Signal Detection Based on Power-Spectrum Sub-Band Energy Ratio

Abstract

The power-spectrum sub-band energy ratio (PSER) has been applied in a variety of fields, but reports on its statistical properties and application in signal detection have been limited. Therefore, the statistical characteristics of the PSER were investigated and a signal detection method based on the PSER was created in this paper. By analyzing the probability and independence of power spectrum bins, as well as the relationship between F and beta distributions, we developed a probability distribution for the PSER. Our results showed that in a case of pure noise, the PSER follows beta distribution. In addition, the probability density function exhibited no relationship with the noise variance—only with the number of bins in the power spectrum. When Gaussian white noise was mixed with the signal, the resulting PSER followed a doubly non-central beta distribution. In this case, the probability density and cumulative distribution functions were represented by infinite double series. Under the constant false alarm strategy, we established a signal detector based on the PSER and derived the false alarm probability and detection probability of the PSER. The main advantage of this detector is that it did not need to estimate noise variance. Compared with time-domain energy detection and local spectral energy detection, we found that the PSER had better robustness under noise uncertainty. Finally, the results in the simulation and real signal showed that this detection method was valid.

Two error controllable computing algorithms for the CDF of doubly non-central beta distribution

“…In practice, the doubly non-central beta or F distributions are widely used. Li et al [2] confirmed that in the presence of a signal, the detection statistic, that is, the power spectrum sub-band energy ratio, conforms to the doubly non-central beta distribution. Giner-Bosch et al [3] confirmed that the multivariate coefficient of variation used in monitoring obeys the singly non-central F distribution, which is a special case of the doubly non-central F distribution.…”

Motor fault detection using sound signature and wavelet transform

“…The signal-to-noise ratio (SNR) is a regularly used process to evaluate the quality of a signal and estimate the influence of noise on a signal. In this process, the power ratio of the signal power to the total noise is estimated by the spectral data [20], [21]. In fast Fourier transform (FFT), the captured waveform data samples will be transformed into the frequency domain where the captured signal will be in the form as shown in (1).…”

“…That is, a discrete signal X[n] decomposition can be presented as in (7). followed by a down-sampling by two driven by mother wavelet and the scaling function [20], [21], [28], as shown in Figure 1, which makes DWT suitable for signal analysis with fewer data samples and particularly for transient signals. However, in this work, instantaneous amplitude measurements and waveform dynamic range will be based on the low-pass approximation coefficients to eliminate noises and obtain an accurate reading.…”

“…As a result, detection of sound changes can be determined through waveform amplitude voltage change and dynamic range increases (ratio of the largest and smallest component of a signal that can be measured expressed in dB [21]). DR can be given by (10).…”

Nonlinear dielectric spectroscopy biosensor for SARS-CoV-2 detection

“…Power Spectrum Analysis has been a major tool to detect particular characteristics of the event(s), including amplitudes, energy ratio, frequency, noise, correlation, probability density, cumulative distribution function, etc. occurred in the recorded signal from different sources through the Fast Fourier Transform (FFT) 8 . The relevant statistical signal analysis aspects have been applied to detect single nanoparticles and biological molecules such as yeast ribosomes floating in fluids exposed to laser beams 9 .…”