Add randomness to DTFT Touch tone generation

Hi everyone, I want to add some form of noise to touch tone generation to make the generation more random. I don't really know how to go about it. Any ideas to get started are welcomed

Answer 1

[Walter Roberson]

If you already have the non-noisy signal then https://www.mathworks.com/help/comm/ref/awgn.html awgn()

[Daniel Manu]

Ok thanks. How would you plot "probability of noise" vs "SNR" after applying fft to the noisy signal.

[Walter Roberson]

Simulation ?

Theory is discussed at https://dsp.stackexchange.com/questions/14862/measure-the-snr-of-a-signal-in-the-frequency-domain

[Daniel Manu]

With the AWGN function, you input the SNR value as well, so it seems a bit different from what you posted. Since I already input the SNR value to the AWGN to generate the noisy signal, Do I have to measure again the SNR value in the noisy signal.

[Walter Roberson]

Yes you do. You need to prove that the input SNR gets reflected in the value you calculate after transformation with fft. One could imagine, for example, that fft might give you sqrt(SNR) or SNR / number of points, or might "spread out" the SNR. For example if you have 2 seconds at one SNR followed in the same signal by 2 seconds at a different SNR, then what does the fft give you as the SNR?

You are working on investigating the properties, so even if you measure the same SNR after fft that is important for your investigation. Suppose someone told you that you could increase the SNR on transmission by sqrt(2) by sending the fft of the signal instead of the signal itself, on the grounds that the extra information carried on the complex coefficients reduced the uncertainty: are they wrong? Wrong including the case where the original signal is real valued and you are sending both the real and imaginary parts (twice as much data)?

[Daniel Manu]

The link here makes it more simpler so I used that. It works well too...... https://www.mathworks.com/matlabcentral/fileexchange/47946-bpsk-ber-vs-snr-with-awgn