Local Maxima of White Noise Spectrograms and Gaussian Entire Functions
نویسندگان
چکیده
Abstract We confirm Flandrin’s prediction for the expected average of local maxima spectrograms complex white noise with Gaussian windows (Gaussian or, equivalently, modulus weighted Entire Functions), a consequence conjectured double honeycomb mean model network zeros and maxima, where area centered hexagons is three times larger than zero hexagons. More precisely, we show that spectrograms, normalized such their density 1, have an 5/3 critical points, among those 1/3 are 4/3 saddle compute distributions ordinate values (heights) spectrogram extrema. This done by first writing in terms Functions (GEFs). The extrema considered under translation invariant derivative Fock space (which this case coincides Chern connection from differential geometry). also observe points GEF precisely random function higher Landau level. discuss natural extensions these functions: Weyl–Heisenberg functions bi-entire functions. paper reviews recent results on applications connections between several developments, partially intended as pedestrian introduction to topic.
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ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2022
ISSN: ['1531-5851', '1069-5869']
DOI: https://doi.org/10.1007/s00041-022-09979-7