The Geometry of Frequency

Harmonic Analysis · Reading Series

Starting with Fourier atoms, explore frequency direction, surfaces of constant phase, and spatial scale.

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Frequency is more than a number describing how fast something changes. This series starts with a single Fourier atom and explores how the frequency vector encodes the direction of variation, surfaces of constant phase, and spatial scale.

PART I · 2026-10-10

The Basic Geometric Meaning of Frequency in Fourier Analysis (1)

Fourier atoms and frequency · Directional smoothness and frequency localization · Spatial scale versus frequency scale.

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Further articles will appear here as they are published.