1.  presented by- ARPIT GARG ISHU MISHRA KAJAL SINGHAL B.TECH(ECE) 3RD YEAR

2. FFT stands for fast fourier transform 4k stands for 4000 But normally we consider 4096 point because of N=12 FFT is an Algorithm that efficiently computes the Discrete Fourier Transform(DFT) An FFT is a DFT, but is much faster for calculations. The whole point of the FFT is speed in calculating a DFT.

3.  All Periodic Waves Can be Generated by Combining Sin and Cos Waves of Different Frequencies  Number of Frequencies may not be finite  Fourier Transform Decomposes a Periodic Wave into its Component Frequencies

4.  FFT = Fast Fourier Transform. The FFT is a faster version of the Discrete Fourier Transform (DFT). The FFT utilizes some clever algorithms to do the same thing as the DTF, but in much less time(In the presence of round-off error, many FFT algorithms are also much more accurate than evaluating the DFT definition directly.)round-off error

6.  Assume that N=2 n and let where u=0,1,2,...,N-1 Since N=2 n, there exist M such that N=2M

7.  Sample consists of n points, wave amplitude at fixed intervals of time: (p 0,p 1,p 2,..., p n-1 ) (n is a power of 2)  Result is a set of complex numbers giving frequency amplitudes for sin and cos components  Points are computed by polynomial: P(x)=p 0 +p 1 x+p 2 x 2 +... +p n-1 x n-1

8.  For DFT N*N operations are required in multiplication case For FFT Nlog2(N) operations are required in same case  For ex- we take 1024 samples so 1048576 operations are required in DFT case And in FFT case 10240 operations are required which is 102.4 times faster than DFT.

9.  The twiddle factor, W, describes a "rotating vector", which rotates in increments according to the number of samples, N. Here are graphs where N = 2, 4 and 8 samples. A twiddle factor, in fast Fourier transform (FFT) algorithms, is any of the trigonometric constant coefficients that are multiplied by the data in the course of the algorithmfast Fourier transformtrigonometric

11.  At algorithmic level, the focus is on the development and analysis of FFT algorithms. With this goal, a new approach based on binary tree decomposition. *It uses the Cooley Tukey algorithm to generate a large number of FFT algorithms. *These FFT algorithms have identical butterfly operations and data flow but differ in the value of the rotations. *Along with this, a technique for computing the indices of the twiddle factors based on the binary tree representation has been proposed. We have analyzed the algorithms in terms of switching activity, coefficient memory size.

12.  Higher point FFT (fast Fourier transform) algorithms for a single delay feedback pipelined FFT architecture considering the 4096-point FFT. These algorithms are different from each other in terms of twiddle factor multiplication. Twiddle factor multiplication complexity comparison is presented when implemented on Field- Programmable Gate Arrays (FPGAs) for all proposed algorithms. We also discuss the design criteria of the twiddle factor multiplication. Finally it is shown that there is a trade-off between twiddle factor memory complexity and switching activity in the introduced algorithms.

13. FOR Complexity and Switching Activity

14. 1- INCREASE THE ACCURACY 2- REDUNDANCY 3- REDUCE THE COMPLEXITY

15.  FFT is a high-resolution audio analysis tool for the iPhone and iPod touch. It uses the Fast Fourier Transform to analyze incoming audio, and displays a very detailed graph of amplitude vs. frequency

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