What is a transform?
What is a transform in the first place? We define a transform as any operation that takes input data and outputs a new representation of it. That is vague, but we think it captures the spirit.
Some common examples are the log transform or an exponential transform as follows:
x is the original data and x’ is the transformed data. Note that in this case, these transforms undo each other. So, our data is recoverable if we apply either of the preceding transformations. This is not always the case. We call these kinds of transformations invertible. The Fourier transform and its discrete counterpart, which we will also discuss, are also invertible transformations!
