Model fitting by least squares |

The second term is called a ``

Equation (3) yields our earlier common-sense guess . It also leads us to wider areas of application in which the elements are complex vectors and matrices.

With Fourier transforms,
the signal is a complex number at each frequency .
Therefore we generalize equation (2) to:

The derivative is the complex conjugate of . Therefore, if either is zero, the other is also zero. Thus, we do not need to specify both and . I usually set equal to zero. Solving equation (5) for gives equation (1).

Equation (1) solves for ,
giving the solution for what is called
``the **deconvolution** problem with a known wavelet .''
Analogously, we can use when the filter is unknown,
but the input and output are given.
Simply interchange and in the derivation and result.

Model fitting by least squares |

2014-12-01