![Maharashtra Institute of Technology, Aurangabad
Electrical Engineering
FAST FORIER TRANSFORM (FFT)
Presented by:
Sumedh A. Bhagat [EE1180]](https://image.slidesharecdn.com/sumedhbhagatdspppt-221222041933-52813a02/85/Digital-signal-processing-DSP-PPT-pptx-1-320.jpg)
Digital signal processing (DSP PPT).pptx
- 1. Maharashtra Institute of Technology, Aurangabad Electrical Engineering FAST FORIER TRANSFORM (FFT) Presented by: Sumedh A. Bhagat [EE1180]
- 2. Fast Fourier Transform FFT A fast Fourier transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT) and inverse of DFT. There are many FFT algorithms which involves a wide range of mathematics,. A Discrete Fourier transform decomposes a sequence of values into components of different frequencies. This operation is very useful in many fields but computing it directly from the definition is often too slow to be practical .
- 3. Cont .. • FFT are special algorithms for speedier implementation of DFT. • FFT requires a smaller number of arithmetic operations such as multiplications and additions than DFT. • FFT also requires lesser computational time than DFT .
- 4. Fast Fourier Transform Algorithms • • Direct computation of the DFT is less efficient because it does not exploit the properties of symmetry and periodicity of the phase factor WN = e–j2π/N. These properties are: - Symmetry property. - Periodicity property. • As we already know that all computationally efficient algorithms for DFT are collectively known as FFT Algorithms and these algorithms exploit the above two properties of phase factor, WN.
- 5. Alternate DIT FFT structures • DIT structure with input natural, output bit-reversed (OSB 9.14):
- 6. Alternate DIT FFT structures • DIT structure with input bit-reversed, output natural
- 7. • • Example Find the DFT of the following discrete-time sequence . s(n) = {1, -1, -1, -1, 1, 1, 1, -1} using Radix-2 decimation-in-frequency FFT algorithm. • Solution. The Twiddle factor or phase rotation factor WN= involved in the FFT calculation are found out as follows for N= 8.