What are Wavelets?

Fourier Analysis · Axiom Academy

Discover a new way to analyze signals with localized oscillating functions. A wavelet means "small wave" - it's a wave that starts at zero, oscillates briefly, and returns to zero. Move the slider to adjust the "width" of this wavelet. Compare a sine wave (which extends forever) with a wavelet (which is localized). Move the position slider to shift the wavelet along the time axis. Extends infinitely in both directions Concentrated in a specific region Step 3: Capturing Transient Events Imagine you're analyzing a signal with a sudden burst or spike. Click the "Show Transient Event" button to see how a localized event appears in a signal. Step 4: Wavelets as Building Blocks Just like Fourier analysis decomposes signals into sine waves, wavelet analysis decomposes signals into wavelets at different positions and scales. Click to see this decomposition in action. Decomposes signals into sine and cosine waves. Perfect for analyzing stationary signals - signals whose frequency content doesn't change over time. Tells us "what frequencies" are present. Decomposes signals into localized wavelets. Perfect for analyzing non-stationary signals - signals with time-varying frequency content. Tells us "what frequencies" and "when" they occur. Wavelets don't replace Fourier analysis - they complement it! Use Fourier for steady-state analysis, use wavelets for time-varying phenomena. Together, they give us a complete toolkit for understanding signals.

This is the written version of the interactive lesson above. See the full Fourier Analysis course.