Research And Implementation Of Low Complexity Fast Fourier Transform(FFT)

Automatic gain control(AGC)technology is widely used in digital signal processing field,especially inco-channel interference OFDM modulation system.The automatic gain truncation method can save the storage space and reduce the bit width requirement of the the fast Fourier transform(FFT)calculation unit,but it has the problem of calculation precision,especially when the spectral amplitude of the overall data distribution is not uniform,the calculation accuracy will be significantly reduced.And the above error will be amplified with the iterative transfer,and ultimately make the FFT results decline in accuracy.Firstly,this dissertation improves the FFT algorithm based on the 2~r-DFT calculation unit,the data need calculation is divided into some groups and each data is indexed,and the data of the same group has a same group index;by reusing the 2~r-DFTcalculation unit,the proposed FFT algorithm has simpler circuit structure and additional memory storage compared with the FFT algorithm of prior art.When the size of the whole data need calculation is not uniform,the data will be grouped by setting the number of data thresholds,each of data has data index,the data of a group has the same data index,that is,each group has different group index,the data of each group has the same group index,the data of each group shall be calculated with 2~r-DFT calculation unit,and FFT calculation results of each group shall be superimposed,scanned,updated the data index,stored,and the above process will repeat unless all the data of a stage completes butterfly calculation.The dissertation describes and simulates the FFT algorithm with the Matlab software,and achieves bit-match with the completed design circuit.The simulation results show that the calculation precision of the proposed FFT algorithm is the same as the FFT algorithm of the prior art when the size of the whole data is uniform,and the proposed FFT algorithm has higher calculation precision than FFT algorithm of prior art when the size of the whole data is not uniform,which can improve the calculation precision of the 2-3 bit data bit width.The proposed FFT algorithm can be widely used in the applications of digital signal processing,especially applied in the receiver and signal generator.