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Suppose $x(t)$ is a signal containing a voice. How can one derive a signal playing the same voice faster.

I tried $x(t+\lfloor{100t\rfloor}/100)$ to double the speed; But it adds a buzz sound. Is there a better formula?

Clearly $x(2t)$ changes the voice. I want to change just the speed.

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    $\begingroup$ See other posts that mention “phase vocoder”; changes the speed without changing the pitch or vice versa $\endgroup$
    – Dan Boschen
    Commented Oct 28, 2018 at 2:41

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You can increase the sampling rate, instead of the signal $x(nT_s) = x(n/F_s)$, you can play it at say $\frac{11}{10}F_s, \frac{12}{10}F_s, \text{or}\ 2F_s$. So you have: \begin{align} x\left(\frac{n}{\frac{11}{10}F_s}\right) &=x\left(\frac{10n}{11F_s}\right) = x\left(n\frac{10}{11}T_s\right)\\ x\left(\frac{n}{\frac{12}{10}F_s}\right) &=x\left(\frac{10 n}{12F_s}\right) = x\left(n\frac{10}{12}T_s\right)\\ x\left(\frac{n}{2F_s}\right) &=x\left(\frac{1}{2}\frac{n}{F_s}\right) = x\left(n\frac{1}{2}T_s\right) \end{align} In MATLAB for instance, you can try the code below. 

clear all

load handel.mat
sound(y, Fs) % original 
sound(y, 1.1*Fs) % at 1.1*Fs
sound(y, 1.2*Fs) % at 1.2*Fs
sound(y, 2*Fs) % at twice Fs

Gradually increasing the frequency to hear the changes in speed. You can try even higher, like 4 times, to hear the differences. The handel.mat file should be in there by default.

EDIT:

You $x(t)$ in your program is samples of the signal for a certain time duration, check how many samples you have per second (i.e. the sampling rate or frequency $F_s$), and $T_s = 1/F_s$. And $x(t) = x(nT_s) = x(n/F_s)$ with $n = 0, \ldots, N-1$ where $N$ is the number of samples. Taking a higher $F_s$ corresponds to taking smaller $T_s$.

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  • $\begingroup$ Thanks. But I have C# program which gets $x(t)$ as a continuous function and uses it to produce a wave file. I have the sampling machine code but I prefer to change $x(t)$ itself. Can you recommend a change in $x(t)$? $\endgroup$
    – Minimus Heximus
    Commented Oct 28, 2018 at 12:09
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    $\begingroup$ @nano please see my edit. $\endgroup$
    – Gilles
    Commented Oct 28, 2018 at 14:06
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    $\begingroup$ Isn't it the same as sampling $x(at)$ where $a$ is a constant? The problem with this is that the pitch changes. $\endgroup$
    – Minimus Heximus
    Commented Oct 28, 2018 at 14:09
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    $\begingroup$ @nano search DSP.SE for pitch shift or associated techniques (like "time stretching"). This is a frequent question on this board and you can find some useful stuff in addition to the method that Gilles is suggesting to you here. $\endgroup$
    – A_A
    Commented Oct 29, 2018 at 9:53

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