Package xal.tools.dsp

Class DigitalSignalProcessor

java.lang.Object
xal.tools.dsp.DigitalSignalProcessor
public class DigitalSignalProcessor extends Object

Convenience class for packaging common digital processing operations. This class relies heavily upon most of the other classes on the xal.tools.dsp package.

Rather than making this a utility class, it has been designed to be instantiated. In this manner it can be tuned by the users. Although this capability is not available now, this class may evolve.

Author:
Christopher K. Allen

  • Constructor Summary

    Constructors
    Constructor
    Description
    DigitalSignalProcessor(int szSignal)
    Create a new DigitalSignalProcessor object for processing signals of length szSignal.

  • Method Summary

    Modifier and Type
    Method
    Description
    double[]
    autoCorrelation(double[] arrSignal)
    Compute and return the auto-correlation function for the given discrete signal.
    double[]
    average(double[] arrSignal)
    Compute and return the (running) average of the given signal.
    double[]
    crossCorrelation(double[] arrStat, double[] arrShft)
    Compute and return the cross-correlation function for the given signals.
    double[]
    differentiate(double[] arrSignal)
    Compute and return the differential of the given signal.
    int
    getSignalSize()
    Return the signal size that this instance can process.
    double[]
    integrate(double[] arrSignal)
    Compute and return the integral of the given signal (zero constant of integration).
    double[]
    powerSpectrum(double[] arrSignal)
    Compute and return the power spectrum of the given signal.
    double[]
    signalIndicator(double[] arrSignal)
    Compute and return the signal presence indicator function for the given signal.
    double[]
    totalVariation(double[] arrSignal)
    Compute and return the total variation of the given signal.

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • DigitalSignalProcessor

      public DigitalSignalProcessor(int szSignal)
      Create a new DigitalSignalProcessor object for processing signals of length szSignal.
      Parameters:
      szSignal - size of signal to be processed

  • Method Details

    • getSignalSize

      public int getSignalSize()
      Return the signal size that this instance can process.
      Returns:
      digital signal size expected for processing

    • differentiate

      public double[] differentiate(double[] arrSignal) throws IllegalArgumentException
      Compute and return the differential of the given signal.
      Parameters:
      arrSignal - signal to differentiate
      Returns:
      differentiated signal
      Throws:
      IllegalArgumentException - this should not occur (serious internal error)

    • integrate

      public double[] integrate(double[] arrSignal) throws IllegalArgumentException
      Compute and return the integral of the given signal (zero constant of integration).
      Parameters:
      arrSignal - signal to integrate
      Returns:
      integrated signal
      Throws:
      IllegalArgumentException - this should not occur (serious internal error)

    • average

      public double[] average(double[] arrSignal) throws IllegalArgumentException
      Compute and return the (running) average of the given signal.
      Parameters:
      arrSignal - signal to average
      Returns:
      averaged signal
      Throws:
      IllegalArgumentException - this should not occur (serious internal error)

    • totalVariation

      public double[] totalVariation(double[] arrSignal)
      Compute and return the total variation of the given signal. The total variation TV(f) of a signal f(·) is defined as

         TV[f](t) ≡ ∫t|df(τ)/dt|dτ
      Parameters:
      arrSignal - target signal
      Returns:
      total variation of the argument

    • signalIndicator

      public double[] signalIndicator(double[] arrSignal) throws IllegalArgumentException

      Compute and return the signal presence indicator function for the given signal. The indicator function is computed by subtracting the (running) average from the signal then computing the total variation. In this manner we hope to observe variation over the noise floor.

      The returned function is normalized so that its maximum value is unity. It has the form of a cumulative distribution function so that increasing value is indicative of signal likelihood.

      Parameters:
      arrSignal - target signal
      Returns:
      signal presence indicator function
      Throws:
      IllegalArgumentException - this should not occur (serious internal error)
      See Also:

    • autoCorrelation

      public double[] autoCorrelation(double[] arrSignal) throws IllegalArgumentException

      Compute and return the auto-correlation function for the given discrete signal.

      In the spirit of the Z transform we assume that the function is periodic so that f[n + N] = f[n]. In this manner the auto-correlation Rxx[k] function is also periodic, specifically, Rxx[-k] = Rxx[N - k].

      Assuming periodicity gives us the follow fact: it's value will never fall to zero if the data contains a noise process with non-zero mean. Indeed, by the property of the auto-correlation Rxx[-k] = Rxx[k] and, therefore, Rxx[k] = Rxx[N - k] by periodicity. If the underlying signal has support small enough the minimum value of the auto-correlation (at k = N/2) will depend only upon the noise process. If we assumed the original data non-periodic, this condition would not occur.

      Parameters:
      arrSignal - function to auto-correlate
      Returns:
      (one-sided) auto-correction function
      Throws:
      IllegalArgumentException - this should not occur (serious internal error)

    • crossCorrelation

      public double[] crossCorrelation(double[] arrStat, double[] arrShft) throws IllegalArgumentException

      Compute and return the cross-correlation function for the given signals. Note that the second argument is the signal that is shifted in the calculation.

      In the spirit of the Z transform we assume that each function is periodic so that f[n + N] = f[n]. In this manner the cross-correlation Rxy[k] function is also periodic. More importantly, it's value will never fall to zero if the data contains a noise process with non-zero mean. If the underlying signal has support small enough the minimum value of the cross-correlation will depend only upon the noise process. If we assumed the original function non-periodic, this condition would not occur.

      Parameters:
      arrStat - stationary function
      arrShft - shifted function
      Returns:
      (one-sided) cross-correction function
      Throws:
      IllegalArgumentException - the arguments are of different sizes

    • powerSpectrum

      public double[] powerSpectrum(double[] arrSignal) throws IllegalArgumentException
      Compute and return the power spectrum of the given signal. The spectral components are returned in the usual DFT arrangement. Namely, the first N/2 components are the positive frequency components with zero frequency first in ascending order. The next N/2 components are the negative components with the highest negative frequency (-N/2) first then in descending order. This arrangement is due to the topology of the unit circle in the complex plane.
      Parameters:
      arrSignal - signal to analyze
      Returns:
      frequency spectrum of given signal
      Throws:
      IllegalArgumentException - this should not occur (serious internal error)
      See Also: