Geometrical Representation of Signals
The next eBook I am working on is “Geometrical Representation of Signals”.
In Shannon’s “Communication in the Presence of Noise” he explains the power of representing signals as multi-dimensional geometric vectors. Filters can then be viewed as projections into a region, and transforms as rotations. This way of viewing things has extraordinary power but is not dealt with very much in standard texts. Even more surprisingly, it fits very well with the programming languages Matlab and Octave which are inherently vector/matrix languages, but most examples using those languages do not make the vector nature of the operations explicit and clear.
It is an interesting topic and one I am finding fascinating to address. Not least of the challenges is how to make the idea of the MPEG bitstream for the X-Factor being a 5-trillion-trillion-trillion-dimensional vector, seem like a simplification.