Quantitative SNR Analyses Of Frequency Modulated Signals In The Time-Frequency Domains

Many kinds of nature signals and artificial signals are non-stationary signals, thestatistical properties of these signals will change over time. As a class of widespreadnon-stationary signals, frequency modulated signals has important research value. Thetime-frequency representations can concentrate frequency modulated signals whilespreading noise in the time-frequency domain, therefore the regional signal-to-noise ratio(SNR) could be substantially improved in these concentrated areas, thus, quantitative SNRanalyses of frequency modulated signals in different time-frequency domain has importantresearch significance.Linear frequency modulated (LFM) signals are the most typical non-stationary signals,which have a wide range of applications in communications, sonar, radar and other fields. Ifa kind of time-frequency distribution can not provide a good time-frequency concentratingperformance, it’s not suitable to be a time-frequency analysis tool for non-stationary signals.In this paper, we presented a quantitative SNR analysis of LFM signals in the linearcanonical transform (LCT) domain, theoretically got the functional expression of the SNRin the LCT domain for LFM signals with the parameters of LCT and window function, thenwe found the condition which made the SNR obtain its maximum value. We also comparedthe SNR in the LCT domain, the short time Fourier transform (STFT) domain, and thepseudo-Wigner distribution (PWVD) domain, to prove the SNR of LFM signals in the LCTdomain can achieve a significantly higher level than that in the STFT domain and thePWVD domain. We also presented some Matlab simulation results to verify our theoreticalresult.Quadratic frequency modulated (QFM) signals widely exists in communications, radar,astronomy, remote sensing, mapping and other disciplines. Third-order local polynomialFourier transform (LPFT) is suitable for processing QFM signals because it uses athird-order polynomial phase signal as its kernel function. In this paper, we proved thatQFM signals can achieve a higher SNR when the three-order coefficient of the LPFT equalsto the quadratic chirp rate of the QFM signals, then we presented a quantitative SNRanalysis of QFM signals in this case, and theoretically got the functional expression of theSNR in the LPFT domain for QFM signals with the parameters of LPFT and window function, then we found the condition which made the SNR obtain its maximum value. Wepresented some Matlab simulation results to verify our theoretical result. We also presentedsome Matlab simulations to compare the SNR in the LPFT domain and the LCT domain,and proved the SNR of QFM signals in the LPFT domain can achieve a significantly higherlevel than that in the LCT domain.