Why do we use DIT-FFT and DIF-FFT when we have simple FFT?

Inbaraj, your question is quite curious. There is no "simple FFT". There are many different approaches to compute DFT fast. The DIT-FFT and DIF-FFT are two most widely recognized (and probably most simple) algorithms proposed by Cooley and Tukey. You may use both universally instead of DFT expecting even for lower errors (if round-off is of concern). Sometimes DIT (or DIF) produces a computational error (kind of instability). But it is very rare that both have large errors at the same time index. You may thus select the proper one from two of them.

Agreed with Shmaily answer: I don't get what do you mean by simple FFT. May be you refer to the commands in matlab?. If so, it is not true. FFT can be obtained by widely used DIT/DIF algorithms.

Shmaliy addressed correctly the question. The best implementation of FFT depends on the application, and even the hardware architecture. For example: we was implementing the FFT on FPGA (Field Programmable Gate Array). However, FPGA has a lower frequency than CPU. We realized that FFT is an algorithm where the first step has more independent computation, and in a second step there are more exchange information. Therefore, our implementation was: the first part of the FFT algorithm was executed by FPGA, and the second part goes back to the CPU. In our implementation, the FPGA and CPU work in parallel - see attached paper, other FPGA implementation: http://link.springer.com/chapter/10.1007%2F978-3-642-36812-7_5 .

Hi Haroldo, Thanks for a good example. It shows a typical trade-off at the operation frequency bound of two devices. I guess CPU is the central processing unit - just to those who deal with soft and not well aware of the hardware. And, well, to me who is now more theoretically oriented.

Hi Yuriy: Coorect. CPU is Central Processing Unit. And you are right again: my example is to deal with FFT implementation: software (CPU) and hardware (FPGA).

Thank you for answering my question. It was very helpful.

Mr.InbarajAnbalagan,

If you want to know basic info of any thing as to what it is and brief idea about related topics,always go to Wikipedia Result in Google Search and then you can go for other Search Results for additional info and for highly technical info go for Google Scholar Search Results.

P.S.

Decimation in time FFT and Decimation in frequency FFT are just 2 algorithms to compute the DFT. Mathematically they should obtain EXACTLY the same value as the DFT. In DIT one breaks (decimates) the input signal in time, into even-indexed values and odd-indexed values, so the x(n) series (N=0,1,2...N-1) becomes the x(2r) series and the x(2r+1) series (r=0,1,2...N/2-1), if doing it in radix 2. In the DIF the x(n) series is broken in x(n) for the first half (n=0,1,2...N/2-1) and then for the second half x(n) (n=N/2,N/2+1,...N-1). One can show that this is equivalent to doing the 'evens' and 'odds' breaking in the frequency domain values X(k). The computational difficulty is the same (same numbers of multiplications and sums) for DIT or DIF-FFT: in the DIT butterfly you multiply one of the two input values by the twiddle factor and then add/subtract from the other, in the DIF, you first add/subtract the 2 input values and then multiply the result by the twiddle factor. Open any good book on DSP and it should explain this in detail.

To minimize the calculation time.

The DFT is one of the most powerful tools in digital signal processing which enables us to find the spectrum of a finite-duration signal. There are many circumstances in which we need to determine the frequency content of a time-domain signal. This can be achieved by the discrete Fourier transform (DFT)