Quadrature Demod: Difference between revisions

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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.


As this is a basic template, it's also in the [[:Category:Stub_Docs|"Stub Docs category"]]. Please improve it.
The '''Quadrature Demod''' block accepts a stream of complex samples, such as the narrow baseband stream containing the desired signal, and produces a stream of floats that represent a frequency demodulation. This block is most useful in demodulating FM, FSK, GMSK, and similar modulations that carry information through changes in frequency.
 
This block does not support C++ output, so it cannot be used when the output language of a flowgraph in GRC is C++.
 
== Mathematical Description ==
 
The output of the block is the signal frequency in relation to the sample
rate, multiplied with the gain. It produces this by calculating the product of the one-sample delayed-&-conjugated input and the undelayed signal, and then calculates the argument (a.k.a. angle, in radians) of the resulting complex number:
 
<math>y[n] = \mathrm{arg}\left(x[n] \, \bar x [n-1]\right)</math>
 
Let x be a complex sinusoid with amplitude A>0, (absolute)
frequency <math>f\in\mathbb R</math> and phase <math>\phi_0\in[0;2\pi]</math> sampled at
f_s>0 so, without loss of generality,
 
<math>x[n]= A e^{j2\pi( \frac f{f_s} n + \phi_0)}</math>
 
then
 
<math>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)\ </math>
 
<math>
= \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)\
</math>
 
<math>
= \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)\
</math>
 
<math>
= \mathrm{arg}\left( A^2 e^{j2\pi\left( \frac f{f_s} \left(n-(n-1)\right)\right)}\right)\
</math>
 
<math> = \mathrm{arg}\left( A^2 e^{j2\pi \frac f{f_s}}\right)
</math>
 
<math>A</math> is real, and so is <math>A^2</math>, and hence only scales, therefore <math>\mathrm{arg}(\cdot)</math> is invariant: = arg <math>\left( e^{j2 \pi \frac{f}{f_s}} \right) = \frac{f}{f_s}</math>


== Parameters ==
== Parameters ==
(''R''): <span class="plainlinks">[https://wiki.gnuradio.org/index.php/GNURadioCompanion#Variable_Controls ''Run-time adjustable'']</span>


; Param 1 (''R'')
; Gain
: 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).
: Gain setting to adjust the output amplitude. Set based on converting the phase difference between samples to a nominal output value. Default: "samp_rate/(2*math.pi*fsk_deviation_hz)".


; Param 2
== Example Flowgraph ==
: blah blah blah


== Example Flowgraph ==
=== Example 1 ===
 
 
[[File:Quadrature_Demod_flowgraph.png|800px]]
 
An example flowgraph of this block, demonstrating the demodulation of a narrow FSK signal inside a wideband capture file.
 
[[File:Quadrature_Demod_example.png|800px]]
 
The Quadrature Demod block in practice extracts the symbols from the FSK signal. Random noise is produced before and after the signal.
 
 
This flowgraph shows the Quadrature Demod block as a Frequency Shift Keying detector. First, the [[Frequency Xlating FIR Filter]] acts as a channelizer, extracting a narrow baseband signal from a wider stream. Then the Quadrature Demod block returns floats that are >1 if the upper frequency is louder, 0 if they are equal, and <0 if the lower frequency is louder, thus demodulating FSK. In this scenario, if <code>fsk_deviation</code> is defined as the difference between the upper and lower frequencies, and the baseband sampling rate is known (after the decimating from the Freq Xlating FIR Filter block), then a good formula for the Gain parameter would be <code>baseband_samp_rate / (math.pi * fsk_deviation)</code>. This causes the block to produce output floats that will never have a magnitude greater than 1.0 for the actual symbols.
 
=== Example 2 ===
 
[[File:RTTY_rcv.png|800px]]
 
This flowgraph shows BFSK signal recovery using Quadrature Demod block
 
[[File:FSK2_mod_demod.png|800px]]
 
Transmitted and received bits using above example


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.
[[File:BFSK_tx_rx.png|500px]]


== Source Files ==
== Source Files ==


; 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 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 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 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 analog_quadrature_demod_cf.block.yml]

Latest revision as of 14:56, 18 April 2023


The Quadrature Demod block accepts a stream of complex samples, such as the narrow baseband stream containing the desired signal, and produces a stream of floats that represent a frequency demodulation. This block is most useful in demodulating FM, FSK, GMSK, and similar modulations that carry information through changes in frequency.

This block does not support C++ output, so it cannot be used when the output language of a flowgraph in GRC is C++.

Mathematical Description

The output of the block is the signal frequency in relation to the sample rate, multiplied with the gain. It produces this by calculating the product of the one-sample delayed-&-conjugated input and the undelayed signal, and then calculates the argument (a.k.a. angle, in radians) of the resulting complex number:

Let x be a complex sinusoid with amplitude A>0, (absolute) frequency and phase sampled at f_s>0 so, without loss of generality,

then

is real, and so is , and hence only scales, therefore is invariant: = arg

Parameters

Gain
Gain setting to adjust the output amplitude. Set based on converting the phase difference between samples to a nominal output value. Default: "samp_rate/(2*math.pi*fsk_deviation_hz)".

Example Flowgraph

Example 1

Quadrature Demod flowgraph.png

An example flowgraph of this block, demonstrating the demodulation of a narrow FSK signal inside a wideband capture file.

Quadrature Demod example.png

The Quadrature Demod block in practice extracts the symbols from the FSK signal. Random noise is produced before and after the signal.


This flowgraph shows the Quadrature Demod block as a Frequency Shift Keying detector. First, the Frequency Xlating FIR Filter acts as a channelizer, extracting a narrow baseband signal from a wider stream. Then the Quadrature Demod block returns floats that are >1 if the upper frequency is louder, 0 if they are equal, and <0 if the lower frequency is louder, thus demodulating FSK. In this scenario, if fsk_deviation is defined as the difference between the upper and lower frequencies, and the baseband sampling rate is known (after the decimating from the Freq Xlating FIR Filter block), then a good formula for the Gain parameter would be baseband_samp_rate / (math.pi * fsk_deviation). This causes the block to produce output floats that will never have a magnitude greater than 1.0 for the actual symbols.

Example 2

RTTY rcv.png

This flowgraph shows BFSK signal recovery using Quadrature Demod block

FSK2 mod demod.png

Transmitted and received bits using above example

BFSK tx rx.png

Source Files

C++ files
quadrature_demod_cf_impl.cc
Header files
quadrature_demod_cf_impl.h
Public header files
quadrature_demod_cf.h
Block definition
analog_quadrature_demod_cf.block.yml