Generate pure tone sequence in frequence domain

Hi, i'm trying to generate a sequence of pure tones in the frequency domain and later on, convert to the time domain and execute the sound. The frequencies are 1000 Hz, 2000 Hz, 3000 Hz, 4000 Hz and 5000 Hz. I already managed to do this using only time domain, but i am having a very hard time to do this in the frequency domain. Can someone help me ?

[Bjorn Gustavsson]

Why not do it in the time-domain and Fourier-transform it.

Answer 1

[Scott MacKenzie]

Seems you want to start by specifying your signals in the frequency domain, then convert to the time domain. I think this does the trick:

% system spec's (adjust as needed)
sRate = 16584; % sampling rate
sPeriod = 1 / sRate;
n1 = sRate/2; % number of samples in one-sided freq spectrum

% create spectrum in frequency domain
fOneSide = (1:n1)';
specOneSide = zeros(n1,1);

% add sinusoids with varying amplitudes
specOneSide(1000) = 1.0;
specOneSide(2000) = 0.5;
specOneSide(3000) = 0.4;
specOneSide(4000) = 0.6;
specOneSide(5000) = 0.3;

% plot the frequency spectrum
figure;
set(gcf, 'color', 'w', 'units', 'normalized', 'Position', [.2 .4 .6 .4]);
tiledlayout(1,3);
nexttile;
plot(fOneSide,specOneSide);
title('One-sided Frequency Spectrum');
xlabel('Frequency (Hz)');
ylabel('Magnitude Spectrum');

% create the two-sided frequency spectrum
specTwoSide = [flip(specOneSide(1:end)); specOneSide(2:end-1)];
n2 = length(specTwoSide);
f = (-sRate/2:sRate/n2:sRate/2-sRate/n2)';

% plot it
nexttile;
plot(f, specTwoSide);
title('Two-sided Frequency Spectrum');
xlabel('Frequency (Hz)');
ylabel('Magnitude Spectrum');

% ifft the two-sided frequency spectrum to get signals in the time domain
y = ifft(fftshift(specTwoSide));
t = (0:n2-1) / sRate;

% plot it
nexttile;
plot(y(1:100)); % part of the signal only (better visual)
title('Time Domain Signal');
xlabel('Time');
ylabel('Amplitude');

% play it
soundsc(y, sRate);

[D2snc]

thanks for the answer, how could i play the sound longer, for example for 30 seconds? Would you be able to tell me if I wanted to use other frequencies?

[Scott MacKenzie]

@D2snc, you're welcome. Glad to help.

To play the tones longer, you can add something like this after conversion to the time domain:

% lengthen the duration of the tones 
repetitions = 15;
y = repmat(y, repetitions, 1);
t = (0:(length(y)-1)) / sRate;

To change the mix of frequencies, just edit the lines specifying the frequencies and amplitudes:

specOneSide(1000) = 1.0; % frequency = 1000 Hz, amplitude = 1
specOneSide(2000) = 0.5; % etc.
specOneSide(3000) = 0.4;
specOneSide(4000) = 0.6;
specOneSide(5000) = 0.3;

[D2snc]

Thanks for the help, do you have any solution if i want to put a frequency like 326.6 Hz , that have a decimal ? Because i cant put decimals in the indice

[Bjorn Gustavsson]

You just have to make the spectrum sufficiently long that the frequencies of all your signal components end up at integrer indices.

[Scott MacKenzie]

Yes, and as an example, if you add

n1 = 10*n1;

after the initialization of n1, you are increasing the size of the spectrum by a factor or 10. So, with this, each frequency is specified x10. To get 326.6 Hz, use

specOneSide(3266) = 1.0; % frequency = 326.6 Hz, amplitude = 1

[D2snc]

thanks for the help, i understand very well, grateful !