Quadrature Demod: Difference between revisions

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This can be used to demod FM, FSK, GMSK, etc.  The input is complex
This is the template for the [[:Category:Block_Docs|"Page-per-block Docs"]].  This first section should describe what the block does and how to use it, using however many paragraphs necessary.  Note that the title of the wiki page should match the block's name in GRC, i.e. the one defined in the block's .grc file.  Look at the [[FFT]] Block for a good example.
baseband, output is the signal frequency in relation to the sample
rate, multiplied with the gain.


As this is a basic template, it's also in the [[:Category:Stub_Docs|"Stub Docs category"]]. Please improve it.
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}\\
 
A rendered version of the equations is available there: [https://www.gnuradio.org/doc/doxygen/classgr_1_1analog_1_1quadrature__demod__cf.html]


== Parameters ==
== Parameters ==
(''R''): <span class="plainlinks">[https://wiki.gnuradio.org/index.php/GNURadioCompanion#Variable_Controls ''Run-time adjustable'']</span>
; Param 1 (''R'')
: Description of parameter, provide any tips or recommended values.  Note that the name of the parameter above should match the param's label that shows up in grc (e.g. Sample Rate).


; Param 2
; Gain
: blah blah blah
: Gain setting to adjust the output amplitude. Set based on converting the phase difference between samples to a nominal output value.


== Example Flowgraph ==
== Example Flowgraph ==
Line 21: Line 34:


; C++ files
; C++ files
: [https://github.com/gnuradio/gnuradio TODO]
: [https://github.com/gnuradio/gnuradio/blob/master/gr-analog/lib/quadrature_demod_cf_impl.cc]


; Header files
; Header files
: [https://github.com/gnuradio/gnuradio TODO]
: [https://github.com/gnuradio/gnuradio/blob/master/gr-analog/lib/quadrature_demod_cf_impl.h]


; Public header files
; Public header files
: [https://github.com/gnuradio/gnuradio TODO]
: [https://github.com/gnuradio/gnuradio/blob/master/gr-analog/include/gnuradio/analog/quadrature_demod_cf.h]


; Block definition
; Block definition
: [https://github.com/gnuradio/gnuradio TODO]
: [https://github.com/gnuradio/gnuradio/blob/master/gr-analog/grc/analog_quadrature_demod_cf.block.yml]

Revision as of 14:08, 28 August 2019

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 rate, 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}\\

A rendered version of the equations is available there: [1]

Parameters

Gain
Gain setting to adjust the output amplitude. Set based on converting the phase difference between samples to a nominal output value.

Example Flowgraph

Insert description of flowgraph here, then show a screenshot of the flowgraph and the output if there is an interesting GUI. Currently we have no standard method of uploading the actual flowgraph to the wiki or git repo, unfortunately. The plan is to have an example flowgraph showing how the block might be used, for every block, and the flowgraphs will live in the git repo.

Source Files

C++ files
[2]
Header files
[3]
Public header files
[4]
Block definition
[5]
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