Math Transforms

First, I would like ask to readers that you comment the posts, because I need know your preference about the issues.

Now, talking about math transforms, I want to "open the reader's eyes".

The idea over any math transform is see the information of other form, for example: the Fourier Transform enables a frequency analysis if the signal is in time, ou temporal analysis if the signal is in frequency.

The transformations can be linears, non-linears, inversibles, non-inversibles, unambiguous, etc....

The transformation y = A x is a linear transformation, where x is the input information, A is the matrix of transformation and y is the output information.

The Discrete Fourier Transform (DFT) can be calculated by: dft(x) = A x, where each element of A is a complex exponencial exp(w n). If the matrix A is inversible, the transformation y = A x is inversible.

Some transformations are very non-linear as Hough Transform, used in image processing, where the output is a vector that represents the suport straight of the most significant axis on the image. In this case, the transformation is non-inversible because many images have similars principal axis.

Closing the post: math transforms are functions that mapping a set in other set.