DFT of an audio signal stored as a multi-dimensional array

1. What is DFT of a signal?
2. Why DCT is used instead of DFT?
3. What is DFT explain with example?
4. What happens if we apply DFT twice to a signal?

What is DFT of a signal?

The Discrete Fourier Transform (DFT) is of paramount importance in all areas of digital signal processing. It is used to derive a frequency-domain (spectral) representation of the signal.

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.

What is DFT explain with example?

the DFT spectrum is periodic with period N (which is expected, since the DTFT spectrum is periodic as well, but with period 2π). Example: DFT of a rectangular pulse: x(n) = 1, 0 ≤ n ≤ (N − 1), 0, otherwise.

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.