Radix-2 2 Based Low Power Reconfigurable FFT Processor Presented by Cheng-Chien Wu, Master Student of CSIE,CCU 1 Author: Gin-Der Wu and Yi-Ming Liu Department of Electrical Engineering NCNU Source: IEEE International Symposium on Industrial Electronics(ISIE2009)
Outline – Introduction – Discrete Fourier Transform(DCT) – Radix - 4 Fast Fourier Transform(FFT) – Radix FFT – Architecture of Radix – Conclusion 2
Outline – Introduction – Discrete Fourier Transform(DCT) – Radix - 4 Fast Fourier Transform(FFT) – Radix FFT – Architecture of Radix – Conclusion 3
Introduction 4 Fast Fourier Transform (FFT) is widely applied in the speech processing, image processing, and communication system.
Introduction(cont’d) 5 Important FFT issues – High throughput – FFT size – Power consumption
Outline – Introduction – Discrete Fourier Transform(DCT) – Radix - 4 Fast Fourier Transform(FFT) – Radix FFT – Architecture of Radix – Conclusion 6
Discrete Fourier Transform(DCT) 7 DFT definition equation: – x: Input array – X: Output array – N: FFT size – W: Twiddle Factor – n: Input element – K: Output element NxN adders NxN multipliers
DCT(cont’d) 8 Twiddle factor: – e: natural number – X: Output array – N: FFT size – n: Input element – K: Output element – i: Imaginary unit
Outline – Introduction – Discrete Fourier Transform(DCT) – Radix - 4 Fast Fourier Transform(FFT) – Radix FFT – Architecture of Radix – Conclusion 9
DCT to FFT 10 An FFT computes the DFT and produces exactly the same result as evaluating the DFT definition directly the only difference is that an FFT is much faster
Radix-4 FFT 11 Based on the radix-4 algorithm, the DFT of signal is divided into four partitions Where F = 0,1,2,3…..N-1 ; k = 0,1,2,3…..N/4-1
Radix-4 FFT(cont’d) 12
Radix-4 FFT(cont’d) 13
Radix-4 FFT(cont’d) 14
Radix-4 FFT(cont’d) 15 According to the above equations, we use the same manner to obtain the other samples as the following equations
Radix-4 FFT(cont’d) 16 Butterfly graph of Radix-4 FFT
2 Stage Butterfly graph of Radix-4 17
Butterfly graph of Radix-2 FFT 18
Outline – Introduction – Discrete Fourier Transform(DCT) – Radix - 4 Fast Fourier Transform(FFT) – Radix FFT – Architecture of Radix – Conclusion 19
Radix-2 2 FFT 20 We rewrite the previous equation of radix -4 FFT algorithm as follows
Radix-2 2 FFT Insert T1,T2,T3,T4 into equation 21
Radix-2 2 FFT BF Butterfly graph of the radix-2 2 FFT 22
Compared with the radix - 2 and 4 reduce the multiplication complexity of radix - 4 Much faster than the conventional radix -2 FFT 23
Outline – Introduction – Discrete Fourier Transform(DCT) – Radix - 4 Fast Fourier Transform(FFT) – Radix FFT – Architecture of Radix – Conclusion 24
Hardware architecture Pipeline based – Single delay feedback pipeline (SDF) – Multiple-path delay commutator pipeline (MDC) Memory based 25
Hardware architecture Pipeline based – Single delay feedback pipeline (SDF) – Multiple-path delay commutator pipeline (MDC) Memory based 26
Reconfigurable FFT Processor 27
Input data with the radix-2 2 The inputs and outputs have 4 real part and 4 imaginary part respectively 28
radix-2 2 butterfly unit architecture 29
Reconfigurable FFT Processor 30
FFT Register array 31
Bank 32
Analysis The total gate count of the FFT processor is about synthesized and estimated with TSMC.13 μm standard. The max clock frequency is 100 MHz. The total execution needs 332 clock cycles. The latency is about 3.32μs(332X10ns) 33
Power Consumption The main source of power consumption in a typical CMOS logic gate is due to the switching power, Psw. 34
Power Consumption(cont’d) Vdd : supply voltage F : clock frequency C load : load capacitance of the gate K : the average number of times that the gate makes an active transition in a single clock cycle. 35
Comparison of Several Researches 36
Outline – Introduction – Discrete Fourier Transform(DCT) – Radix - 4 Fast Fourier Transform(FFT) – Radix FFT – Architecture of Radix – Conclusion 37
Conclusions The Radix FFT processor is low power consumption. The Radix FFT processor has more flexibility. 38
Thanks for Listening 39