Overview: In chapter two, the most basic waveform in signal processing, the cosine wave, is presented. The mathematical formula for the cosine wave, in its most general form is given below: $$x(t)=A \cos(2 \pi f_0 t + \varphi)$$ Where \(x(t)\) is a function of the time variable \(t\). The amplitude of the cosine is given by the real number \(A\). The frequency of the of the cosine wave is \(f_0\), and in the audio experiments that follow, it is the frequency that determines what we hear. Finally, the phase of the sinusoid is given by the parameter \(\varphi\). A plot of a cosine is given in the figure below:

Also in chapter two, the phasor representation of sinusoids is presented. A new signal is introduced called the complex exponential:

$$x(t)= A e^{j(2 \pi f_0 t + \varphi)}$$

The generalization to complex exponentials is important for later work in Fourier analysis, so we are laying a foundation for the future. The real part of the complex exponential is a cosine, and its imaginary part is the sine function, so a plot of the complex exponential is a rotating vector with a constant length \(A\). This signal is called a rotating phasor.

Demos - MATLAB 6

Demos - LabVIEW 3

Labs - MATLAB 4

Labs - LabVIEW 2