PUZZLE #4240: Gabor Wavelet Frequency Detection (diff 3)
Analyze a 1000-sample signal with 4 candidate frequencies. Apply a Gabor wavelet (Gaussian windowed sinusoid) at each candidate frequency and find the one with maximum magnitude response.
DATA
| Signal |
0.36566, -1.552603, -3.030852, -2.500689, -0.35894, 1.446389, 1.588446, 0.635119, -0.004524, 0.083375, 0.102026, -0.441005, -0.731147, 0.320207, 2.313202, 3.326555, 1.938134, -1.074795, -3.4596, -3.787106, -2.598227, -1.234627, -0.113958, 1.286461, 2.944712, 3.611294, 2.142545, -0.766348, -2.841203, -2.457217, -0.274993, 1.630476, 2.016559, 1.392558, 0.759412, 0.11303, -1.23491, -3.086885, -3.91184, -2.435462, 0.627935, 3.01091, 3.166466, 1.721557, 0.450293, 0.167749, 0.15661, -0.386823, -1.025899, -0.718796, 0.49429, 1.170332, 0.151294, -1.833829, -2.799991, -1.727532, 0.318907, 1.509022, 1.303434, 0.726694, 0.724325, 0.913077, 0.364549, -0.759562, -1.095755, 0.176599, 1.983347, 2.308275, 0.453376, -2.12297, -3.402694, -2.864684, -1.578735, -0.510276, 0.570839, 2.19297, 3.723703, 3.605047, 1.249304, -1.817474, -3.234573, -2.169021, -0.007403, 1.34766, 1.410085, 1.020499, 0.710906, -0.069226, -1.808875, -3.57129, -3.541776, -1.095035, 2.175902, 3.911688, 3.308756, 1.615894, 0.39174, -0.173579, -0.869526, -1.826583, -2.04307, -0.800819, 0.985019, 1.49146, 0.090871, -1.787757, -2.212787, -0.87662, 0.757996, 1.336735, 1.071608, 1.033983, 1.434131, 1.304842, 0.019116, -1.486179, -1.603322, -0.073982, 1.467931, 1.264221, -0.581894, -2.300992, -2.510032, -1.546318, -0.579077, 0.085418, 1.157961, 2.851644, 3.933435, 2.897328, -0.055585, -2.807053, -3.362419, -1.804521, 0.092756, 0.957712, 0.994448, 1.004687, 0.887576, -0.194312, -2.211809, -3.571494, -2.59571, 0.456824, 3.377696, 4.172607, 2.899328, 1.124743, -0.080551, -1.01574, -2.198231, -3.040975, -2.366596, -0.164653, 1.852985, 1.911752, 0.157525, -1.492426, -1.495417, -0.235189, 0.793524, 0.935109, 0.914372, 1.433482, 1.902575, 1.146626, -0.809676, -2.351767, -2.012865, -0.25294, 0.994671, 0.519535, -0.89759, -1.613192, -1.097282, -0.262944, 0.07025, 0.349087, 1.458587, 3.057259, 3.487854, 1.652775, -1.42875, -3.442766, -3.122899, -1.360278, 0.111932, 0.660994, 0.932629, 1.343397, 1.183965, -0.31804, -2.42951, -3.164004, -1.376957, 1.778249, 3.898817, 3.715355, 2.041501, 0.382769
|
| Samplerate |
1000
|
| Candidate Freqs |
59.65, 97.74, 115.6, 193.91
|
| Sigma |
0.6
|
| Difficulty |
3
|
| Hint |
Gabor transform: G(τ,f) = ∫ s(t)·g(t-τ)·e^(-2πift) dt, where g(t) is Gaussian with σ=0.60. 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 3
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