Question

Which of the following signal does not have Fourier series representation ?

• A. $x\left(t\right)=sin\left(\frac{2\pi }{t}\right),0<1\le 1,withtimeperiodT=1$
• B. $x\left(t\right)=1-|t|,-1<t\le 1,withtimeperiodT=2$
• C. $x\left(t\right)=|sin4t|,0<t\le \frac{\pi }{4},withtimeperiodt=\frac{\pi }{4}$
• D. $x\left(t\right)=|t|,-1<t\le 1,withtimeperiodT=2$

Answer 1

The correct option is A $x\left(t\right)=sin\left(\frac{2\pi }{t}\right),0<1\le 1,withtimeperiodT=1$

$x\left(t\right)=sin\left(\frac{2\pi }{t}\right),0<t\le 1$

With time period, T = 1
This function has infinite number of maxima and minima in one time period.
$\therefore$ This signal is not satisfying dirichlet conditions of Fourier series.