Build a signal from harmonics — apply filters — see time & frequency domains
Fourier analysis decomposes any periodic signal into a sum of sinusoids. Low-pass filters remove high-frequency components (detail/noise); high-pass filters remove low-frequency components (trend). Band-pass filters isolate a frequency range — the basis of radio tuning and EQ.
The Fourier transform reveals the frequency content hidden in a signal. Real-world applications include audio equalization, MRI reconstruction, noise cancellation, and digital communications — all rely on the ability to isolate or remove specific frequency bands.