Commit f23d1dff authored by thomas.forbriger's avatar thomas.forbriger
Browse files

libpsdxx [WP][DOC]: document inverse of log construction

parent 912457b4
......@@ -41,14 +41,15 @@ namespace psd {
/*! \brief return a logarithmic frequency scale
*
* \par mapping function
* The series of frequencies with logarithmic spacing is
* \f[
* f_l = \Delta f \, \left\{ c \, \left(10^{\frac{l}{m}}-1 \right) +1
* \right\}
* \f]
* Where
* where
* - \f$ \Delta f =\f$ \p df
* - \f$ m= \f$ \p n_per_decade
*
* .
* This mapping ensures \f$ f_0 = \Delta f \f$.
* Adjust \f$ c \f$ such that
* \f[
......@@ -75,6 +76,27 @@ namespace psd {
* \f]
* if \f$ N= \f$ \p nsamples.
*
* \par coefficients obtained from frequency values
* \f[
* f_0 = \Delta f
* \f]
* \f[
* f_1 = \Delta f \, c\, 10^{\frac{1}{m}} - \Delta f \, c + \Delta f
* \f]
* \f[
* f_2 = \Delta f \, c\, 10^{\frac{1}{m}}\, 10^{\frac{1}{m}}
* - \Delta f \, c + \Delta f
* \f]
* Hence
* \f[
* \Delta f = f_0
* \f]
* \f[
* 10^{\frac{1}{m}} = \frac{f_2-f_1}{f_1-f_0}
* \f]
* \f[
* c = \frac{f_1-f_0}{f_0\,\left(\frac{f_2-f_1}{f_1-f_0}-1\right)}
* \f]
*/
TDseries log_frequency(const double& df,
const unsigned int& nsamples,
......
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