Commit f23d1dff by thomas.forbriger

### 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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