Decomposing Signals

Fourier Analysis · Axiom Academy

How can we break complex waves into simple sine and cosine components? Click each wave type to see how sine and cosine waves look with different parameters. Adjust the amplitudes to see how waves combine. The sum appears in green. Click "Add Harmonic" to see how we can approximate a square wave using only sines! Given a complex wave, how do we find its sine and cosine components? This wave is made of hidden components. Can you guess which ones? Sine and cosine waves at different frequencies (harmonics) are our fundamental components. Complex waves are built by adding simple waves with different amplitudes. Any periodic function can be written as: f(x) = a₀ + Σ[aₙcos(nx) + bₙsin(nx)] The Fourier coefficients (aₙ, bₙ) tell us how much of each harmonic is present.

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