Correlation > Autocorrelation of a frequency sweep

A vibro-seismic signal is obtained from a frequency sweep. The modulus of its FT is close to that of a boxcar function. We restore the temporal signal to a normal seismic impulsion by correlating the received signal with the theoretical source signal.
In ideal conditions, the equivalent wavelet has the form of the autocorrelation of the emitted signal. The example shows the modulus of the FT of the theoretical emitted signal (up), the emitted signal (middle), its autocorrelation and the envelope of its autocorrelation. The envelope of the correlation function is a cardinal sine.

It is possible to fix the limits of the frequency sweep, to verify that the greater the bandwidth is, the more that the equivalent wavelet is of short duration. The bandwidth is the difference between the high and the low frequencies of the sweep.