Abstract
The purpose of this paper is to present a quantitative SNR analysis of quadratic frequency modulated (QFM) signals. This analysis is located in the continuous-time local polynomial Fourier transform (LPFT) domain using a Gaussian window function based on the definition of 3 dB signal-to-noise ratio (SNR). First, the maximum value of the local polynomial periodogram (LPP), and the 3 dB bandwidth in the LPFT domain for a QFM signal is derived, respectively. Then, based on these results, the 3 dB SNR of a QFM signal with Gaussian window function is given in the LPFT domain with one novel idea highlighted: the relationship among standard SNR, parameters of QFM signals and Gaussian window function is clear, and the potential application is demonstrated in the parameter estimation of a QFM signal using the LPFT. Moreover, the 3 dB SNR in the LPFT domain is compared with that in the linear canonical transform (LCT) domain. The validity of theoretical derivations is confirmed via simulation results. It is shown that, in terms of SNR, QFM signals in the LPFT domain can achieve a significantly better performance than those in the LCT domain.
Similar content being viewed by others
References
Wang J Z, Su S Y, Chen Z P. Parameter estimation of chirp signal under low SNR. Sci China Inf Sci, 2015, 58: 020307
Cohen L. Time-frequency distributions-a review. Proc IEEE, 1989, 77: 941–981
Whitelonis N, Ling H. Radar signature analysis using a joint time-frequency distribution based on compressed sensing. IEEE Trans Antenn Propagat, 2014, 62: 755–763
Chen V C, Ling H. Joint time-frequency analysis for radar signal and image processing. IEEE Signal Process Mag, 1999, 16: 81–93
Pitton J W, Wang K S, Juang B H. Time-frequency analysis and auditory modeling for automatic recognition of speech. Proc IEEE, 1996, 84: 1199–1215
Amin M G. Interference mitigation in spread spectrum communication systems using time-frequency distributions. IEEE Trans Signal Process, 1997, 45: 90–101
Xia X-G. A quantitative analysis of SNR in the short-time Fourier transform domain for multicomponent signals. IEEE Trans Signal Process, 1998, 46: 200–203
Bai G, Tao R, Zhao J, et al. Fast FOCUSS method based on bi-conjugate gradient and its application to space-time clutter spectrum estimation. Sci China Inf Sci, 2017, 60: 082302
Mu W F, Amin M G. SNR analysis of time-frequency distributions. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Turkey, 2000. II645–II648
Li X M, Bi G A, Ju Y T. Quantitative SNR analysis for ISAR imaging using LPFT. IEEE Trans Aerosp Electron Syst, 2009, 45: 1241–1248
Xia X-G, Wang G Y, Chen V C. Quantitative SNR analysis for ISAR imaging using joint time-frequency analysis-short time Fourier transform. IEEE Trans Aerosp Electron Syst, 2002, 38: 649–659
Stankovic L, Ivanovic V, Petrovic Z. Unified approach to noise analysis in the Wigner distribution and spectrogram. Ann Telecommun, 1996, 11: 585–594
Stankovic L, Stankovic S. Wigner distribution of noisy signals. IEEE Trans Signal Process, 1993, 41: 956–960
Ouyang X, Amin M G. Short-time Fourier transform receiver for nonstationary interference excision in direct sequence spread spectrum communications. IEEE Trans Signal Process, 2001, 49: 851–863
Song J, Niu Z Y, Zhang J Y. OFD-LFM signal design and performance analysis for distributed aperture fully coherent radar. Sci China Inf Sci, 2015, 45: 968–984
Xia X-G, Chen V C. A quantitative SNR analysis for the pseudo Wigner-Ville distribution. IEEE Trans Signal Process, 1999, 47: 2891–2894
Li X M, Bi G, Stankovic S, et al. Local polynomial Fourier transform: a review on recent developments and applications. Signal Process, 2011, 91: 1370–1393
Wu Y, Li B Z, Cheng Q Y. A quantitative SNR analysis of LFM signals in the linear canonical transform domain with Gaussian windows. In: Proceedings of IEEE International Conference on Mechatronic Sciences, Electric Engineering and Computer (MEC), Shengyang, 2013. 1426–1430
Li Y, Liu K, Tao R, et al. Adaptive viterbi-based range-instantaneous Doppler algorithm for ISAR imaging of ship target at sea. IEEE J Ocean Eng, 2015, 40: 417–425
O’Shea P. A fast algorithm for estimating the parameters of a quadratic FM signal. IEEE Trans Signal Process, 2004, 52: 385–393
Bai X, Tao R, Wang Z, et al. ISAR imaging of a ship target based on parameter estimation of multicomponent quadratic frequency-modulated signals. IEEE Trans Geosci Remote Sens, 2014, 52: 1418–1429
Wang Y, Zhao B. Inverse synthetic aperture radar imaging of nonuniformly rotating target based on the parameters estimation of multicomponent quadratic frequency-modulated signals. IEEE Sens J, 2015, 15: 4053–4061
Katkovnik V. Discrete-time local polynomial approximation of the instantaneous frequency. IEEE Trans Signal Process, 1998, 46: 2626–2637
Djurović I, Thayaparan T, Stanković L. Adaptive local polynomial Fourier transform in ISAR. EURASIP J Adv Signal Process, 2006, 2006: 36093
Katkovnik V, Gershman A B. A local polynomial approximation based beamforming for source localization and tracking in nonstationary environments. IEEE Signal Process Lett, 2000, 7: 3–5
Guo Y, Li B Z. Blind image watermarking method based on linear canonical wavelet transform and QR decomposition. IET Image Process, 2016, 10: 773–786
Xu T Z, Li B Z. Linear Canonical Transform and Its Application. Beijing: Science Press, 2013
Bu H X, Bai X, Tao R. Compressed sensing SAR imaging based on sparse representation in fractional Fourier domain. Sci China Inf Sci, 2012, 55: 1789–1800
Liu F, Xu H F, Tao R, et al. Research on resolution between multi-component LFM signals in the fractional Fourier domain. Sci China Inf Sci, 2012, 55: 1301–1312
Wei D Y, Li Y M. Generalized sampling expansions with multiple sampling rates for lowpass and bandpass signals in the fractional Fourier transform domain. IEEE Trans Signal Process, 2016, 64: 4861–4874
Feng Q, Li B Z. Convolution and correlation theorems for the two-dimensional linear canonical transform and its applications. IET Signal Process, 2016, 10: 125–132
Shi J, Liu X P, He L, et al. Sampling and reconstruction in arbitrary measurement and approximation spaces associated with linear canonical transform. IEEE Trans Signal Process, 2016, 64: 6379–6391
Zhang Z C. Tighter uncertainty principles for linear canonical transform in terms of matrix decomposition. Digital Signal Process, 2017, 69: 70–85
Wei D Y, Li Y M. The dual extensions of sampling and series expansion theorems for the linear canonical transform. Optik -Int J Light Electron Opt, 2015, 126: 5163–5167
Kou K I, Xu R H. Windowed linear canonical transform and its applications. Signal Process, 2012, 92: 179–188
Kou K I, Zhang R H, Zhang Y H. Paley-Wiener theorems and uncertainty principles for the windowed linear canonical transform. Math Method Appl Sci, 2012, 35: 2212–2132
Tao R, Li Y L, Wang Y. Short-time fractional Fourier transform and its applications. IEEE Trans Signal Process, 2010, 58: 2568–2580
Yin Q, Shen L, Lu M, et al. Selection of optimal window length using STFT for quantitative SNR analysis of LFM signal. J Syst Eng Electron, 2013, 24: 26–35
Varadarajan V S. Some problems involving Airy functions. Commun Stoch Anal, 2012, 1: 65–68
Popescu S A. Mathematical analysis II integral calculus. https://doi.org/civile.utcb.ro/cmat/cursrt/ma2e.pdf
Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 61671063), and also by Foundation for Innovative Research Groups of National Natural Science Foundation of China (Grant No. 61421001).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhang, YN., Li, BZ., Goel, N. et al. Quantitative SNR analysis of QFM signals in the LPFT domain with Gaussian windows. Sci. China Inf. Sci. 62, 22302 (2019). https://doi.org/10.1007/s11432-017-9322-2
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11432-017-9322-2