xal.tools.dsp

Class LtiDigitalFilter

java.lang.Object

xal.tools.dsp.AbstractDigitalFilter

xal.tools.dsp.LtiDigitalFilter

Direct Known Subclasses:

DigitalDifferentiator, DigitalIntegrator

public class LtiDigitalFilter
extends AbstractDigitalFilter

Implements the fundamental behavior and characteristics of a Linear, Time-Invariant (LTI) digital filter of finite order with real coefficients. Child classes can implement methods for determining the filter coefficients for desired bandwidth and other transfer characteristics (i.e., Butterworth, Chebychev, etc.). Once the filter coefficients are determined this class contains most of the common behavior of a general digital filter.

The transfer characteristics for an N^th order digital filter are given by the following:

b₀y_n + b₁y_n-1 + … + b_Ny_n-N = a₀x_n + a₁x_n-1 + … + a_Nx_n-N

where n is the current ("time") index, the {x_n} are the inputs to the filter at time n, the {a_k} are the input coefficients for delay k, the {y_n} are the filter outputs at time n, and the {b_k} are the output coefficients for delay k. The equation can be rearranged to explicitly demonstrate the current output y_n in terms of the past N inputs and outputs

y_n = ( a₀x_n + a₁x_n-1 + … + a_Nx_n-N - b₁y_n-1 - … - b_Ny_n-N )/b₀

Note that the coefficient b₀ is essentially just an attenuation/amplification factor. (In fact, a zeroth-order digital filter is just that.) The current class initializes itself with the value b₀ = 1.0. This case is the only nonzero initial value for the input and output coefficients and is done simply to avoid a pathological filter.

Taking the Z transform of the above equations yields the transfer function H(z) where z is the transform variable (whose domain is the unit circle in the complex plane). The transfer function has the general form

	a0 + a1z-1 + … + aNz-N
H(z) =	———————————
	b0 + b1z-1 + … + bNz-N

Clearly then the filter is linear. Note that for the Discrete Fourier Transform (DFT) and the frequencies ν = 1,…,Ν-1 the transform variable is equal to z_ν = e^i2πν/Ν.

See Also:

gov.sns.tools.dsp.AbstractDigitalFilter

Constructor Summary

Constructors

Constructor and Description
LtiDigitalFilter(int intOrder) Create a new filter object for processing discrete signal trains.

Method Summary

Modifier and Type	Method and Description
double	getInputCoefficient(int iDelay) Return the input coefficient at the given delay index.
double	getInputCoefficient(int iTime, int iDelay) Return the indicated input coefficient determined by the call to setInputCoefficient(int, double).
double	getOutputCoefficient(int iDelay) Return the output coefficient at the given delay index.
double	getOutputCoefficient(int iTime, int iDelay) Return the indicated output coefficient determined by the call to setOutputCoefficient(int, double).
void	setInputCoefficient(int iDelay, double dblVal) Sets an input signal coefficient.
void	setInputCoefficients(double[] arrCoeffs) Sets all the input signal coefficients.
void	setOutputCoefficient(int iDelay, double dblVal) Sets an output signal coefficient.
void	setOutputCoefficients(double[] arrCoeffs) Sets all the output signal coefficients.
java.lang.String	toString() Write out the configuration and state of this filter as a string for inspection.
JSci.maths.Complex	transferFunction(JSci.maths.Complex z) Compute and return the value of the discrete transfer function for the given value of z, the Z-transform variable.

Methods inherited from class xal.tools.dsp.AbstractDigitalFilter

getCoefficientCount, getOrder, getTimeIndex, reset, response, response

Methods inherited from class java.lang.Object

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

Constructor Detail

LtiDigitalFilter

public LtiDigitalFilter(int intOrder)

Create a new filter object for processing discrete signal trains.

Parameters:

intOrder - filter order

Method Detail

getInputCoefficient

public double getInputCoefficient(int iTime,
                                  int iDelay)

Return the indicated input coefficient determined by the call to setInputCoefficient(int, double). Note that this value is time-independent, that is, the argument iTime is ignored.

Specified by:

getInputCoefficient in class AbstractDigitalFilter

Parameters:

iTime - current time index (ignored)

iDelay - delay index of the filter coefficient

Returns:

the input coefficient for the given delay index

See Also:

gov.sns.tools.dsp.LtiDigitalFilter#setInputCoefficient(int, double), gov.sns.tools.dsp.AbstractDigitalFilter#getInputCoefficient(int, int)

getOutputCoefficient

public double getOutputCoefficient(int iTime,
                                   int iDelay)

Return the indicated output coefficient determined by the call to setOutputCoefficient(int, double). Note that this value is time-independent, that is, the argument iTime is ignored.

Specified by:

getOutputCoefficient in class AbstractDigitalFilter

Parameters:

iTime - current time index (ignored)

iDelay - delay index of the filter coefficient

Returns:

the output coefficient for the given delay index

See Also:

gov.sns.tools.dsp.LtiDigitalFilter#setOutputCoefficient(int, double), gov.sns.tools.dsp.AbstractDigitalFilter#getOutputCoefficient(int, int)

setInputCoefficient

public void setInputCoefficient(int iDelay,
                                double dblVal)
                         throws java.lang.IllegalArgumentException

Sets an input signal coefficient.

Parameters:

iDelay - delay index of the coefficient

dblVal - coefficient value

Throws:

java.lang.IllegalArgumentException - index outside interval [0,Order]

setInputCoefficients

public void setInputCoefficients(double[] arrCoeffs)
                          throws java.lang.IllegalArgumentException

Sets all the input signal coefficients. The elements of the argument array should be indexed by delay; that is, the 0^th element corresponds to no delay, the 1^st element to the unit delay, etc.

Parameters:

arrCoeffs - array of input coefficients

Throws:

java.lang.IllegalArgumentException - argument has wrong array size

setOutputCoefficient

public void setOutputCoefficient(int iDelay,
                                 double dblVal)
                          throws java.lang.IndexOutOfBoundsException

Sets an output signal coefficient. Note that since an index of zero represents the current output it is an inverse scaling value.

Parameters:

iDelay - delay index of the coefficient

dblVal - coefficient value

Throws:

java.lang.IndexOutOfBoundsException - index outside interval [0,Order]

setOutputCoefficients

public void setOutputCoefficients(double[] arrCoeffs)
                           throws java.lang.IllegalArgumentException

Sets all the output signal coefficients. The elements of the argument array should be indexed by delay; that is, the 0^th element corresponds to no delay, the 1^st element to the unit delay, etc.

Parameters:

arrCoeffs - array of output coefficients

Throws:

java.lang.IllegalArgumentException - argument has wrong array size

getInputCoefficient

public double getInputCoefficient(int iDelay)
                           throws java.lang.IndexOutOfBoundsException

Return the input coefficient at the given delay index.

Parameters:

iDelay - delay index of coefficient

Returns:

input coefficient at delay given delay index.

Throws:

java.lang.IndexOutOfBoundsException - delay index larger than filter order

See Also:

setInputCoefficient(int, double)

getOutputCoefficient

public double getOutputCoefficient(int iDelay)
                            throws java.lang.IndexOutOfBoundsException

Return the output coefficient at the given delay index.

Parameters:

iDelay - delay index of coefficient

Returns:

output coefficient at delay given delay index.

Throws:

java.lang.IndexOutOfBoundsException - delay index larger than filter order

See Also:

setOutputCoefficient(int, double)

transferFunction

public JSci.maths.Complex transferFunction(JSci.maths.Complex z)

Compute and return the value of the discrete transfer function for the given value of z, the Z-transform variable.

Parameters:

z - Z-transform variable (lies on the unit circle)

Returns:

value of this filter's transfer function at z

toString

public java.lang.String toString()

Write out the configuration and state of this filter as a string for inspection.

Overrides:

toString in class AbstractDigitalFilter

Returns:

configuration and state of this filter in text form

See Also:

Object.toString()