Also known as: Fourier transform

The Fourier transform decomposes a signal into the frequencies that compose it, converting between the time and frequency domains.¹ It is the mathematical foundation of spectrum analysis, named for Joseph Fourier.

The Fourier transform expresses a signal as a sum of frequencies — converting time into spectrum.

How it works

Any signal can be expressed as a sum of sinusoids; the transform reports how much energy exists at each frequency. Its discrete, efficient form is the FFT.

Relevance to SDR

Turning IQ samples into a spectrum — and thus a waterfall — is a Fourier transform, the reason you can see signals on an SDR.

Sources

1. Fourier transform — Wikipedia, for the mathematical definition and time/frequency-domain background. ↩

See also

• Fast Fourier transform (FFT)
• Joseph Fourier
• Bandwidth
• Software-defined radio (SDR)

Learn it step by step

• The FFT & reading a waterfall

From the blog

• SDR Internals, Part 8: Equalization, diversity & the FFT