Wideband spectrum sensing for GHz-wideband spectrum generally in a large number of sample points and a high computational load.Using the signal spectrum sparsity,Sparse Fourier Transform computes wideband signal spectrum efficiently and its computational complexity is lower than the FFT algorithms.In this paper,one of Sparse Fourier Transform algorithm,Hash mapping is studied in detail and spectrum permutation property is proved.In order to reduce the probability of missing sampling points,the signal spectrum is permuted and the signal is window weighted.Then,the signal is aliased in time-domain to realize the spectral down-sampling.Finally,using inverse Hash mapping and voting loop the original spectrum is recovered accurately.The simulation results show that the computational time of this method is about 19 times and 47 times lower than that of the OMP algorithm when the sampling length is increased from 1024 points to 2048 points.%宽带频谱感知一般要求对高达数GHz带宽信号进行频谱分析,信号的采样点数大,计算量大.稀疏傅里叶变换算法利用信号频谱稀疏性,高效计算宽带信号频谱,其计算复杂度低于快速傅里叶变换算法.本文详细研究了稀疏傅里叶变换的哈希映射法,证明了频谱重排性质.为了降低频谱漏采的概率,需先对信号进行频谱重排和时域加窗处理;然后进行时域混叠以实现频谱降采样;最后利用哈希反映射和循环投票方法尽可能准确地从降采样的频谱中恢复宽带信号原频谱,从而实现频谱感知.仿真结果表明当采样长度由1024点增加到2048点时,本文方法的运算时间分别比OMP算法减少约19倍和47倍.
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