Discrete Fourier Transform as Memory?

1. What is discrete Fourier transform used for?
2. Why DCT is used instead of DFT?
3. Is DFT lossless?
4. What is the drawback of DFT?

What is discrete Fourier transform used for?

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.

Is DFT lossless?

> The DFT over the reals is not lossless.

What is the drawback of DFT?

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.