian frequencies associated with Ak. That is, the n-th values in Ak and Wk, Ak(n) and Wk(n) specify an attenuation and associated frequency to be met by the filter. The algorithm assumes that the input data is a piecewise linear description of the attenuation specifications to be met. Wk(1)>0 is required and it is assumed that the attenuation between 0 and Wk(1) has zero slope. It is also assumed that the attenuation slope is zero beyond Wk(end). For best results, frequencies should be scaled into the range 0. 1 to 10, with dominant transition band close to 1 rad/s.

NP is the number of poles (and zeros) to add to the minimum number determined by the algorithm. If not given, NP=2 is chosen. The optimum value for NP cannot be predetermined. Simple attenuation characteristics may work well with NP=0. Attenuation characteristics having sharper transitions or a greater number of passbands often require a greater NP. Increasing NP does not always lead to greater fit accuracy.

MINPHASEFIT(Wk, Ak, NP, OPTIONS) includes the structure variable OPTIONS which sets options for the function FMINSEARCH that is used to find the optimum transfer function. See the help text for FMINSEARCH for information on setting options.

[N, D, K]=MINPHASEFIT(Wk, Ak, NP) finds the filter transfer function K*N(s)/D(s) of minimum order that fits the attenuation data in Ak and Wk.

Ak is a vector of attenuations in dB and Wk is a vector of radian frequencies associated with Ak. That is, the n-th values in Ak and Wk, Ak(n) and Wk(n) specify an attenuation and associated frequency to be met by the filter. The algorithm assumes that the input data is a piecewise linear description of the attenuation specifications to be met. Wk(1)>0 is required and it is assumed that the attenuation between 0 and Wk(1) has zero slope. It is also assumed that the attenuation slope is zero beyond Wk(end). For best results, frequencies should be scaled into the range 0. 1 to 10, with dominant transition band close to 1 rad/s.

NP is the number of poles (and zeros) to add to the minimum number determined by the algorithm. If not given, NP=2 is chosen. The optimum value for NP cannot be predetermined. Simple attenuation characteristics may work well with NP=0. Attenuation characteristics having sharper transitions or a greater number of passbands often require a greater NP. Increasing NP does not always lead to greater fit accuracy.

MINPHASEFIT(Wk, Ak, NP, OPTIONS) includes the structure variable OPTIONS which sets options for the function FMINSEARCH that is used to find the optimum transfer function. See the help text for FMINSEARCH for information on setting options.

**• MATLAB Release: R14SP1**

**Demands:****Minimum Phase Filter from Attenuation Data 1.0 scripting tags:**greater, filter, number, minimum phase filter, frequencies, function, attenuation data, signal processing.

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