Plotting Signals Using Singularity Functions with Application to Convolution and Fourier Series of Square/Triangular Wave Signals

Singularity functions are an important topic in undergraduate studies covered primarily in signal processing. Some of those functions are the step function, the ramp function and the parabolic function. Using the step function, several different periodic square waves can be formed. Using the ramp function several periodic triangular waves can be formed. To achieve this, MATLAB functions called stp_fn, rmp_fn, par_fn, and cub_fn were written. This allows the study of Fourier Series of such signals which is a method of expressing a periodic signal as a sum of sinusoids. To obtain such series the complex exponential form was used. MATLAB programs were written to see how many sinusoidal terms (harmonics) are needed to approximate a square wave and a triangular wave. The Gibbs phenomenon is observed as well. The Fourier Series allows someone to observe the components of a signal which would otherwise be very difficult to observe. Moreover, Fourier Series makes filtering or manipulating the components of a signal possible. A convolution of two signals is included in this work as well.