Mathematics for Engineering $3$

Ihs$0-$December $2023-$ Lecture notes and calculators authorised

Consider the periodic function $\backslash ($ P$($t$)\backslash )($square pulse$)$ shown in Figure $1.$

Find the Fourier series approximation of $\backslash ($ P$($t$)\backslash )$

For the particular case where $\backslash ($ t$=\backslash$frac$\{$T$\}\{2\}\backslash )$

$-$ Verify that the Fourier coefficients are correct using the results about the square wave signal in the lecture notes. Clear explanations, please!

$-$ Draw the discrete spectrun of $\backslash ($ P$($t$)\backslash )$

$-$ Using Parseval's theorem, find how many harmonics are needed to represent $\backslash (95\backslash \%\backslash )$ of this signal power?

$-$ Find the Fourier series coefficients of $\backslash ($ P$($t$-$a$)\backslash )$

$-$ Consider the square wave signal in Figure $2($non$-$periodic $-$ a single pulse is considered$)$