Exponential Chirp
signal-synthesis · 37 views
signal-synthesisperiodic
What It Is
Exponential frequency sweep --- instantaneous frequency grows geometrically, creating equal time per octave. Used in acoustic measurements and radar
Interpretation
Standard analysis sees: bounded / light-tailed; smooth / autocorrelated; long-range memory (persistent); red spectrum (low-frequency / 1-over-f power); low-complexity (predictable, not noise-like); volatility-clustering (bursty); low-dimensional. The atlas additionally detects Multifractal Spectrum:hurst_estimate. It sits beside Chua's Circuit in the atlas (standard-bank rank 87) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.10
asymmetry0.64
occupancy0.74
short-range corr0.96
long-range memory0.94
spectral colour0.12
periodicity0.57
complexity0.06
time-irreversibility0.79
volatility clustering0.93
multifractality0.83
dimensionality0.13
nonstationarity0.82
What the atlas adds
Multifractal Spectrum:hurst_estimate+2.4z
self-affinity H = τ(2)/2 (alternate to Hölder hurst)
Atlas-extreme metrics the standard bank can’t predict for this source
Nonstationarity:variance_trend | +6.8z | bank-miss 1.5σ |
Nonstationarity:ac1_trend | +5.2z | bank-miss 1.3σ |
Dodecagonal (Stampfli):pisot_triplet_coherence | +3.2z | bank-miss 1.7σ |
Hölder Regularity:holder_min | +2.4z | bank-miss 1.4σ |
Visibility Graph:degree_exponent_gamma | -2.3z | bank-miss 1.4σ |
Symplectic:phase_volume_explored | +2.2z | bank-miss 1.9σ |
Composition
dtypefloat64
range[-1, 1]
unique values16384 / 16384
mean ± std0.0637 ± 0.709
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Exponential_Chirp.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Exponential_Chirp.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Exponential_Chirp.png)
Inflation (Substitution) > barcode
/d_curve/Exponential_Chirp.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/Exponential_Chirp.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/Exponential_Chirp.png)
Ulam Spiral (Sacks) > default
/default/Exponential_Chirp.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Duffing Oscillator | 3.54 | cross-origin |
| Chua's Circuit | 3.63 | cross-origin |
| FPUT N=16 | 3.82 | cross-origin |
Which Geometries Light Up
Catch24 › Catch24:SB_BinaryStats_diff_longstretch0 | rank 3/307 | 1993.0000 |
Laplacian › Laplacian:cross_scale_curvature_coherence | rank 3/307 | 0.9994 |
Laplacian › Laplacian:curvature_autocorrelation | rank 3/307 | 0.9994 |
Laplacian › Laplacian:gradient_sign_persistence | rank 3/307 | 0.9969 |
Laplacian › Laplacian:biharmonic_ratio | rank 305/307 | 0.0000 |
Möbius-S³ › Möbius-S³:hopf_fiber_coherence | rank 4/307 | 0.8027 |
Nonstationarity › Nonstationarity:variance_trend | rank 2/307 | 0.7280 |
Nonstationarity › Nonstationarity:ac1_trend | rank 3/307 | 0.3768 |
Projective ℙ² › Projective ℙ²:mean_distance | rank 304/307 | 0.0000 |
Projective ℙ² › Projective ℙ²:distance_std | rank 305/307 | 0.0000 |
Symplectic › Symplectic:flux_sign_persistence | rank 2/307 | 320.7402 |
Symplectic › Symplectic:phase_volume_explored | rank 2/307 | 0.8310 |
Visibility Graph › Visibility Graph:nvg_hvg_reach_divergence | rank 1/307 | 0.9985 |
Wasserstein › Wasserstein:transport_variability | rank 1/307 | 0.2082 |
Wasserstein › Wasserstein:recurrence_distance | rank 2/307 | 0.0999 |
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