# 18.6.2 Algorithms (Deconvolution)

## Fast algorithm for Deconvolution

Deconvolution is performed with a fast algorithm based on the convolution theorem, which states that the Fourier transform of a convolution is equal to the product of the Fourier transforms of the signal and the response.

Let y be the known response and let g be the signal. Then the deconvolution can be computed as follows:

$f=ifft[\frac{fft(y)}{fft(g)}]\,\!$

where fft() and ifft() denote fast Fourier transform and its inverse respectively.

Users should be aware that the above procedure can give inaccurate results mathematically because fft(g) is sometimes equal to zero for some responses. When this is the case, it suggests that the response has lost its information, and it is not possible to reconstruct the original signal. When fft(g) is too small, the division will sometimes lead to an inaccurate result.

## Automatic Computation of Sampling Interval

When <Auto> is selected for Sampling Interval, the sampling interval needed in the computation is computed automatically by Origin.

The automatically computed sampling interval is the average increment of the time sequence, which is usually from the X column associated with the input signal. If there is no associated X column, the row numbers will be used. Note that if Origin fails to get the average increment, the sampling interval will be set to 1.