Template Classes for Digital Signal Analysis

This article briefly describes a collection of template classes that can be used in digital signal analysis.

This collection consists of four classes:

1. Template class WFastHT—implements algorithm of Fast Haara's Transformation (by Anatoly Beletsky). The template has two type parameters:
   
   • T_in—type of input values (input signal)
   • T_out—type of output values (spectrum)
   Input signal has any type (int, double, complex<T>). Spectrum is double or complex.
2. Template class WIFastHT—implements algorithm of Inverse Fast Haara's Transformation.
3. Template class WFastFT—implements algorithm of Fast Fourier Transformation (Tim Kientzle "A Programmer's Guide To Sound" Copyright © 1998 Tim Kientzle).
4. Template class WFastWT—implements algorithm of Fast Walsh's Transformation in different bases:
   
   • HADOMARD—Walsh's-Hadomar's basis
   • PELEY—Peley's basis
   • WALSH—"classical" basis
   • COOLEY—Cooley's basis (discovered by Anatoly Beletsky in 1999)
   It uses a new type of operation: Grey's "right-handed" inverse coding. The complete group of operations that forms the so-called "Grey's algebra" consists of five operations:
1. Binary inversion
2. Grey's "left-handed" coding operation
3. Grey's "left-handed" inverse coding operation
4. Grey's "right-handed" coding operation
5. Grey's "right-handed" inverse coding operation

For details, contact me.

Here is an example of the code's usage:

#include <iostream>
using std::cout;
using std::cin;

#include "transform.h"

const int Val = 8;
const int fr = 7;

int main()
{

  try {
    WFastHT< double, double > haaras( Val );
    WIFastHT< double, double > ihaaras( Val );
    double data[Val] = { 1,2,3,4,4,3,2,1 };
    double *pD, *pS;

    haaras.setData( data );
    haaras.doTransform();
    pD = haaras.getSpectrum();

    cout << "Input signal: \n";
    for( int i = 0; i < Val; i++ ) {
      cout << data[ i ] << "\n";
    }

    cout << "\nSpectrum: \n";
    for( i = 0; i < Val; i++ ) {
      cout << pD[ i ] << "\n";
    }

    ihaaras.setData( pD );
    ihaaras.doTransform();
    pS = ihaaras.getSpectrum();

    cout << "\nInverse haara's transformation: \n";
    for( i = 0; i < Val; i++ ) {
      cout << pS[ i ] << "\n";
    }
  }
  catch( TransError::badNValue ) {
    cout << "Bad N!\n";
  }
  catch( TransError::noData ) {
    cout << "No data available!\n";
  }
  catch( TransError::noSuchBasis ) {

  }
  return 1;
}

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