biz.source_code.dsp.filter

Class BesselFilterDesign

java.lang.Object

biz.source_code.dsp.filter.BesselFilterDesign

public class BesselFilterDesign
extends Object

Bessel filter design routines.

Method Summary

Modifier and Type	Method and Description
static double	computeGain(double[] polyCoeffs, double w) Computes the normalized gain of a Bessel filter at a given frequency.
static Complex[]	computePoles(int n) Returns the frequency normalized s-plane poles for a Bessel filter.
static double[]	computePolynomialCoefficients(int n) Returns the polynomial coefficients for the Bessel polynomial of the given order.
static double	findFrequencyForGain(double[] polyCoeffs, double gain) This method uses appoximation to find the frequency for a given gain.
static double	findFrequencyScalingFactor(double[] polyCoeffs) Returns the frequency normalization scaling factor for a Bessel filter.
static Complex	transferFunction(double[] polyCoeffs, Complex s) Evaluates the transfer function of a Bessel filter.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

computePolynomialCoefficients

public static double[] computePolynomialCoefficients(int n)

Returns the polynomial coefficients for the Bessel polynomial of the given order.

Reference: Wikipedia.

Parameters:

n - The order of the polynomial.

Returns:

An array a[] with the coefficients, ordered in descending powers, for: a[0] * x^n + a[1] * x^(n-1) + ... a[n-1] * x + a[n]

transferFunction

public static Complex transferFunction(double[] polyCoeffs,
                                       Complex s)

Evaluates the transfer function of a Bessel filter. The gain is normalized to 1 for DC.

Parameters:

polyCoeffs - Coefficients of the reverse Bessel polynomial.

s - Complex frequency.

Returns:

A complex number that corresponds to the gain and phase of the filter output.

computeGain

public static double computeGain(double[] polyCoeffs,
                                 double w)

Computes the normalized gain of a Bessel filter at a given frequency.

Parameters:

polyCoeffs - Coefficients of the reverse Bessel polynomial.

w - Relative frequency.

Returns:

The normalized gain.

findFrequencyForGain

public static double findFrequencyForGain(double[] polyCoeffs,
                                          double gain)

This method uses appoximation to find the frequency for a given gain. It is used to find the 3dB cutoff frequency, which is then used as the scaling factor for the frequency normalization of the filter.

If anyone knows a better way than approximation to find the 3dB cuttoff frequency, please let me know (chdh@inventec.ch).

Parameters:

polyCoeffs - Coefficients of the reverse Bessel polynomial.

gain - A normalized gain.

Returns:

The relative frequency.

findFrequencyScalingFactor

public static double findFrequencyScalingFactor(double[] polyCoeffs)

Returns the frequency normalization scaling factor for a Bessel filter. This factor is used to normalize the filter coefficients so that the gain at the relative frequency 1 is -3dB. (To be exact, we use 1/sqrt(2) instead of -3dB).

Parameters:

polyCoeffs - Coefficients of the reverse Bessel polynomial.

Returns:

The frequency normalization scaling factor.

computePoles

public static Complex[] computePoles(int n)

Returns the frequency normalized s-plane poles for a Bessel filter.

Parameters:

n - The filter order.

Returns:

The complex poles of the filter,