# Which transformation in frequency domain equals a x-axis shift of a signal in time domain?

I have discrete Fourier transformation results from measurements. Looking at the signal from the time domain perspective, I want to shift the signal on the $x$-axis to the left or right.

Which transformation in the frequency-domain results in a left/right shift in the time-domain?

• This question belongs on dsp.SE, not on stats.SE. Please ask the moderators to migrate it there. You can contact the moderators by clicking on the flag link below your question. Feb 24 '16 at 21:58
• Thanks for the advice, i did send a message to moderators
– user259819
Feb 26 '16 at 8:44

If $s(t)$ is your signal in time domain, you want to make the operation $s(t+\Delta t)$, which according to the Fourier's transform properties, is equivalent to the operation : $$S(f)e^{j2\pi f\Delta t}$$ $S(f)$ being $s(t)$ Fourier's transform.
In case of a discrete Fourier's transform, which is defined as $$S[k] = \sum^{N-1}_{n=0}{s[n]e^{\frac{-i2\pi kn}{N}}}$$ with $s$ the signal and N the number of points of both signal and DFT.
The operation to be applied in order to induce a shift by a number c of samples to $s[n]$ and obtain $s[n+c]$ is : $$e^{\frac{-i2\pi kc}{N}}S[k]$$
exp(-j*2*pi*(1:(N-1))*c/N).*S_fdt;