void WFIR::WindowData(double *Data, int N, TWindowType WindowType, double Alpha,
double Beta, bool UnityGain)
{
if (WindowType == wtNONE)
return;
int j, M, TopWidth;
double dM, *WinCoeff;
if (WindowType == wtKAISER || WindowType == wtFLATTOP)
Alpha = 0.0;
if (Alpha < 0.0)
Alpha = 0.0;
if (Alpha > 1.0)
Alpha = 1.0;
if (Beta < 0.0)
Beta = 0.0;
if (Beta > 10.0)
Beta = 10.0;
WinCoeff = new (std::nothrow) double[N + 2];
if (WinCoeff == 0)
{
std::cerr
<< "Failed to allocate memory in FFTFunctions::WindowFFTData() "
<< std::endl;
return;
}
TopWidth = (int) (Alpha * (double) N);
if (TopWidth % 2 != 0)
TopWidth++;
if (TopWidth > N)
TopWidth = N;
M = N - TopWidth;
dM = M + 1;
// Calculate the window for N/2 points, then fold the window over (at the bottom).
// TopWidth points will be set to 1.
if (WindowType == wtKAISER)
{
double Arg;
for (j = 0; j < M; j++)
{
Arg = Beta * sqrt(1.0 - pow(((double) (2 * j + 2) - dM) / dM, 2.0));
WinCoeff[j] = Bessel(Arg) / Bessel(Beta);
}
}
else if (WindowType == wtSINC) // Lanczos
{
for (j = 0; j < M; j++)
WinCoeff[j] = Sinc((double) (2 * j + 1 - M) / dM * M_PI);
for (j = 0; j < M; j++)
WinCoeff[j] = pow(WinCoeff[j], Beta);
}
else if (WindowType == wtSINE) // Hanning if Beta = 2
{
for (j = 0; j < M / 2; j++)
WinCoeff[j] = sin((double) (j + 1) * M_PI / dM);
for (j = 0; j < M / 2; j++)
WinCoeff[j] = pow(WinCoeff[j], Beta);
}
else if (WindowType == wtHANNING)
{
for (j = 0; j < M / 2; j++)
WinCoeff[j] = 0.5 - 0.5 * cos((double) (j + 1) * M_2PI / dM);
}
else if (WindowType == wtHAMMING)
{
for (j = 0; j < M / 2; j++)
WinCoeff[j] = 0.54 - 0.46 * cos((double) (j + 1) * M_2PI / dM);
}
else if (WindowType == wtBLACKMAN)
{
for (j = 0; j < M / 2; j++)
{
WinCoeff[j] = 0.42 - 0.50 * cos((double) (j + 1) * M_2PI / dM)
+ 0.08 * cos((double) (j + 1) * M_2PI * 2.0 / dM);
}
}
// See: http://www.bth.se/fou/forskinfo.nsf/0/130c0940c5e7ffcdc1256f7f0065ac60/$file/ICOTA_2004_ttr_icl_mdh.pdf
else if (WindowType == wtFLATTOP)
{
for (j = 0; j <= M / 2; j++)
{
WinCoeff[j] = 1.0
- 1.93293488969227 * cos((double) (j + 1) * M_2PI / dM)
+ 1.28349769674027
* cos((double) (j + 1) * M_2PI * 2.0 / dM)
- 0.38130801681619
* cos((double) (j + 1) * M_2PI * 3.0 / dM)
+ 0.02929730258511
* cos((double) (j + 1) * M_2PI * 4.0 / dM);
}
}
else if (WindowType == wtBLACKMAN_HARRIS)
{
for (j = 0; j < M / 2; j++)
{
WinCoeff[j] = 0.35875 - 0.48829 * cos((double) (j + 1) * M_2PI / dM)
+ 0.14128 * cos((double) (j + 1) * M_2PI * 2.0 / dM)
- 0.01168 * cos((double) (j + 1) * M_2PI * 3.0 / dM);
}
}
else if (WindowType == wtBLACKMAN_NUTTALL)
{
for (j = 0; j < M / 2; j++)
{
WinCoeff[j] = 0.3535819
- 0.4891775 * cos((double) (j + 1) * M_2PI / dM)
+ 0.1365995 * cos((double) (j + 1) * M_2PI * 2.0 / dM)
- 0.0106411 * cos((double) (j + 1) * M_2PI * 3.0 / dM);
}
}
else if (WindowType == wtNUTTALL)
{
for (j = 0; j < M / 2; j++)
{
WinCoeff[j] = 0.355768
- 0.487396 * cos((double) (j + 1) * M_2PI / dM)
+ 0.144232 * cos((double) (j + 1) * M_2PI * 2.0 / dM)
- 0.012604 * cos((double) (j + 1) * M_2PI * 3.0 / dM);
}
}
else if (WindowType == wtKAISER_BESSEL)
{
for (j = 0; j <= M / 2; j++)
{
WinCoeff[j] = 0.402 - 0.498 * cos(M_2PI * (double) (j + 1) / dM)
+ 0.098 * cos(2.0 * M_2PI * (double) (j + 1) / dM)
+ 0.001 * cos(3.0 * M_2PI * (double) (j + 1) / dM);
}
}
else if (WindowType == wtTRAPEZOID) // Rectangle for Alpha = 1 Triangle for Alpha = 0
{
int K = M / 2;
if (M % 2)
K++;
for (j = 0; j < K; j++)
WinCoeff[j] = (double) (j + 1) / (double) K;
}
// This definition is from http://en.wikipedia.org/wiki/Window_function (Gauss Generalized normal window)
// We set their p = 2, and use Alpha in the numerator, instead of Sigma in the denominator, as most others do.
// Alpha = 2.718 puts the Gauss window response midway between the Hanning and the Flattop (basically what we want).
// It also gives the same BW as the Gauss window used in the HP 89410A Vector Signal Analyzer.
// Alpha = 1.8 puts it quite close to the Hanning.
else if (WindowType == wtGAUSS)
{
for (j = 0; j < M / 2; j++)
{
WinCoeff[j] = ((double) (j + 1) - dM / 2.0) / (dM / 2.0) * 2.7183;
WinCoeff[j] *= WinCoeff[j];
WinCoeff[j] = exp(-WinCoeff[j]);
}
}
else // Error.
{
std::cerr << "Incorrect window type in WindowFFTData" << std::endl;
delete[] WinCoeff;
return;
}
// Fold the coefficients over.
for (j = 0; j < M / 2; j++)
WinCoeff[N - j - 1] = WinCoeff[j];
// This is the flat top if Alpha > 0. Cannot be applied to a Kaiser or Flat Top.
if (WindowType != wtKAISER && WindowType != wtFLATTOP)
{
for (j = M / 2; j < N - M / 2; j++)
WinCoeff[j] = 1.0;
}
// This will set the gain of the window to 1. Only the Flattop window has unity gain by design.
if (UnityGain)
{
double Sum = 0.0;
for (j = 0; j < N; j++)
Sum += WinCoeff[j];
Sum /= (double) N;
if (Sum != 0.0)
for (j = 0; j < N; j++)
WinCoeff[j] /= Sum;
}
// Apply the window to the data.
for (j = 0; j < N; j++)
Data[j] *= WinCoeff[j];
delete[] WinCoeff;
}
mat dBessel(double w, int order){
mat AB_ = Bessel(w,order);
AB_(1,1) = AB_(0,0);
AB_(1,0) = 0;
return AB_;
}
mat Bessel_d(double T, double w, int order){
return Tustin(T,w,Bessel(w,order));
}
static double BlackmanBessel(const double x, const double support)
{
return(Blackman(x/support,support)*Bessel(x,support));
}
