Now, on to the subject of complex numbers. We have stayed away from this subject until now simply because we did not want to confuse things. Initially, it is easy to think of signals as “real valued.” ...

All kinds of parameters can be described using complex numbers of the form real + j * imaginary. The numerical values of real and imaginary can vary over very wide ranges. Trying to graph them ...

Physicists construct theories to describe nature. Let us explain it through an analogy with something that we can do in our everyday life, like going on a hike in the mountains. To avoid getting lost, ...

Several years ago one of us, Toni, asked another of us, Marco, to come to his office at the Institute of Photonic Sciences, a large research center in Castelldefels near Barcelona. “There is a problem ...

A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth ...