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gslfft.hh File Reference
#include <bse/gsldefs.hh>
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Functions

void gsl_power2_fftac (const uint n_values, const double *ri_values_in, double *ri_values_out)
 
void gsl_power2_fftsc (const uint n_values, const double *ri_values_in, double *ri_values_out)
 
void gsl_power2_fftsc_scale (const unsigned int n_values, const double *ri_values_in, double *ri_values_out)
 
void gsl_power2_fftar (const uint n_values, const double *r_values_in, double *ri_values_out)
 
void gsl_power2_fftsr (const unsigned int n_values, const double *ri_values_in, double *r_values_out)
 
void gsl_power2_fftsr_scale (const unsigned int n_values, const double *ri_values_in, double *r_values_out)
 
void gsl_power2_fftar_simple (const uint n_values, const float *real_values, float *complex_values)
 
void gsl_power2_fftsr_simple (const uint n_values, const float *complex_values, float *real_values)
 
void gsl_power2_fftsr_scale_simple (const unsigned int n_values, const float *complex_values, float *real_values)
 

Function Documentation

void gsl_power2_fftac ( const uint  n_values,
const double ri_values_in,
double ri_values_out 
)
Parameters
n_valuesNumber of complex values
ri_values_inComplex sample values [0..n_values*2-1]
ri_values_outComplex frequency values [0..n_values*2-1]

This function performs a decimation in time fourier transformation in forward direction, where the input values are equidistant sampled data, and the output values contain the frequency proportions of the input. The input and output arrays are complex values with real and imaginery portions interleaved, adressable in the range [0..2*n_values-1], where n_values must be a power of two. Frequencies are stored in-order, the K-th output corresponds to the frequency K/n_values. (If you want to interpret negative frequencies, note that the frequencies -K/n_values and (n_values-K)/n_values are equivalent).

In general for the gsl_power2_fft*() family of functions, normalization is only performed during backward transform if the gsl_power2_fftsc_scale() is used. No normalization is performed if gsl_power2_fftsc() is used.

However, a popular mathematical strategy of defining the FFT and IFFT in a way that the formulas are symmetric is normalizing both, the forward and backward transform with 1/sqrt(N) - where N is the number of complex values (n_values).

Compared to the above definition, in this implementation, the analyzed values produced by gsl_power2_fftac()/gsl_power2_fftar() will be too large by a factor of sqrt(N), which however are cancelled out on the backward transform (for _scale variants).

Note that the transformation is performed out of place, the input array is not modified, and may not overlap with the output array.

void gsl_power2_fftar ( const uint  n_values,
const double r_values_in,
double ri_values_out 
)
Parameters
n_valuesNumber of real sample values
r_values_inReal sample values [0..n_values-1]
ri_values_outComplex frequency values [0..n_values-1] Real valued variant of gsl_power2_fftac(), the input array contains real valued equidistant sampled data [0..n_values-1], and the output array contains the positive frequency half of the complex valued fourier transform. Note, that the complex valued fourier transform H of a purely real valued set of data, satisfies H(-f) = Conj(H(f)), where Conj() denotes the complex conjugate, so that just the positive frequency half suffices to describe the entire frequency spectrum. However, the resulting n_values/2+1 complex frequencies are one value off in storage size, but the resulting frequencies H(0) and H(n_values/2) are both real valued, so the real portion of H(n_values/2) is stored in ri_values_out[1] (the imaginery part of H(0)), so that both arrays r_values_in and ri_values_out can be of size n_values.

The normalization of the results of the analysis is explained in gsl_power2_fftac(). Note that in the real valued case, the number of complex values N for normalization is n_values/2.

Note that the transformation is performed out of place, the input array is not modified, and may not overlap with the output array.

void gsl_power2_fftsc ( const uint  n_values,
const double ri_values_in,
double ri_values_out 
)
Parameters
n_valuesNumber of complex values
ri_values_inComplex frequency values [0..n_values*2-1]
ri_values_outComplex sample values [0..n_values*2-1]

This function performs a decimation in time fourier transformation in backwards direction with normalization. As such, this function represents the counterpart to gsl_power2_fftac(), that is, a value array which is transformed into the frequency domain with gsl_power2_fftac() can be reconstructed by issuing gsl_power2_fftsc() on the transform. This function does not perform scaling, so calling gsl_power2_fftac() and gsl_power2_fftsc() will scale the data with a factor of n_values. See also gsl_power2_fftsc_scale().

More details on normalization can be found in the documentation of gsl_power2_fftac().

Note that the transformation is performed out of place, the input array is not modified, and may not overlap with the output array.

void gsl_power2_fftsc_scale ( const unsigned int  n_values,
const double ri_values_in,
double ri_values_out 
)
Parameters
n_valuesNumber of complex values
ri_values_inComplex frequency values [0..n_values*2-1]
ri_values_outComplex sample values [0..n_values*2-1] This function performs a decimation in time fourier transformation in backwards direction with normalization. As such, this function represents the counterpart to gsl_power2_fftac(), that is, a value array which is transformed into the frequency domain with gsl_power2_fftac() can be reconstructed by issuing gsl_power2_fftsc() on the transform.

This function also scales the time domain coefficients by a factor of 1.0/n_values which is required for perfect reconstruction of time domain data formerly transformed via gsl_power2_fftac(). More details on normalization can be found in the documentation of gsl_power2_fftac().

Note that the transformation is performed out of place, the input array is not modified, and may not overlap with the output array.

void gsl_power2_fftsr ( const unsigned int  n_values,
const double ri_values_in,
double r_values_out 
)
Parameters
n_valuesNumber of real sample values
ri_values_inComplex frequency values [0..n_values-1]
r_values_outReal sample values [0..n_values-1]

Real valued variant of gsl_power2_fftsc(), counterpart to gsl_power2_fftar(), using the same frequency storage format. A real valued data set transformed into the frequency domain with gsl_power2_fftar() can be reconstructed using this function.

This function does not perform normalization, so data that is transformed back from gsl_power2_fftar() will be scaled by a factor of n_values. See also gsl_power2_fftsr_scale().

More details on normalization can be found in the documentation of gsl_power2_fftac().

Note that the transformation is performed out of place, the input array is not modified, and may not overlap with the output array.

void gsl_power2_fftsr_scale ( const unsigned int  n_values,
const double ri_values_in,
double r_values_out 
)
Parameters
n_valuesNumber of real sample values
ri_values_inComplex frequency values [0..n_values-1]
r_values_outReal sample values [0..n_values-1] Real valued variant of gsl_power2_fftsc(), counterpart to gsl_power2_fftar(), using the same frequency storage format. A real valued data set transformed into the frequency domain with gsl_power2_fftar() can be reconstructed using this function.

This function also scales the time domain coefficients by a factor of 1.0/(n_values/2) which is required for perfect reconstruction of time domain data formerly transformed via gsl_power2_fftar(). More details on normalization can be found in the documentation of gsl_power2_fftac().

Note that the transformation is performed out of place, the input array is not modified, and may not overlap with the output array.

Referenced by gsl_filter_fir_approx().

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