Fourier transform-based signal analyzers

Signal analyzers based on the Fourier transform, sometimes simplistically referred to as "spectrum analyzers", are essential and constantly evolving instruments. They are used to analyze a signal in both time and frequency domains, and even in the joint time-frequency domain. They can also provide other information such as autocorrelation and intercorrelation functions, spectral density, transfer function and impulse response of a system, and measure useful parameters such as time and statistical averages, dispersion, signal-to-noise ratio, time-frequency resolution... They represent one of the most promising segments of the test and measurement market, and are growing by almost 8% a year. This growth is driven by the need for bandwidth in applications such as military radar and telecommunications for 5G or even 6G technology.

This article provides an almost exhaustive treatment of advances in the field of Fourier transform-based signal analyzers, both in terms of methodology and functionality. It complements, updates and extends classical Fourier transform-based signal analysis, taking into account recent developments in "analog" and digital systems.

Such an approach paves the way for design, measurement, analysis and processing tools adapted to today's digital and artificial intelligence revolution.

Indeed, since 1996 – when the first version of this article was published –, the world has seen a veritable digital revolution in terms of both technology and socio-economics, with the explosion of Internet use and exponential progress in computing and artificial intelligence. All human activities have undergone unprecedented upheaval, whether in radio and television, medicine, industry (industry 4.0 and 4.1 and the beginnings of industry 5.0) or in the global networking of people and all human organizations, thanks to new forms of communication such as electronic mail or e-mail, social networks, instant messaging, blogs and the proliferation of websites. The technological breakthrough of this century is undoubtedly linked to the advent of the Internet and its many technological variations, from intelligent robotics with the famous Sophia to ChatGPT, as well as the lightning advances in telecommunications, in particular mobile telephony, which is moving from the first generation (1G) to 5G, with 6G and its undreamt-of possibilities on the horizon:

• holograms and virtual/augmented reality;

• ever-increasing data throughput (up to 1,000 times greater than 5G);

• the bandwidth or need for frequencies beyond millimeter waves (gigahertz), now focusing on the terahertz spectrum (radiation between microwaves and infrared);

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