Why is the last value of an RFFT always real?

1. Is the FFT of a real signal real?
2. What is a real FFT?
3. What is the output of FFT?
4. What is the difference between DFT and DCT?

Is the FFT of a real signal real?

Most real-world signals are real-valued. Therefore, you can use the real fast Fourier transform (FFT) for most applications. You also can use the complex FFT by setting the imaginary part of the signal to zero.

What is a real FFT?

The real portion of an FFT result is how much each frequency component resembles a cosine wave, the imaginary component, how much each component resembles a sine wave.

What is the output of FFT?

These frequencies actually represent the frequencies of the two sine waves which generated the signal. The output of the Fourier transform is nothing more than a frequency domain view of the original time domain signal.

What is the difference between DFT and DCT?

Like the discrete Fourier transform (DFT), a DCT operates on a function at a finite number of discrete data points. The obvious distinction between a DCT and a DFT is that the former uses only cosine functions, while the latter uses both cosines and sines (in the form of complex exponentials).