Existence and estimation of impropriety in real rhythmic signals

In this paper, we relax a commonly-used assumption about a class of nonstationary random processes composed of modulated wide-sense stationary random processes: that the fundamental frequency of the modulator is stationary within the analysis window. To compensate for the relaxation of this assumption, we define the generalized DEMON ("demodulated noise") spectrum representing modulation frequency, which we use to increase the coherence time of such signals. Increased coherence time means longer analysis windows, which provides higher SNR estimators. We use the example of detection on both synthetic and real-world passive sonar signals to demonstrate this increase.

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“…Clark et al examined the spectral impropriety of real-valued signals in [10]. Here we do the same, though with a different formulation.…”

Section: Connection To Spectral Improprietymentioning

confidence: 89%

Extending coherence time for analysis of modulated random processes

Wisdom

Atlas

Pitton

2014

2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…Recently, several researchers have begun analyzing the noncircularity of real-valued signals in complex-valued transform domains. In particular, Clark, Kirsteins, and Atlas [16] studied the spectral circularity of real time-domain signals using a modulation model and showed that certain properties of a real timedomain signal can produce noncircularity in the spectral domain. In the work presented here, we study the circularity of complex-valued subbands for a class of signals modeled on voiced speech.…”

Section: A Backgroundmentioning

confidence: 99%

“…As in (1), we demodulate the signal with a complex exponential of frequency and apply a lowpass filter. When , the subband is given by (14) Assuming that the cutoff frequency of is lower than , the subband is (15) The sample circularity coefficient for is (16) Substituting the relation in (15), (16) reduces to (17) Thus, ; the perfectly demodulated sinusoid is rectilinear.…”

Section: Signal Subband Noncircularitymentioning

confidence: 99%

“…Intuitively, when the demodulator is mistuned to the signal, the error will cause a slow rotation over time of the estimated modulator. When the sample circularity coefficient of is computed using (16), the slow rotation causes the estimated modulator to look more circular. The speed of this slow rotation is simply .…”

Section: B Effect Of Demodulation Mistuning On Subband Noncircularitymentioning

confidence: 99%

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Speech Analysis With the Strong Uncorrelating Transform

Okopal

Wisdom

Atlas

2015

IEEE/ACM Trans. Audio Speech Lang. Process.

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The strong uncorrelating transform (SUT) provides estimates of independent components from linear mixtures using only second-order information, provided that the components have unique circularity coefficients. We propose a processing framework for generating complex-valued subbands from real-valued mixtures of speech and noise where the objective is to control the likely values of the sample circularity coefficients of the underlying speech and noise components in each subband. We show how several processing parameters affect the noncircularity of speech-like and noise components in the subband, ultimately informing parameter choices that allow for estimation of each of the components in a subband using the SUT. Additionally, because the speech and noise components will have unique sample circularity coefficients, this statistic can be used to identify time-frequency regions that contain voiced speech. We give an example of the recovery of the circularity coefficients of a real speech signal from a two-channel noisy mixture at 25 dB SNR, which demonstrates how the estimates of noncircularity can reveal the time-frequency structure of a speech signal in very high levels of noise. Finally, we present the results of a voice activity detection (VAD) experiment showing that two new circularity-based statistics, one of which is derived from the SUT processing, can achieve improved performance over state-of-the-art VADs in real-world recordings of noise.

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“…This work highlights the importance of SOS characterization for complex analysis of Gaussian RVs and higher order statistics for other RVs. Many real-world problems render improper random signals in diverse fields requiring appropriate analysis and treatment e.g., in medicine [6], [20], [21], [102], [124], [145]- [147], oceanography [13], [148], [149], geology [12], [14]- [16], [103], [150]- [152], optics [10], [153], [154], acoustics [11], [155], [156], power systems [18], [19], [157], [158]. and communication systems [4]- [7], [9], [22]- [26], [28], [32], [48], [67]- [69], [107], [108], [159]- [161].…”

Section: Overviewmentioning

confidence: 99%

A Journey From Improper Gaussian Signaling to Asymmetric Signaling

Javed

Amin

Shihada

et al. 2020

IEEE Commun. Surv. Tutorials

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The deviation of continuous and discrete complex random variables from the traditional proper and symmetric assumption to a generalized improper and asymmetric characterization (accounting correlation between a random entity and its complex conjugate), respectively, introduces new design freedom and various potential merits. As such, the theory of impropriety has vast applications in medicine, geology, acoustics, optics, image and pattern recognition, computer vision, and other numerous research fields with our main focus on the communication systems. The journey begins from the design of improper Gaussian signaling in the interference-limited communications and leads to a more elaborate and practically feasible asymmetric discrete modulation design. Such asymmetric shaping bridges the gap between theoretically and practically achievable limits with sophisticated transceiver and detection schemes in both coded/uncoded wireless/optical communication systems. Interestingly, introducing asymmetry and adjusting the transmission parameters according to some design criterion render optimal performance without affecting the bandwidth or power requirements of the systems. This dual-flavored article initially presents the tutorial base content covering the interplay of reality/complexity, propriety/impropriety and circularity/non-circularity and then surveys majority of the contributions in this enormous journey.

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Existence and estimation of impropriety in real rhythmic signals

Cited by 9 publications

References 15 publications

Extending coherence time for analysis of modulated random processes

Extending coherence time for analysis of modulated random processes

Speech Analysis With the Strong Uncorrelating Transform

A Journey From Improper Gaussian Signaling to Asymmetric Signaling

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