What is the need of FFT?

FFT and DFT yields same result and are actually same transforms of converting time or spatial domain signal into frequency domain signal. FFT is actually an optimized way of getting DFT of a time domain signal. Computers use FFT method for faster processing to convey time domain signal to frequency domain signal. The no. of multiplications and additions in case of FFT are way less than using the actual DFT formula.

This picture has dimensions 240×320240×320, which is 76,800 pixels.

It takes roughly 7.67 milliseconds to perform a two-dimensional FFT of this image. How long does it take to evaluate the DFT without using the FFT algorithm? As far as I know, it’s over one minute. I stopped the program when one minute had passed.

Another comparison is below : 

N-point DFT	N-point FFT
Multiplications: N2	Multiplications: (N/2) log2(N)
Addition: N(N-1)	Addition: Nlog2(N)
Example: N =1000 Additions: 1000x999 Multiplications: 106	Example: N =1000 Additions: 1000log2(1000) = 104(approx.) Multiplications: 5120 (approx..)