Quantitative analysis of SNR in bilinear time frequency domain
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ORIGINAL PAPER
Quantitative analysis of SNR in bilinear time frequency domain Zahra Seddighi1 · Mohammad Reza Ahmadzadeh1 · Mohammad Reza Taban1 Received: 12 May 2019 / Revised: 9 December 2019 / Accepted: 25 April 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Signal-to-noise ratio (SNR) is an essential concept or quantity on the result of a process or on the output of a filter, which helps us in designing, analyzing or evaluating a system. In this paper, we study SNR for bilinear time–frequency transform (TFT). Firstly, according to the definition of SNR in time domain, we define a proper form for SNR in time–frequency (T–F) plane for bilinear TFT; then, we extract SNR relation in terms of TFT kernel, signals power and noise power in time domain. The extracted relation of SNR for bilinear TFT that can be represented in terms of Wigner–Ville distribution (WVD) shows its dependence on the kernel used in the TFT. Finally, to illustrate the applicability of the proposed SNR, the relations of SNR for several distributions are extracted in the T–F domain, and the variation of SNR versus the noise variance is shown by curves. The results show that the WVD has higher SNR than the Rihaczek, Page, spectrogram and Levin respectively. Keywords SNR · Bilinear time–frequency transform · Time–frequency plane · Wigner–Ville distribution
1 Introduction Non-stationary signals have frequency content that varies with time; so time domain representation cannot completely shows what frequencies are present, and frequency domain representation cannot specify when frequencies are present. Time–Frequency (T–F) domain representation can show both of them; so T–F analysis has become a useful technique for analyzing the non-stationary signals with various applications such as radar imaging [1, 2], signal detection and estimation [3–5], image processing [6], speech signal processing [7], signal classification with various modulations [8] and biomedical signal processing [9]. One of the main reasons for the use of T–F analysis is that signal-to-noise ratio (SNR) usually increases in T–F domain over time or frequency domains, so that the signals that are difficult to detect in the time or frequency domains can be more easily detected in the T–F domain. In other * Mohammad Reza Taban [email protected] Zahra Seddighi [email protected] Mohammad Reza Ahmadzadeh [email protected] 1
Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan 84156‑83111, Iran
words, a joint time–frequency transform (TFT) spreads the noise power in the whole T–F domain, while it usually concentrates the signals power on the localized regions. Thus, the SNR can be improved by defining the signals power in these localized regions. Moreover, SNR analysis is a key factor to evaluate the performance of different time–frequency distributions (TFDs). Clearly, SNR analysis in T–F domain is important in terms of applications since one of the most important applications of TFDs is signal detection
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