PUZZLE #4941: Gabor Wavelet Frequency Detection (diff 2)
Analyze a 1000-sample signal with 3 candidate frequencies. Apply a Gabor wavelet (Gaussian windowed sinusoid) at each candidate frequency and find the one with maximum magnitude response.
DATA
| Signal |
2.709489, 3.682204, 1.382171, -1.818875, -2.875521, -1.072761, 1.422368, 1.937759, 0.085704, -1.917762, -1.683512, 0.747314, 2.865473, 2.281322, -0.733498, -3.389645, -3.101434, -0.050004, 2.97915, 3.294791, 0.829803, -1.955202, -2.573128, -0.847156, 1.177482, 1.475913, 0.055162, -1.257812, -0.879684, 0.836097, 2.001257, 1.198902, -1.007842, -2.586296, -2.009862, 0.280855, 2.319075, 2.4419, 0.721295, -1.27117, -1.977652, -1.143478, 0.216921, 0.929657, 0.681693, 0.072351, -0.156891, 0.13932, 0.468818, 0.28069, -0.447685, -1.143526, -1.117826, -0.175716, 1.133975, 1.849715, 1.311418, -0.253568, -1.772814, -2.082888, -0.878996, 0.943187, 1.956159, 1.403094, -0.125124, -1.225583, -1.001311, 0.090859, 0.741063, 0.187617, -0.912509, -1.126568, 0.165192, 1.894499, 2.205461, 0.373888, -2.208375, -3.158843, -1.398407, 1.648876, 3.272024, 2.036003, -0.819143, -2.585799, -1.747012, 0.575563, 1.856362, 0.819011, -1.240573, -1.860613, -0.104532, 2.304192, 2.682912, 0.242029, -2.887595, -3.636317, -1.073287, 2.544423, 3.89044, 1.79058, -1.666294, -3.23114, -1.678794, 1.121348, 2.256571, 0.773042, -1.456815, -1.830089, 0.170364, 2.395718, 2.29088, -0.363086, -3.088553, -3.144954, -0.296798, 2.889564, 3.519372, 1.134717, -1.946976, -2.963795, -1.320302, 1.066844, 1.865493, 0.630507, -0.975182, -1.097791, 0.34354, 1.65389, 1.223734, -0.735414, -2.358438, -1.983944, 0.194698, 2.301086, 2.537454, 0.793678, -1.374113, -2.23496, -1.354378, 0.250886, 1.216485, 1.023519, 0.227814, -0.286217, -0.173314, 0.179539, 0.179033, -0.329248, -0.89738, -0.890145, -0.082793, 1.063394, 1.681521, 1.155759, -0.321429, -1.759159, -2.045575, -0.849021, 1.001115, 2.088125, 1.568487, -0.069764, -1.404505, -1.359568, -0.194516, 0.787135, 0.581142, -0.456862, -0.971065, -0.097298, 1.452176, 1.957667, 0.484128, -1.921395, -3.009977, -1.50063, 1.490824, 3.324008, 2.308144, -0.622957, -2.761549, -2.237454, 0.190439, 1.973628, 1.401285, -0.674256, -1.801686, -0.591455, 1.720277, 2.504768, 0.554824, -2.460217, -3.520287, -1.310894, 2.303263, 3.97744, 2.135765, -1.473695, -3.493285, -2.227092
|
| Samplerate |
1000
|
| Candidate Freqs |
113.74, 164.7, 174.94
|
| Sigma |
0.5
|
| Difficulty |
2
|
| Hint |
Gabor transform: G(τ,f) = ∫ s(t)·g(t-τ)·e^(-2πift) dt, where g(t) is Gaussian with σ=0.50. Compute magnitude at each candidate frequency. The frequency with the highest peak is the answer.
|
| Answer Format |
frequency in Hz with unit (e.g., '112.7hz')
|
author's note: Pool fill: gabor-wavelet diff 2
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