# Logaritmic amplitude squarewave

This morning i was experimenting with GNU Octave. I created several signals(Sine, Saw tooth, square wave and noise). After this i used the periodogram. in the periodogram the square wave weren't showed.
I tried a test file from where the square wave is broken.

A = 1;
f = 2;
T = 2;
fs = 512;

if isOctave = exist('OCTAVE_VERSION', 'builtin') ~= 0;
clear isOctave;
end

t = 0:1/fs:T-1/fs ;
sine = A * sin(2*pi*f*t);
sq =  A * square(2*pi*f*t);
F = 0:(fs/(T*fs)):fs/2;
SINE = fft(sine);SINE = abs(SINE(1,1:(T*fs)/2+1));
SQ = fft(sq); SQ = abs(SQ(1,1:(T*fs)/2+1));

figure;
subplot(2,1,1); plot(t,sine, t,sq);
legend('Sine', 'Square','Location','northoutside','Orientation','horizontal')
subplot(2,1,2); plot( F, 20*log10(1/(length(SINE))*SINE), F,20*log10(1/(length(SQ))* SQ));

figure
periodogram(sine,[],length(sine),fs,'power'); hold all
periodogram(sq,[],length(sq),fs,'power')
legend('sine','square')


What i found out is that till the fft everything works as suspected.
But when i take the log of the square wave. the result disappears.

My question is why does this happening?

1. what cause this problem.
2. Happens this also in Matlab or python.
3. What solution fix this problem?

Your array SQ has many zero-valued elements:

SQ =
Columns 1 through 6:
0.00000     0.00000     0.00000     0.00000   651.91501     0.00000
Columns 7 through 12:
0.00000     0.00000     0.00000     0.00000     0.00000     0.00000


Taking the logarithm gives a minus infinity for the zeros:

octave> 20*log10(1/(length(SQ))*SQ)
ans =
Columns 1 through 8:
-Inf      -Inf      -Inf      -Inf    2.0815      -Inf      -Inf      -Inf
Columns 9 through 16:
-Inf      -Inf      -Inf      -Inf   -7.4592      -Inf      -Inf      -Inf


You can clamp those values to some more reasonable limit using max, which does the right thing handling minus infinities (unlike plot):

octave> max(20*log10(1/(length(SQ))*SQ), -120)
ans =
Columns 1 through 7:
-120.0000  -120.0000  -120.0000  -120.0000     2.0815  -120.0000  -120.0000
Columns 8 through 14:
-120.0000  -120.0000  -120.0000  -120.0000  -120.0000    -7.4592  -120.0000


Plotting:

plot( F, 20*log10(1/(length(SINE))*SINE), F, max(20*log10(1/(length(SQ))*SQ), -120));


You can do the same thing with the sine wave, which by luck had a spectral floor of numerical error. With audio, you rarely care about things more quiet than -120 dB.

The library function log of zero results in a NaN (not a real number, -inf). So the log of a square with a base of zero can't be plotted.

I don't know what you mean by "disappears". Your only 'log' command has been commented out, so no 'log' operation is executed.

I tried to run your code in Matlab. Everything was fine until the 'periodogram()' commands. Matlab did not recognize those commands as you have typed them. Taking a wild guess here, I wonder if your Octave 'periodogram()' command merely computes a frequency-domain sequence of numbers, but it does not perform any plotting. Your:

subplot(2,1,2); plot( F, 20*log10(1/(length(SINE))*SINE), F,20*log10(1/(length(SQ))* SQ),F,1/(length(SQ))* SQ);


command is strange. You seem to be plotting two logarithmic curves and one linear curve in the same window. Is that what you want? Try the following log plotting (it worked for me in Matlab):

subplot(2,1,2); plot(F,20*log10(1/(length(SQ))* SQ), '-bo');

• I see when plotting only one curve in both in subplot(2,1,2) and in the periodogram(). I added the question: I added a picture with what showed on my screen and i deleted some test code (I was playing around with what works and what was broken...) – Jan-Bert Dec 30 '15 at 14:18