Equations
One of my favorite features of this website is the ability to include equations!
Let \(x(t)\) denote a continuous-time signal, corresponding to a current or voltage in an electrical circuit. The time variable \(t\) takes values on the real line, i.e., \(t\in \mathbb{R}=(-\infty,+\infty)\), and is measured in units of seconds.
The continuous-time Fourier transform (CTFT) of the signal \(x(t)\) is defined as \[ X(f) := \int_{-\infty}^{+\infty} x(t) e^{-j2\pi f t} dt, \tag{1}\] where the frequency variable \(f\) also takes values on the real line, i.e., \(f\in\mathbb{R}\), and is measured in units ofcycles per second or Hertz, which is abbreviated Hz1.
As we see in Equation 1, there is an infinite integral, which should be interpreted as the limit \[ X(f) := \lim_{T\rightarrow\infty} \int_{-T}^{+T} x(t) e^{-j2\pi f t} dt, \] assuming the limit exists.
Citations
In (Kleber 2021), the author studies system-level characterization of wideband spectrum sensor networks based upon very low-cost, individual RF sensors.
In (Pezeski 2018), the author explores a new communication approach in which a given transmission can be decoded by any of a number of potential receivers in a network, instead of having a specific association to and requiring decoding by a particular receiver.
References
Footnotes
The units of natural frequency are named after the German physicist Heinrich Hertz, who experimented with electromagnetic waves.↩︎