Can I make sound and soundsc not make a sound when playing a constant value?

I was exploring what a ramp sounds like. Something like

1:10000 

played in soundsc. To remove the click from snapping back to zero I left my vector as

ones(1,10000)*10000 

afterwards. However, playing this sound, there is a humming even when the sound reaches the constant part. It is clearly heard in

wave = [ones(1,16000)];
soundsc(wave);

Why is this humming there? Does it have something to do with the hardware? Can I remove it?

[Walter Roberson]

Datapoint: on my Mac, R2020b, all I hear is a click at the beginning and the end.

[Adam Danz]

If the volume is turned up I can hear the humming between the two clicks (20b) using sound() or soundsc().

[Nikolaj Andreasen Klahn]

Using MATLAB R2020a on windows 10 - both headphones and loudspeaks have the issue.

[Adam Danz]

That means everything is working correctly. The issue is with the inputs or the expectation of what the inputs do, not with the sound function or with speakers or headphones.

Answer 1

[Adam Danz]

> I was exploring what a ramp sounds like [using 1:10000]

I think you're interpretting the audio data incorrectly but to your defense, Matlab's description of the audio data input y is terse. You're treating the input as though it represents pitch, hense values 1:10000 would be a ramp sound. But that's not what the audio data represents.

A quick intro to audio data

Consider this example of 3 notes followed by a chord.

duration = 1;
Fs = 10000;
t = 1/Fs : 1/Fs : duration; 

A = sin(880*pi*t)';
Csh = sin(1100*pi*t)'; 
E = sin(1320*pi*t)'; 
chord = A + Csh + E;
chord = chord./max(chord);

wave = [A;Csh;E;chord];
sound(wave,Fs) % Play sound (4 sec.)

The first 200 samples of each note and the chord are shown below.

clf
T = table(A,Csh,E,chord,'VariableNames',{'Note 1','Note 2','Note 3','Chord'});
T(201:end,:) = [];
T.time = seconds(t(1:200)'); 
h = stackedplot(T,'XVariable','time');
ax = findobj(h.NodeChildren, 'Type','Axes');
set(ax, 'YLim', [-1,1], 'YTick', -1:.5:1)
grid on

The data you see above are the audio data played by the sound() function. The x-axis is time and the y-axis can be understood as amplitude or as a continuous sequence of pressure variation entering the ear. Pitch arises from the variation along the y axis through time or, more specificially, the frequency of the repeating patterns. If there is no variation, there are no tones. The amplitude also affects volume where larger amplitudes (+|-) across segments of data will be louder and amplitudes near 0 are quieter.

For example, compare the volume of the sound above and when its amplitudes are reduced to 1/10th.

sound(wave, Fs)     % louder
sound(wave*.1, Fs)  % quieter, same pitches

So when I play sound(ones(1,16000)) why do I hear a click at the beginning and end and some faint humming in between?

The clicks at the beginning and end are because that's the only part or your data that vary. The beginning goes from nothing (0) to 1 and the end goes from 1 to nothing. The faint humming is the sound of roundoff error due to floating point representation of computed values very close to 0 and other sources (see comments below).

So, how do I create a sound that ramps-up in pitch?

Ramp up in frequency.

x = 1:.2:5000;
f = x/1e+5;
y = cos(10*pi*f.*x);
sound(y,5000) % Play sound (~5 sec)

[Nikolaj Andreasen Klahn]

Thank you for the answer!

I learned a bit more about floating points.

Specifically talking about the humming; I still don't understand where the round-off error occurs since the issue occurs even when my vector only contains the integer 1 - and doesn't occur if it's a zeros vector. But maybe it's somewhere in the sound function?

You also make a good point in your comment stating that the issue could be expectation of what the input does. I have no idea of the inner workings of the sound function, I just assumed it maps directly onto spatial position of some part of the speaker so that a vector of ones would keep it motionless thus generating no sound between the start and the end. I'll try to find an explanation of the function.

[Adam Danz]

Where does the roundoff error come from?

Note: my background is in neuroscience, not CS and I'd be better explaining how the ear and auditory cortex work but I'll try to explain how the brain-wannabe (ie, computer) works with sound.

First of all, the roundoff error is not the only source of noise.

Consider this 10ms segment of the the chord from my answer.

Fs = 10000;
t = 1/Fs : 1/Fs : 1; 
chord = sin(880*pi*t)' + sin(1100*pi*t)' + sin(1320*pi*t)';
chord = chord./max(chord);

clf()
sampleDur = 10; %ms
nSamp = ceil(sampleDur/(1/Fs*1000));
plot(linspace(0,sampleDur,nSamp), chord(1:nSamp))
yline(0)
axis tight
grid on
ylim([-1,1])
title(sprintf('Chord, %dms',sampleDur))
xlabel('time (ms)')
ylabel('amplitude')

It may look continuous, and it would be continuous if it were an analog signal, but it's actually composed of discrete values.

hold on
stem(linspace(0,sampleDur,nSamp), chord(1:nSamp));

The first limitation is the finite representation of the infinitely precise amplitude values leading to roundoff error. Ultimately these values need to be converted from their 16 bit representation (or whatever bit depth is specified) to a voltage signal sent to your speakers. I don't know the specifics of Matlabs sound reconstruction but it probably interpolates the quantized samples back into a smoothly changing voltage signal which introduces another source of external noise within the voltage signal during the digital-to-analog conversion. I don't know if any compression is involved but if so, that would also introduce external noise. Lastly, the speakers themselves have limited dynamic ranges based on thier bit depths and can add noise in the process of converting the voltage signal.

So the humming sound produced by your vector of 1s may be less associated with roundoff error than with the other sources of noise. Noise is always present in an analog signal but most of the time the SNR is so high that you don't notice it. In this case, there is virtually no signal so you hear the noise.

This is all explained in much more detail in this Khan Academy page that starts from analog-to-digital conversion which doesn't apply to the sound() inputs which are already digital and this Audacity manual.

[Adam Danz]

> ...so that a vector of ones would keep [the speakers] motionless thus generating no sound between the start and the end.

Yes, this is what my understanding is, too.

But that differs from the first part of your question where a ramp in pitch was trying to be produced using 1:10000, unless I misunderstood that pat.

[Nikolaj Andreasen Klahn]

Thanks a lot! :)