Application Research on Sparse Fast Fourier Transform Algorithm in White Gaussian Noise

In sparse fast Fourier transform algorithm, noise will increase the difficulty in frequency location. As to this problem, probability of detected frequency are analyzed with respect to noise level and bucket in this paper. Firstly different mean and variance of compressed vector in frequency domain are derived under the hypothesis of whether there is a signal, then these statistical characteristics are used to analyze the impact of signal-to-noise ratio and number of point per bucket on detection probability of frequency. Finally, simulation curves is given under the conditions of different noise and bucket. Simulation shows that frequency of signal with additive white Gaussian noise could be effectively detected when SNR is higher than 10dB and number of point per bucket smaller than 212. And in order to ensure effective detection of frequency, when SNR decrease, number of point per bucket should be reduced. Through the analysis, this paper provides a theoretical support to enhance the reliability of the algorithm.