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Amplitude modulation in scilab

Discussion in 'Electronic Design' started by M. Hamed, Apr 28, 2013.

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  1. M. Hamed

    M. Hamed Guest

    Disclaimer: this may be a tiny bit off topic for this group.

    Now DSP is one of the things that I'm planning to dive deep into at some point. So I know I'm going to get a bunch of those "Get a DSP book". But since I'm going to be working on an AM radio, I decided I would like to understand the mixing process better and demonstrate it in software in a burn before you learn way.

    So I fired up Scilab and did the following:

    1- create a time array
    2- create a bunch of sinusoids at frequencies from 550khz o 1700 khz spacedby 20khz and random phase.
    3- Sum all of these sinusoids to create a composite wave.
    4- perform FFT on the composite wave.
    5- Plot the results

    The code is here, if anyone is interested.

    https://docs.google.com/document/d/1EQp43CK_ooTF66am9pXCOu5k-vEK21wWJhsdSa6NvZQ/edit?usp=sharing

    Now I have to tell you I was a bit surprised by the result. I started playing with both sampling rate and and found the results quite interesting.

    This is a picture of the FFT plot with the sampling rate a bit above Nyquist at 4M samples/s (Max AM frequency is 1.7MHz)

    https://docs.google.com/file/d/0B1hjUVk4ytmvdXBELTRwanBlcTA/edit?usp=sharing

    Now you can see 58 sinusoids which is the correct number created in the time domain, but I expected them to have equal amplitudes. I assume the decreasing amplitude is an artifact of the low sampling rate.

    When I increase the sampling rate 10 times more and decrease the time to account for memory shortage, I got what I wanted. 58 sin waves with equal amplitude.

    https://docs.google.com/file/d/0B1hjUVk4ytmvMmdvb3JwOGpneDQ/edit?usp=sharing

    So far my signal sampling time window was 1 ms. As I decrease this further,I start getting more noise in the amplitudes of the sin waves. For examplehere with a time of 100 us.

    https://docs.google.com/file/d/0B1hjUVk4ytmvWGRTdzBfRllZeTQ/edit?usp=sharing

    It eventually reaches a point where the sinusoids are completely messed up,even at only half the previous time window 50 us and even with a 400M samples per second rate, much higher than nyquist.

    https://docs.google.com/file/d/0B1hjUVk4ytmvWFlvWHZqQ2VJWms/edit?usp=sharing

    I am sure there is a DSP explanation for all this. It gives me some motivation to study further. One possibility with relatively short time windows isthat you don't have enough time to capture all the information in the signal that it can't yet be approximated with a sin wave in the discreet domain.. Another possibility is that may be there has to be some relation that needs to be maintained between time window and sampling rate. Don't know.

    Next on my plate is to do actual mixing with a sinusoids then do some filtering then another step of down-conversion and demodulation. I have no idea how to do digital filtering in scilab yet but I'll find out.

    It was interesting to me, thought It's worth sharing and may be I can get some hints.
     
    Suyash likes this.
  2. Fred Abse

    Fred Abse Guest

    <URL snipped>

    Why not post it to this newsgroup, instead of that Javascript ridden hell?
     
  3. M. Hamed

    M. Hamed Guest

    Thanks for the tips on windowing. I'll take look into it.

    You are absolutely right. I will look into some other alternative that shares files as files.

    Here is the code:

    ///////////////////////
    // Program Constants

    start_freq = 550e3; // starting frquency = 550 kHz
    end_freq = 1700e3; // end frequency = 1700 kHz
    freq_spacing = 20e3; // channel spacing = 20 kHz
    t_end = 1e-2; // last time sample = 10 us
    amplitude = 1;
    sample_rate = 4e6;
    random_phase = 1;
    fftplot = 1;
    nf = 20000 // number of frequency samples to plot

    ///////////////////////

    // create time variable

    time = 0:1/sample_rate:t_end;
    szt = size(time, '*');

    // create station frequencies spaced by 20khz
    frq = start_freq:freq_spacing:end_freq;
    // transpose
    frq = frq';
    szf = size(frq, '*');

    //phase = (2*%pi/szf):(2*%pi/szf):2*%pi;
    phase = 2*%pi*rand(1,szf);
    phase = phase'
    phase_matrix = random_phase*phase*ones(1,szt);

    // time frequency matrix, one row for each frequency and time is in columns
    time_freq = amplitude*sin((2*%pi*frq*time)+phase_matrix);

    // sum all the sinusoids
    composite = sum(time_freq,:);

    // Now calculate and plot FFT
    if fftplot then
    N = szt;

    y = fft(composite);

    f=sample_rate*(0:(N/2))/N;
    n=size(f,'*');

    clf()
    if nf=0 then
    nf = n
    end
    plot(f(1:nf),abs(y(1:nf)))
    end

    //////////////////////////////////////////////////
     
  4. Fred Abse

    Fred Abse Guest

    Thanks.

    Unfortunately it runs my scilab out of memory. I'll see whether I can
    translate it into octave code.
     
  5. josephkk

    josephkk Guest

    Interesting. Much of what you are discovering is normal artifacts of the
    FFT algorithms themselves. Or properties finite time FT. Yes, everything
    that you saw in these examples. You could really profit from E. Oran
    Brighams book on FFT and applications. Not much heavy math but much
    explanation.

    ?-)
     
  6. josephkk

    josephkk Guest

    Well, not everybody here has scilab. It does not help much for a google
    grouper trying to post graphics.

    Fred, if you want a wake up call try scilab.org itself with a recent
    version of firefox.

    Reccomendation for M. Hamed, get pan (news client and email client) and
    use eternal-september for free posting. I think that they do carry
    alt.binaries.schematic.electronic (abse or a.b.s.e in common parlance).

    ?-)
     
  7. Fred Abse

    Fred Abse Guest

    I hardly ever use scilab, preferring octave, mainly because it makes a
    better fist of running matlab stuff.
    What I asked for wasn't graphics, but scilab code, ie. text.
    No thanks, I climbed off the upgrade bandwagon aeons ago. Too many
    dependency changes.
    Seconded.
     
  8. M. Hamed

    M. Hamed Guest

    I'm currently trying to go through "The scientist and engineer's guide to dsp". Most of these DSP books try to include very little mathematics and I feel this takes away from my understanding. I am thinking I should go for a Signals and Systems book for a better groundwork then move to DSP (except that it takes a long time this way :( ).

    Back in my school days we had a Signal Analysis course and the book was Signal Analysis by Papoulis. It was a bit difficult to follow back then but itwould probably be easier now. Can't find a good copy though.

    I'm not sure what the standard bible would be nowadays for Signal Analysis books.

    Thanks. I'll check it out.
     
  9. josephkk

    josephkk Guest

    So not the point i wanted to make, that site is a script and cookie laden
    hell. I quit instead of getting a download.
     
  10. josephkk

    josephkk Guest

    ooOn Sat, 4 May 2013 13:42:51 -0700 (PDT), "M. Hamed"
    And you are correct on the low math aspect. Perhaps taking a senior or
    graduate level course at a local uni or online would appropriate.
    Search engines are your friend.
    Is this the book you mean:?
    < http://www.amazon.com/Signal-Analysis-Athanasios-Papoulis/dp/0070484600
     
  11. Robert Macy

    Robert Macy Guest

    I don't use Scilab [I think that was its name] after a giant battle
    with them over accuracy. They essentially told me tough.

    After floundering for a few years, I discovered octave and have NOT
    changed again. I do EXTENSIVE DSP work and octave not only predicted,
    but taught me, a great deal about what was going on. During DSP
    development after trying a process of manipulation in octave, it was a
    piece of cake to write C/C++ real-time code to do the same thing. As
    you know, battling code errors is enough to take on, not trying to
    design the DSP processing at the same time.

    Either you have to make certain you have a complete set of cycles for
    each waveform in your FFT window, else you 'scatter' the energy of non
    matching sinusoid into adjacent segments. Like 30% in one and 70% in
    the next one, which makes your display look ghastly - but it is
    correct by mathematical definitions. So...if you make the FFT window
    of time match ALL waves THEN you'll get your expected results. If
    impossible to match, you can use a window. Think of the window as
    gently sliding into the data and then gently sliding back out, so the
    'accidental' abrupt start and stop of your window over the waveforms
    just doesn't happen. There are two very effective windows to use. go
    to TI's ap note on their incredible ADS1282 24 bit data acquisition
    system. They use a window that is a great compromise between
    preserving energy and injecting noise into adjacent segments. In the
    interim, I simply use an 'adjusted' hanning window which is fairly
    easy and doesn't 'splatter' the energy around. Note, I said Hanning,
    not Hamming. The shape of the hanning window is one cycle of a cos
    wave, starts at zero goes to amplitude of 2, then returns to zero and
    is EXACTLY the length of your FFT window. Octave provides that as a
    supplied function so it's easy to use, but you can construct one
    mathematically for your needs. Just keep in mind that whatever window
    you use you MUST make the area under that window equal to one, else
    you'll shift the amplitudes of your FFT, losing quantified answers,
    only getting qualified answers.

    Be FAR easier to talk in octave, rather than Scilab.
     
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