VF_spectrum  VD_spectrum  VE_spectrum 

Function  Powerdensity spectrum 

Syntax C/C++  #include <VFstd.h>
float VF_spectrum( fVector Spc, ui specsiz, fVector X, ui xsiz, fVector Win ); 
C++ VecObj  #include <OptiVec.h>
T vector<T>::spectrum( const vector<T>& X, const vector<T>& Win ); 
Pascal/Delphi  uses VFstd;
function VF_spectrum( Spc:fVector; specsiz:UIntSize; X:fVector; xsiz:UIntSize; Win:fVector ): Single; 

CUDA function C/C++  #include <cudaVFstd.h>
int cudaVF_spectrum( float *h_psdfNyq, fVector d_Spc, ui specsiz, fVector d_X, ui xsiz, fVector d_Win );
int cusdVF_spectrum( float *d_psdfNyq, fVector d_Spc, ui specsiz, fVector d_X, ui xsiz, fVector d_Win );
float VFcu_spectrum( fVector h_Spc, ui specsiz, fVector h_X, ui xsiz, fVector h_Win );

CUDA function Pascal/Delphi  uses VFstd;
function cudaVF_spectrum( var h_psdfNyq:Single; d_Spc:fVector; specsiz:UIntSize; d_X:fVector; xsiz:UIntSize; d_Win:fVector ): IntBool;
function cusdVF_spectrum( d_psdfNyq:PSingle; d_Spc:fVector; specsiz:UIntSize; d_X:fVector; xsiz:UIntSize; d_Win:fVector ): IntBool;
function VFcu_spectrum( h_Spc:fVector; specsiz:UIntSize; h_X:fVector; xsiz:UIntSize; h_Win:fVector );


Description  The data set X is analyzed for its power spectral density (PSD), i.e. the mean square amplitude. The result is stored in Spc. xsiz must be at least 2*specsiz, and specsiz has to be an integer power of 2. Internally, X is divided into xsiz*specsiz/2 segments and the average over the spectra of the individual segments is calculated. Each segment of length 2*specsiz yields the PSD for specsiz+1 frequencies (see VF_FFT). In order to keep specsiz an integer power of 2, there are only specsiz points stored in Spc and the last one, the PSD at the Nyquist frequency f_{Nyquist} = 0.5 / sampling_interval, is given as the return value of the function. It may either be neglected (by calling the function like a void function) or stored as the last element in Spc by calling the function as
Spc[specsiz] = VF_spectrum( Spc, specsiz, X, xsiz, Win );
in this case, Spc must have a length of specsiz+1.
Win is a window that is applied to the data segments. The size of the Win vector must be 2*specsiz. Within the VectorLib library, three functions are available that give suitable Windows: VF_Welch, VF_Parzen, and VF_Hann. A square window (i.e. no windowing at all) is achieved by setting all elements of Win to 1.0 using VF_equ1. Use of the square window is not recommended here, though.
You may wish to test the quality of the calculated spectrum by applying Parseval's theorem (provided you called VF_spectrum as in the above example and stored the PSD for the Nyquist frequency):
1.0/xsize * VF_ssq( X, xsize ) must be about equal to VF_sum( Spc, specsiz+1 ).
If the deviation between both results is large, the sampling interval in X probably is too large.
For an example for this function, see the demo program VDEMO.


Error handling  If size is not a power of 2, VF_FFT (on which VF_spectrum is based) complains "Size must be an integer power of 2" and the program is aborted. 

Return value  PSD at the Nyquist frequency 

