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). The atlas finds no named structure, but the source is distinctively extreme on Nonstationarity:variance_trend (+6.9z) — beyond what the standard bank predicts for it. It sits beside Chua's Circuit in the atlas (standard-bank rank 24) — a neighbor conventional features miss.

What standard analysis sees
tail heaviness0.10
asymmetry0.19
occupancy0.81
short-range corr0.95
long-range memory0.95
spectral colour0.11
periodicity0.56
complexity0.05
time-irreversibility0.73
volatility clustering0.93
multifractality0.81
dimensionality0.17
nonstationarity0.80
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Nonstationarity:variance_trend+6.9zbank-miss 1.4σ
Nonstationarity:ac1_trend+5.3zbank-miss 2.1σ
Dodecagonal (Stampfli):pisot_triplet_coherence+3.2zbank-miss 1.3σ
Hölder Regularity:holder_min+2.4zbank-miss 1.2σ
Mostow Rigidity:mean_turn_angle+2.3zbank-miss 1.2σ
Symplectic:phase_volume_explored+2.2zbank-miss 1.8σ
Laplacian:curvature_autocorrelation+2.1zbank-miss 1.2σ
Laplacian:cross_scale_curvature_coherence+2.0zbank-miss 1.2σ

Composition

dtypefloat64
range[-1, 1]
unique values16384 / 16384
mean ± std0.0637 ± 0.709

Render Gallery

Native > phase_plot
Native > phase_plotraw
Native > timeseries
Native > timeseriesraw
Native > triple_lattice
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > lag_map
Boltzmann > spin_grid
Boltzmann > spin_grid
Cayley > default
Cayley > default
Chladni > free_plate_nodal
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_bottom
Chladni > plate_top
Chladni > plate_top
Heisenberg (Nil) (centered) > signed_log_z
Heisenberg (Nil) (centered) > signed_log_z
Heisenberg (Nil) (centered) > xy_path
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
Hodge–Laplacian > default
Inflation (Substitution) > barcode
Inflation (Substitution) > barcode
Inflation (Substitution) > d_curve
Inflation (Substitution) > d_curve
Information Theory > default
Information Theory > default
Julia Set > escape_histogram
Julia Set > escape_histogram
Klein Bottle > default
Klein Bottle > default
Laplacian > default
Laplacian > default
Logarithmic Spiral > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Möbius-S³ > s2_base_map
Ordinal Partition > default
Ordinal Partition > default
Penrose (Quasicrystal) > phi_spectrum
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > barcode
Persistent Homology > h1_diagram
Persistent Homology > h1_diagram
Predictability > default
Predictability > default
Recurrence Quantification > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Analysis > default
Spectral Graph > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > flux_grid
Symplectic > phase_space
Symplectic > phase_space
Ulam Spiral (Sacks) > default
Ulam Spiral (Sacks) > default
Ulam Spiral (Square) > default
Ulam Spiral (Square) > default
Visibility Graph > default
Visibility Graph > default
Wavelet Cascade > default
Wavelet Cascade > default

Atlas Position

Nearest neighborDistance
Duffing Oscillator3.54cross-origin
Chua's Circuit3.64cross-origin
FPUT N=163.83cross-origin

Open in Atlas →

Which Geometries Light Up

Catch24 › Catch24:SB_BinaryStats_diff_longstretch0rank 3/3061993.0000
Laplacian › Laplacian:cross_scale_curvature_coherencerank 3/3060.9994
Laplacian › Laplacian:curvature_autocorrelationrank 3/3060.9994
Laplacian › Laplacian:gradient_sign_persistencerank 3/3060.9969
Laplacian › Laplacian:biharmonic_ratiorank 304/3060.0000
Möbius-S³ › Möbius-S³:hopf_fiber_coherencerank 4/3060.8027
Nonstationarity › Nonstationarity:variance_trendrank 2/3060.7280
Nonstationarity › Nonstationarity:ac1_trendrank 3/3060.3768
Projective ℙ² › Projective ℙ²:mean_distancerank 303/3060.0000
Projective ℙ² › Projective ℙ²:distance_stdrank 304/3060.0000
Symplectic › Symplectic:flux_sign_persistencerank 2/306320.7402
Symplectic › Symplectic:phase_volume_exploredrank 2/3060.8310
Visibility Graph › Visibility Graph:nvg_hvg_reach_divergencerank 1/3060.9985
Wasserstein › Wasserstein:transport_variabilityrank 1/3060.2082
Wasserstein › Wasserstein:recurrence_distancerank 2/3060.0999
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Structure Atlas — Open Atlas · GitHub