What is W ? W is the constant вЂњtwiddle factorвЂќ 3. Why do we divide by 2? To avoid arithmetic overflow 2. Am-1 Bm-1 Am Bm -1 W Am= (Am-1 + Bm-1)/2 Bm= (Am-1 - Bm-1)*W/2 Arish Alreja: Low Power Design for a 64 Point FFT Processor (2006)ДЁ Arish Alreja: Low Power Design for a 64 Point FFT Processor (2006)ДЇFT Complex Butterfly Am-1 Bm-1 Am Bm -1 W 1. O(n2) X(ejпЃ·) = пЃ“ x* e-jпЃ·n With some Mathematical rearrangements we get the Fast Fourier Transform Algorithm FFT Algorithm O(nlog2n) Arish Alreja: Low Power Design for a 64 Point FFT Processor (2006)Д§ Arish Alreja: Low Power Design for a 64 Point FFT Processor (2006)ДЇFT Complex Butterfly The basic operation in the FFT algorithm is the Complex Butterfly calculation. Time Domain Frequency Domain Arish Alreja: Low Power Design for a 64 Point FFT Processor (2006)Д¦ Computation Discrete/Digital FT X(ejпЃ·) = пЃ“ x* e-jпЃ·n DFT Algorithm Motivation FFT is the most computationally intensive part of OFDM 802.11a WiFi standard requires 64 point FFT for OFDM Low Power FFT improves battery life on mobile devices Arish Alreja: Low Power Design for a 64 Point FFT Processor (2006)ДҐ Arish Alreja: Low Power Design for a 64 Point FFT Processor (2006)ДЇourier Transforms Fourier Transforms allow Frequency Domain representation of a signal in the Time Domain. Motivation Orthogonal Frequency Division Multiplexing (OFDM) is used in a WiFi chipsets to achieve higher resiliency against errors due to multipath fading by encoding data over multiple carrier frequencies Arish Alreja: Low Power Design for a 64 Point FFT Processor (2006)Д¤ Arish Alreja: Low Power Design for a 64 Point FFT Processor (2006) Arish Alreja: Low Power Design for a 64 Point FFT Processor (2006)ДЈ Arish Alreja: Low Power Design for a 64 Point FFT Processor (2006) Overview We will discuss Motivation Fourier Transforms and FFTs (briefly) A low power 64 point FFT Processor. 1 Low Power Design for a 64 point FFT ProcessorДў Arish Alreja: Low Power Design for a 64 Point FFT Processor (2006)

Matlab 64 point fft