On the zeros of the spectrogram of white noise |
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Institution: | 1. Department of Mathematics, Florida State University, Tallahassee, FL 32306-4510, USA;2. Department of Mathematics and Department of Computer Science and Engineering, Ohio State University, Columbus, OH 43210-1174, USA;1. National Engineering Laboratory of Speech and Language Information Processing, The University of Science and Technology of China, Hefei, China;2. School of Computing, The University of Kent, Medway, UK;3. European Research Center, Huawei Technologies Duesseldorf GmbH, Munich, Germany |
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Abstract: | In a recent paper, Flandrin 16] proposed filtering based on the zeros of a spectrogram with Gaussian window. His results are based on empirical observations on the distribution of the zeros of the spectrogram of white Gaussian noise. These zeros tend to be uniformly spread over the time–frequency plane, and not to clutter. Our contributions are threefold: we rigorously define the zeros of the spectrogram of continuous white Gaussian noise, we explicitly characterize their statistical distribution, and we investigate the computational and statistical underpinnings of the practical implementation of signal detection based on the statistics of the zeros of the spectrogram. The crux of our analysis is that the zeros of the spectrogram of white Gaussian noise correspond to the zeros of a Gaussian analytic function, a topic of recent independent mathematical interest 24]. |
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Keywords: | Short-time Fourier transform Gaussian analytic functions Spatial point processes Signal detection and reconstruction |
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