/**
* Change frequency-bin order from 'SFT' to fftw-convention
* ie. from f[-(N-1)/2], ... f[-1], f[0], f[1], .... f[N/2]
* to FFTW: f[0], f[1],...f[N/2], f[-(N-1)/2], ... f[-2], f[-1]
*/
int
XLALReorderSFTtoFFTW (COMPLEX8Vector *X)
{
XLAL_CHECK ( (X != NULL) && (X->length > 0), XLAL_EINVAL );
UINT4 N = X->length;
UINT4 Npos_and_DC = NhalfPosDC ( N );
UINT4 Nneg = NhalfNeg ( N );
/* allocate temporary storage for swap */
COMPLEX8 *tmp;
XLAL_CHECK ( (tmp = XLALMalloc ( N * sizeof(*tmp) )) != NULL, XLAL_ENOMEM );
memcpy ( tmp, X->data, N * sizeof(*tmp) );
/* Copy second half of FFTW: 'negative' frequencies */
memcpy ( X->data + Npos_and_DC, tmp, Nneg * sizeof(*tmp) );
/* Copy first half of FFTW: 'DC + positive' frequencies */
memcpy ( X->data, tmp + Nneg, Npos_and_DC * sizeof(*tmp) );
XLALFree(tmp);
return XLAL_SUCCESS;
} // XLALReorderSFTtoFFTW()
int
test_XLALSincInterpolateSFT ( void )
{
REAL8 f0 = 0; // heterodyning frequency
REAL8 sigmaN = 0.001;
REAL8 dt = 0.1; // sampling frequency = 10Hz
LIGOTimeGPS epoch = { 100, 0 };
REAL8 tStart = XLALGPSGetREAL8 ( &epoch );
UINT4 numSamples = 1000;
REAL8 Tspan = numSamples * dt;
REAL8 df = 1.0 / Tspan;
UINT4 numSamples0padded = 3 * numSamples;
REAL8 Tspan0padded = numSamples0padded * dt;
REAL8 df0padded = 1.0 / Tspan0padded;
UINT4 numBins = NhalfPosDC ( numSamples );
UINT4 numBins0padded = NhalfPosDC ( numSamples0padded );
// original timeseries
REAL4TimeSeries* ts;
XLAL_CHECK ( (ts = XLALCreateREAL4TimeSeries ( "test TS_in", &epoch, f0, dt, &emptyLALUnit, numSamples )) != NULL, XLAL_EFUNC );
for ( UINT4 j = 0; j < numSamples; j ++ ) {
ts->data->data[j] = crealf ( testSignal ( tStart + j * dt, sigmaN ) );
} // for j < numSamples
// zero-padded to double length
REAL4TimeSeries* ts0padded;
XLAL_CHECK ( (ts0padded = XLALCreateREAL4TimeSeries ( "test TS_padded", &epoch, f0, dt, &emptyLALUnit, numSamples0padded )) != NULL, XLAL_EFUNC );
memcpy ( ts0padded->data->data, ts->data->data, numSamples * sizeof(ts0padded->data->data[0]) );
memset ( ts0padded->data->data + numSamples, 0, (numSamples0padded - numSamples) * sizeof(ts0padded->data->data[0]) );
// compute FFT on ts and ts0padded
REAL4FFTPlan *plan, *plan0padded;
XLAL_CHECK ( (plan = XLALCreateForwardREAL4FFTPlan ( numSamples, 0 )) != NULL, XLAL_EFUNC );
XLAL_CHECK ( (plan0padded = XLALCreateForwardREAL4FFTPlan ( numSamples0padded, 0 )) != NULL, XLAL_EFUNC );
COMPLEX8Vector *fft, *fft0padded;
XLAL_CHECK ( (fft = XLALCreateCOMPLEX8Vector ( numBins )) != NULL, XLAL_ENOMEM );
XLAL_CHECK ( (fft0padded = XLALCreateCOMPLEX8Vector ( numBins0padded )) != NULL, XLAL_ENOMEM );
XLAL_CHECK ( XLALREAL4ForwardFFT ( fft, ts->data, plan ) == XLAL_SUCCESS, XLAL_EFUNC );
XLAL_CHECK ( XLALREAL4ForwardFFT ( fft0padded, ts0padded->data, plan0padded ) == XLAL_SUCCESS, XLAL_EFUNC );
XLALDestroyREAL4TimeSeries ( ts );
XLALDestroyREAL4TimeSeries ( ts0padded );
XLALDestroyREAL4FFTPlan( plan );
XLALDestroyREAL4FFTPlan( plan0padded );
SFTtype XLAL_INIT_DECL(tmp);
tmp.f0 = f0;
tmp.deltaF = df;
tmp.data = fft;
REAL8 Band = 0.5/dt - f0;
SFTtype *sft = NULL;
XLAL_CHECK ( XLALExtractBandFromSFT ( &sft, &tmp, f0, Band ) == XLAL_SUCCESS, XLAL_EFUNC );
XLALDestroyCOMPLEX8Vector ( fft );
tmp.f0 = f0;
tmp.deltaF = df0padded;
tmp.data = fft0padded;
SFTtype *sft0padded = NULL;
XLAL_CHECK ( XLALExtractBandFromSFT ( &sft0padded, &tmp, f0, Band ) == XLAL_SUCCESS, XLAL_EFUNC );
XLALDestroyCOMPLEX8Vector ( fft0padded );
// ---------- interpolate input SFT onto frequency bins of padded-ts FFT for comparison
UINT4 Dterms = 16;
REAL8 safetyBins = (Dterms + 1.0); // avoid truncated interpolation to minimize errors, set to 0 for seeing boundary-effects [they're not so bad...]
REAL8 fMin = f0 + safetyBins * df;
fMin = round(fMin / df0padded) * df0padded;
UINT4 numBinsOut = numBins0padded - 3 * safetyBins;
REAL8 BandOut = (numBinsOut-1) * df0padded;
SFTtype *sftUpsampled = NULL;
XLAL_CHECK ( XLALExtractBandFromSFT ( &sftUpsampled, sft0padded, fMin + 0.5*df0padded, BandOut - df0padded ) == XLAL_SUCCESS, XLAL_EFUNC );
SFTtype *sftInterpolated;
XLAL_CHECK ( (sftInterpolated = XLALSincInterpolateSFT ( sft, fMin, df0padded, numBinsOut, Dterms )) != NULL, XLAL_EFUNC );
// ----- out debug info
if ( lalDebugLevel & LALINFO )
{
XLAL_CHECK ( write_SFTdata ( "SFT_in.dat", sft ) == XLAL_SUCCESS, XLAL_EFUNC );
XLAL_CHECK ( write_SFTdata ( "SFT_in0padded.dat", sft0padded ) == XLAL_SUCCESS, XLAL_EFUNC );
XLAL_CHECK ( write_SFTdata ( "SFT_upsampled.dat", sftUpsampled ) == XLAL_SUCCESS, XLAL_EFUNC );
XLAL_CHECK ( write_SFTdata ( "SFT_interpolated.dat", sftInterpolated ) == XLAL_SUCCESS, XLAL_EFUNC );
} // if LALINFO
// ---------- check accuracy of interpolation
VectorComparison XLAL_INIT_DECL(tol);
tol.relErr_L1 = 8e-2;
tol.relErr_L2 = 8e-2;
tol.angleV = 8e-2;
tol.relErr_atMaxAbsx = 4e-3;
tol.relErr_atMaxAbsy = 4e-3;
XLALPrintInfo ("Comparing Dirichlet SFT interpolation with upsampled SFT:\n");
XLAL_CHECK ( XLALCompareSFTs ( sftUpsampled, sftInterpolated, &tol ) == XLAL_SUCCESS, XLAL_EFUNC );
// ---------- free memory
XLALDestroySFT ( sft );
XLALDestroySFT ( sft0padded );
XLALDestroySFT ( sftUpsampled );
XLALDestroySFT ( sftInterpolated );
return XLAL_SUCCESS;
} // test_XLALSincInterpolateSFT()
