FFT equivalent for generalized unitary transforms

1. What are the two types of FFT?
2. What is the difference between DFT and IDFT?
3. Why DCT is used instead of DFT?
4. How does Numpy FFT work?

What are the two types of FFT?

These are called the radix-2 and mixed-radix cases, respectively (and other variants such as the split-radix FFT have their own names as well).

What is the difference between DFT and IDFT?

The DFT allows one to convert a set of digital time samples to its frequency domain representation. In contrast, the IDFT can be used to invert the DFT samples, allowing one to reconstruct the signal samples x(k) directly from its frequency domain form, X(m).

Why DCT is used instead of DFT?

> DCT is preferred over DFT in image compression algorithms like JPEG > because DCT is a real transform which results in a single real number per > data point. In contrast, a DFT results in a complex number (real and > imaginary parts) which requires double the memory for storage.

How does Numpy FFT work?

The fft function which uses the functionality of the SciPy package works in a way that, it uses the basic data structures that are used in the numpy arrays, in order to create a module that is required for scientific calculations and programming.