FFT one-sided and Parseval theorem

1. What is Parseval's theorem in Fourier series?
2. What are the two types of FFT?
3. What is FFT and IFFT in DSP?
4. What does parseval's theorem imply?

What is Parseval's theorem in Fourier series?

Parseval's Theorem states that the total energy computed in the time domain must equal the total energy computed in the frequency domain. It is a statement of conservation of energy.

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 FFT and IFFT in DSP?

FFT (Fast Fourier Transform) is able to convert a signal from the time domain to the frequency domain. IFFT (Inverse FFT) converts a signal from the frequency domain to the time domain. The FFT of a non-periodic signal will cause the resulting frequency spectrum to suffer from leakage.

What does parseval's theorem imply?

In mathematics, Parseval's theorem usually refers to the result that the Fourier transform is unitary; loosely, that the sum (or integral) of the square of a function is equal to the sum (or integral) of the square of its transform.