Variant of discrete fourier transform that isolates phase delay?

1. What are types Discrete Fourier Transform?
2. Is DFT shift invariant?
3. What are the limitations of discrete Fourier transform?
4. What is the difference between discrete Fourier series and discrete Fourier transform?

What are types Discrete Fourier Transform?

The discrete Fourier transform is an invertible, linear transformation. with denoting the set of complex numbers. Its inverse is known as Inverse Discrete Fourier Transform (IDFT). In other words, for any , an N-dimensional complex vector has a DFT and an IDFT which are in turn. -dimensional complex vectors.

Is DFT shift invariant?

In spite of being linear, the Fourier transform is not shift invariant. In other words, a shift in the time domain does not correspond to a shift in the frequency domain.

What are the limitations of discrete Fourier transform?

These signals can be represented as the sum of a random discrete signal and harmonics of various frequencies. In the Fourier analysis of mixed-structure signals, the disadvantages of DFT are most significantly manifested. These disadvantages are picket-fence, leakage, aliasing effects and amplitude modulation spectrum.

What is the difference between discrete Fourier series and discrete Fourier transform?

There is no operational difference between what is commonly called the Discrete Fourier Series (DFS) and the Discrete Fourier Transform (DFT).