Comprehensive introduction to analysis of continuous and discrete-time signals and systems. Linear time-invariant systems, convolution; Fourier series representations of periodic signals; Continuous ...

Let f(u) be the Fourier-Stieltjes transform of a real or complex-valued function F(α) of bounded variation on (— ∞, ∞). It is shown that if f(u) belongs to L2 on an interval of infinite range, then ...

Design linear discrete-time systems and filters and analyze their behavior. Represent continuous-time signals and linear systems in discrete time, so that such signals can be recovered in continuous ...

Lie groups provide a natural framework for describing continuous symmetries in both mathematics and physics. These groups, which are simultaneously smooth manifolds, allow for the integration of ...

Amid the chaos of revolutionary France, one man’s mathematical obsession gave way to a calculation that now underpins much of mathematics and physics. The calculation, called the Fourier transform, ...

A key algorithm that quietly empowers and simplifies our electronics is the Fourier transform, which turns the graph of a signal varying in time into a graph that describes it in terms of its ...