Using Inverse DFT to reconstruct a sampled sine wave is not perfect?

1. What is inverse DFT?
2. What are the limitations of discrete Fourier transform?
3. What happens if we apply DFT twice to a signal?
4. Can we use FFT for Idft?

What is inverse DFT?

An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence. The DFT is therefore said to be a frequency domain representation of the original input sequence.

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 happens if we apply DFT twice to a signal?

Applying the DFT twice results in a scaled, time reversed version of the original series. The transform of a constant function is a DC value only.

Can we use FFT for Idft?

The same FFT algorithm can be adapted in many ways to compute IDFT in a faster way.