diff options
| author | Marcus Müller <Marcus.Mueller@ettus.com> | 2015-11-05 20:48:09 +0100 |
|---|---|---|
| committer | Johnathan Corgan <johnathan@corganlabs.com> | 2015-11-08 08:00:40 -0800 |
| commit | 9c4effc646f3518e1e22f066541e347ea88e0470 (patch) | |
| tree | 7f5fbb52d6ecbbfff2ba75c5a1cc48eaa9daa8bc | |
| parent | e5310ac22875bb964e3d6256b8541ea98e25d465 (diff) | |
expanded quadrature_demod_cf docs; added .grc <doc>
| -rw-r--r-- | gr-analog/grc/analog_quadrature_demod_cf.xml | 27 | ||||
| -rw-r--r-- | gr-analog/include/gnuradio/analog/quadrature_demod_cf.h | 29 |
2 files changed, 54 insertions, 2 deletions
diff --git a/gr-analog/grc/analog_quadrature_demod_cf.xml b/gr-analog/grc/analog_quadrature_demod_cf.xml index c8f0b30b46..447acf2ed8 100644 --- a/gr-analog/grc/analog_quadrature_demod_cf.xml +++ b/gr-analog/grc/analog_quadrature_demod_cf.xml @@ -25,4 +25,31 @@ <name>out</name> <type>float</type> </source> + <doc> +This can be used to demod FM, FSK, GMSK, etc. The input is complex +baseband, output is the signal frequency in relation to the sample +rated, multiplied with the gain. + +Mathematically, this block calculates the product of the one-sample +delayed input and the conjugate undelayed signal, and then calculates +the argument of the resulting complex number: + +y[n] = \mathrm{arg}\left(x[n] \, \bar x [n-1]\right). + +Let x be a complex sinusoid with amplitude A>0, (absolute) +frequency f\in\mathbb R and phase \phi_0\in[0;2\pi] sampled at +f_s>0 so, without loss of generality, + +x[n]= A e^{j2\pi( \frac f{f_s} n + \phi_0)}\f + +then + +y[n] = \mathrm{arg}\left(A e^{j2\pi\left( \frac f{f_s} n + \phi_0\right)} \overline{A e^{j2\pi( \frac f{f_s} (n-1) + \phi_0)}}\right)\\ + = \mathrm{arg}\left(A^2 e^{j2\pi\left( \frac f{f_s} n + \phi_0\right)} e^{-j2\pi( \frac f{f_s} (n-1) + \phi_0)}\right)\\ + = \mathrm{arg}\left( A^2 e^{j2\pi\left( \frac f{f_s} n + \phi_0 - \frac f{f_s} (n-1) - \phi_0\right)}\right)\\ + = \mathrm{arg}\left( A^2 e^{j2\pi\left( \frac f{f_s} n - \frac f{f_s} (n-1)\right)}\right)\\ + = \mathrm{arg}\left( A^2 e^{j2\pi\left( \frac f{f_s} \left(n-(n-1)\right)\right)}\right)\\ + = \mathrm{arg}\left( A^2 e^{j2\pi \frac f{f_s}}\right) \intertext{$A$ is real, so is $A^2$ and hence only \textit{scales}, therefore $\mathrm{arg}(\cdot)$ is invariant:} = \mathrm{arg}\left(e^{j2\pi \frac f{f_s}}\right)\\ += \frac f{f_s}\\ + </doc> </block> diff --git a/gr-analog/include/gnuradio/analog/quadrature_demod_cf.h b/gr-analog/include/gnuradio/analog/quadrature_demod_cf.h index 1e13841dc7..1aca5258cb 100644 --- a/gr-analog/include/gnuradio/analog/quadrature_demod_cf.h +++ b/gr-analog/include/gnuradio/analog/quadrature_demod_cf.h @@ -34,8 +34,33 @@ namespace gr { * \ingroup modulators_blk * * \details - * This can be used to demod FM, FSK, GMSK, etc. - * The input is complex baseband. + * This can be used to demod FM, FSK, GMSK, etc. The input is complex + * baseband, output is the signal frequency in relation to the sample + * rated, multiplied with the gain. + * + * Mathematically, this block calculates the product of the one-sample + * delayed input and the conjugate undelayed signal, and then calculates + * the argument of the resulting complex number: + * + * \f$y[n] = \mathrm{arg}\left(x[n] \, \bar x [n-1]\right)\f$. + * + * Let \f$x\f$ be a complex sinusoid with amplitude \f$A>0\f$, (absolute) + * frequency \f$f\in\mathbb R\f$ and phase \f$\phi_0\in[0;2\pi]\f$ sampled at + * \f$f_s>0\f$ so, without loss of generality, + * + * \f$x[n]= A e^{j2\pi( \frac f{f_s} n + \phi_0)}\f$ + * + * then + * + * \f{align*}{ y[n] &= \mathrm{arg}\left(A e^{j2\pi\left( \frac f{f_s} n + \phi_0\right)} \overline{A e^{j2\pi( \frac f{f_s} (n-1) + \phi_0)}}\right)\\ + * & = \mathrm{arg}\left(A^2 e^{j2\pi\left( \frac f{f_s} n + \phi_0\right)} e^{-j2\pi( \frac f{f_s} (n-1) + \phi_0)}\right)\\ + * & = \mathrm{arg}\left( A^2 e^{j2\pi\left( \frac f{f_s} n + \phi_0 - \frac f{f_s} (n-1) - \phi_0\right)}\right)\\ + * & = \mathrm{arg}\left( A^2 e^{j2\pi\left( \frac f{f_s} n - \frac f{f_s} (n-1)\right)}\right)\\ + * & = \mathrm{arg}\left( A^2 e^{j2\pi\left( \frac f{f_s} \left(n-(n-1)\right)\right)}\right)\\ + * & = \mathrm{arg}\left( A^2 e^{j2\pi \frac f{f_s}}\right) \intertext{$A$ is real, so is $A^2$ and hence only \textit{scales}, therefore $\mathrm{arg}(\cdot)$ is invariant:} &= \mathrm{arg}\left(e^{j2\pi \frac f{f_s}}\right)\\ + * &= \frac f{f_s}\\ + * &&\blacksquare + * \f} */ class ANALOG_API quadrature_demod_cf : virtual public sync_block { |