Fourier Transforms: The Bridge Between Time and Frequency

A Fourier transform converts a signal from the time domain into the frequency domain.
It reveals which pure frequencies are hidden inside any complex waveform.
In physics, it connects vibrations in time to energy distributions in frequency.
Radio engineers use it to tune signals and filter noise from broadcasts.
Fourier transforms let doctors see inside the body through MRI imaging.
Quantum mechanics uses them to switch between position and momentum descriptions.
They power modern technologies like speech recognition, radar, and Wi-Fi.
In astronomy, they help decode light from distant stars into spectral fingerprints.
The fast Fourier transform (FFT) makes these calculations practical on computers.
At its heart, the Fourier transform is a translator between the worlds of time and frequency.