Hi Larry,
please answer to the list, and not to the individual people, if possible :)
The quadrature demod gives you the "instantaneous" frequency between
consecutive samples. Mathematically, it's conjugate multiplication of
the samples with a single-sample delayed version of themselves, followed
by calculation of the argument of that complex number:
quadrature demod: input signal x, output y. Notice you're doing digital
signal processing, and hence, it's not $x(t),\, r\in\mathbb R$, but
$x[n],\, n\in \mathbb N_0$.
$y[n] = \mathrm{arg}\left(x[n] \, \bar x [n-1]\right)$.
To answer your question what quadrature demod is like, there's no way
around doing a little bit of math. Don't worry, it'll be fun (at least I
had fun writing this down):
Imagine $x$ is a complex oscillation 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,
$x[n]= A e^{j2\pi( \frac f{f_s} n + \phi_0)}$
then
\documentclass{article} \usepackage[utf8x]{inputenc}
\usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb}
\usepackage{trfsigns} \DeclareMathOperator*{\argmin}{arg\,min}
\usepackage{tikz} \usepackage{circuitikz}
\usepackage[binary-units=true]{siunitx} \sisetup{exponent-product =
\cdot} \DeclareSIUnit{\dBm}{dBm} \newcommand{\imp}{\SI{50}{\ohm}}
\newcommand{\wrongimp}{\SI{75}{\ohm}} \pagestyle{empty} \begin{document}
\begin{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 \end{align*}% \end{document}
So, your quadrature demod gives you /one/ sample output of relative
frequency per input sample, and hence is neither, but it's pretty close
to the "frequency to voltage" converter, if you low-pass filter and
decimate the output of quadrature demod.
Cheers,
Marcus
On 05.11.2015 11:39, larry ho wrote:
> Thank you very much Marcus
>
> The quadrate demodulator did achieve what i wanted. Your advice on Qt
> frequency sink is really interesting, I'll look into it. Regarding
> quadrate modulation block, does it take on the same principle as the
> Qt frequency sink "takes in a period of signal, and shows you all the
> frequencies' magnitudes it can detect at once. It's "one signal over a
> lot of time in, a set of a lot of frequency magnitudes out""?
>
> Regards
>
> Larry
>
> ------------------------------------------------------------------------
> To: [email protected]
> From: [email protected]
> Date: Thu, 5 Nov 2015 10:22:04 +0100
> Subject: Re: [Discuss-gnuradio] Frequency discriminator using a
> frequency to voltage converter
>
> Hi Larry,
> in addition to what Kim said:
> You'll have to consider that what the Qt frequency sink and what a
> frequency to voltage converter does are pretty different things:
>
> * The freq-to-volt converter takes a signal and (ideally) gives you
> a reading determining the (somehow defined) strongest frequency in
> your signal. So it's "one signal over a lot of time in, one number
> out", if you want so.
> * The Qt frequency sink takes in a period of signal, and shows you
> all the frequencies' magnitudes it can detect at once. It's "one
> signal over a lot of time in, a set of a lot of frequency
> magnitudes out".
>
> So the core question is: What do you really want to do, mathematically?
>
> Because I find that highly cool, here's what's happening inside the Qt
> frequency sink, even if that might be unrelated to your problem:
>
> * takes in a vector of N samples
> * Computes a discrete Fourier transform (using FFTw's fast fourier
> transform algorithms) of length N
> * computes the square of the magnitude, the logarithm of that,
> normalizes each of the N complex result values
> * optionally: averages each bin individually
> * regularly updates the plot with the N-vector of PSD
>
>
> Best regards,
> Marcus
>
>
> On 04.11.2015 13:15, larry ho wrote:
>
> Hi
>
>
> I am new to linux and GNU Radio, I am trying to create a frequency
> to voltage converter, I tried looking into the source code of QT
> GUI Frequency Sink to get an idea how it detects frequency.
> However, it seems a little complicated, is there any particular
> function i should look out for in the coding? Or are there any
> alternative in creating a frequency to voltage converter. Greatly
> appreciative if any advise can be provided. Thank you.
>
>
> Regards
>
>
> Larry
>
>
>
> _______________________________________________
> Discuss-gnuradio mailing list
> [email protected] <mailto:[email protected]>
> https://lists.gnu.org/mailman/listinfo/discuss-gnuradio
>
>
>
> _______________________________________________ Discuss-gnuradio
> mailing list [email protected]
> https://lists.gnu.org/mailman/listinfo/discuss-gnuradio
_______________________________________________
Discuss-gnuradio mailing list
[email protected]
https://lists.gnu.org/mailman/listinfo/discuss-gnuradio
