Difference between revisions of "Quadrature Demod"

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(Undo revision 7873 by 777arc (talk))
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<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)\ = \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) </math>
 
<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)\ = \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) </math>
  
<math>A</math> is real, 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>
+
<math>A</math> is real, so is <math>A^2</math> and hence only scales, therefore is invariant: = arg <math>\left( e^{j2\pi \frac{f}{f_s}} \right) \= \frac{f}{f_s}</math>
  
 
== Parameters ==
 
== Parameters ==

Revision as of 06:58, 4 December 2020

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:

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,

then

is real, so is and hence only scales, therefore is invariant: = arg Failed to parse (syntax error): {\displaystyle \left( e^{j2\pi \frac{f}{f_s}} \right) \= \frac{f}{f_s}}

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

This flowgraph shows the Quadrature Demod block as a Frequency Shift Keying detector.

RTTY rcv.png

Source Files

C++ files
[1]
Header files
[2]
Public header files
[3]
Block definition
[4]