Why idft(dft(a) * dft(b)) not equal to convolve(a, b)?

1. Is DFT and Idft same?
2. What is the relation between circular convolution and DFT?
3. What is Idft and DFT?

Is DFT and Idft same?

DFT (Discrete Fourier Transform) is a practical version of the DTFT, that is computed for a finite-length discrete signal. The DFT becomes equal to the DTFT as the length of the sample becomes infinite and the DTFT converges to the continuous Fourier transform in the limit of the sampling frequency going to infinity.

What is the relation between circular convolution and DFT?

It is called circular convolution. The convolution is circular because of the periodic nature of the DFT sequence. Recall that an N-point DFT of an aperiodic sequence is periodic with a period of N. Also recall that the IDFT is essentially a DFT with a small difference.

What is Idft and DFT?

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).