Package xal.tools.dsp

Class DigitalFunctionUtility

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

Utility class for performing common operations on and for digital functions.

Within this package digital functions are taken to be objects of type double[]). Because sub-typing from double[] is illegal in Java, it is necessary to create a utility class to handle the common operations on digital functions.

Author:
Christopher K. Allen

  • Method Summary

    Modifier and Type
    Method
    Description
    static double[]
    abs(double[] arrFunc)
    Compute and return the (functional) absolute value of the given function.
    static double[]
    add(double[] arrFunc1, double[] arrFunc2)
    Compute and return the function sum of the given functions.
    static int
    argGreaterThan(double dblVal, double[] arrFunc)
    Return the index where the function first exceeds the given value.
    static int
    argMaximum(double[] arrFunc)
    Return the index at with the function maximum occurs.
    static int
    argMinimum(double[] arrFunc)
    Return the index at with the function minimum occurs.
    static String
    buildValueTable(double[]... argFuncs)
    Build a table of function values for comparison.
    static double
    compError(double[] arrFunc, double[] arrTarg)
    Computes and returns the l2 distance between the given vector functions normalized by the norm ||arrTarg||2.
    static double[]
    generateCosine(int szArray, int intFreq, double dblPhase)
    Generate a discrete cosine function of the given size, given discrete frequency, and given phase offset.
    static double[]
    generateSine(int szArray, int intFreq, double dblPhase)
    Generate a discrete sine function of the given size, given discrete frequency, and given phase offset.
    static double
    integral(double[] arrFunc)
    Compute and return the integral (i.e., the summation of all the elements) of the given function.
    static double
    maximumValue(double[] arrFunc)
    Return the maximum value of the function.
    static double
    minimumValue(double[] arrFunc)
    Return the minimum value of the function.
    static void
    scaleFunction(double dblVal, double[] arrFunc)
    Scale the function by the given value.
    static double[]
    square(double[] arrFunc)
    Compute and return the (functional) square of the given function.
    static double[]
    subtract(double[] arrFunc1, double[] arrFunc2)
    Compute and return the function difference of the given functions.
    static void
    subtractFrom(double[] arrFunc, double dblVal)
    In place subtraction of the given value from the function.
    static double[]
    totalVariation(double[] arrFunc)
    Compute and return the total variation of the given function.

    Methods inherited from class java.lang.Object

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

  • Method Details

    • compError

      public static double compError(double[] arrFunc, double[] arrTarg)
      Computes and returns the l2 distance between the given vector functions normalized by the norm ||arrTarg||2.
      Parameters:
      arrFunc - vector function
      arrTarg - target vector function
      Returns:
      ||arrFunc1 - arrFunc2||2/||arrTarg||2

    • buildValueTable

      public static String buildValueTable(double[]... argFuncs) throws ArrayIndexOutOfBoundsException
      Build a table of function values for comparison. Each table row consists of the function index, then corresponding function values, all separated by tab characters ("\t").
      Parameters:
      argFuncs - discrete functions to be tabulated
      Returns:
      formatted string of tabulated values
      Throws:
      ArrayIndexOutOfBoundsException - arguments are not all the same size

    • generateSine

      public static double[] generateSine(int szArray, int intFreq, double dblPhase)
      Generate a discrete sine function of the given size, given discrete frequency, and given phase offset. Note that the largest frequency that returns a meaning function is szArray/2. Any frequencies larger than that are unrecognizable due to insufficient resolution.
      Parameters:
      dblPhase - phase offset (in radians)
      szArray - array size of the returned function
      intFreq - frequency component of the returned function
      Returns:
      sin(2πf + φ)

    • generateCosine

      public static double[] generateCosine(int szArray, int intFreq, double dblPhase)
      Generate a discrete cosine function of the given size, given discrete frequency, and given phase offset. Note that the largest frequency that returns a meaning function is szArray/2. Any frequencies larger than that are unrecognizable due to insufficient resolution.
      Parameters:
      dblPhase - phase offset (in radians)
      szArray - array size of the returned function
      intFreq - frequency component of the returned function
      Returns:
      cos(2πf + φ)

    • scaleFunction

      public static void scaleFunction(double dblVal, double[] arrFunc)
      Scale the function by the given value.
      Parameters:
      dblVal - scale factor

    • add

      public static double[] add(double[] arrFunc1, double[] arrFunc2) throws IllegalArgumentException
      Compute and return the function sum of the given functions.
      Parameters:
      arrFunc1 - addend
      arrFunc2 - adder
      Returns:
      sum of arguments
      Throws:
      IllegalArgumentException - arguments are of different sizes

    • subtract

      public static double[] subtract(double[] arrFunc1, double[] arrFunc2) throws IllegalArgumentException
      Compute and return the function difference of the given functions.
      Parameters:
      arrFunc1 - subtractend
      arrFunc2 - subtractor
      Returns:
      difference of arguments
      Throws:
      IllegalArgumentException - argument are of different sizes

    • subtractFrom

      public static void subtractFrom(double[] arrFunc, double dblVal)
      In place subtraction of the given value from the function.
      Parameters:
      arrFunc - subtractend
      dblVal - subtractor
      Throws:
      IllegalArgumentException - argument are of different sizes

    • maximumValue

      public static double maximumValue(double[] arrFunc)
      Return the maximum value of the function.
      Parameters:
      arrFunc - digital function
      Returns:
      function maximum

    • minimumValue

      public static double minimumValue(double[] arrFunc)
      Return the minimum value of the function.
      Parameters:
      arrFunc - digital function
      Returns:
      function minimum

    • argMaximum

      public static int argMaximum(double[] arrFunc)
      Return the index at with the function maximum occurs.
      Parameters:
      arrFunc - digital function
      Returns:
      index of maximum value

    • argMinimum

      public static int argMinimum(double[] arrFunc)
      Return the index at with the function minimum occurs.
      Parameters:
      arrFunc - digital function
      Returns:
      index of minimum value

    • argGreaterThan

      public static int argGreaterThan(double dblVal, double[] arrFunc)
      Return the index where the function first exceeds the given value.
      Parameters:
      dblVal - inspection value
      arrFunc - digital function
      Returns:
      index where function first exceeds value or arrFunc.length if none

    • abs

      public static double[] abs(double[] arrFunc)
      Compute and return the (functional) absolute value of the given function.
      Parameters:
      arrFunc - function to process
      Returns:
      functional absolute value of the argument

    • square

      public static double[] square(double[] arrFunc)
      Compute and return the (functional) square of the given function.
      Parameters:
      arrFunc - function to square
      Returns:
      functional square of the argument

    • totalVariation

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

         TV[f](t) ≡ ∫t|df(τ)/dt|dτ
      Parameters:
      arrFunc - target function
      Returns:
      total variation of given function

    • integral

      public static double integral(double[] arrFunc)
      Compute and return the integral (i.e., the summation of all the elements) of the given function.
      Parameters:
      arrFunc - function to integrate
      Returns:
      the sum of all array elements