Does DFT produces the same output as FFT?

The FFT is an efficient DFT algorithm, so in the limit of infinite precision arithmetic, they will give the same output, albeit the direct DFT implementation will be much slower.

1. Is the result from DFT and FFT same?
2. How is DFT different from FFT?
3. What is the output of a DFT?
4. What is the output of FFT?

Is the result from DFT and FFT same?

The Fast Fourier Transform (FFT) is an implementation of the DFT which produces almost the same results as the DFT, but it is incredibly more efficient and much faster which often reduces the computation time significantly. It is just a computational algorithm used for fast and efficient computation of the DFT.

How is DFT different from FFT?

Discrete Fourier Transform (DFT) is the discrete version of the Fourier Transform (FT) that transforms a signal (or discrete sequence) from the time domain representation to its representation in the frequency domain. Whereas, Fast Fourier Transform (FFT) is any efficient algorithm for calculating the DFT.

What is the output of a DFT?

All DFT outputs for a real N-sample input sequence with even N follow this pattern: 1 real value, N/2-1 complex values, 1 real value, N/2-1 conjugates. A diagram of the 64-point example is shown below, where blue squares indicate non-redundant information.

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.