The Fourier Transform (FT) is a mathematical operation used to analyze and process signals and data. It converts a time-domain signal (e.g., audio waveform or series of data points from a sensor) to its frequency-domain representation (a series of sine and cosine components with unique frequencies and amplitudes).

The Fourier Transform is so interesting because it has real applications in our everyday technology. And it’s not just limited to a single field – it’s generally applicable across nearly every domain.

· Barcode scanners

· Guitar tuning apps

· Noise-canceling headphones

· Voice assistants (speech recognition)

· Hearing aids

· Fingerprint recognition

· Video, audio, image compression

· VoIP

· Radio tuning

· Wireless communication (e.g., modulation/demodulation for 4G, 5G, Bluetooth)

· Medical devices (ECG, MRI, continuous glucose monitoring)

· Weather forecasting

· Sonar systems

· Shazam (audio recognition)

· Image editing software (sharpen, filter, pattern detection, denoising)

· Audio editing software (filtering, equalization, denoising)

· Earthquake monitoring

· Oil and natural gas prospecting

· Pricing options and other financial derivatives

· Steganography / watermarking

· Radio astronomy (e.g., analyze black holes)

There are two important improvements that make the FT easier to implement in so many different contexts – Discrete Fourier Transform (DFT) for a discrete set of data points and the Fast Fourier Transform (FFT), which is a more efficient way to compute the DFT.