Recent questions tagged fourier-series

A time-limited waveform $\mathrm{g}(x)$ is specified as follows:\[g(x)=\left\{\begin{aligned}-k, && -\pi < x \leq 0 \\+k, && 0 < x \leq \pi \\ 0 , && \text { otherwise ...

A periodic function $f(t)$, with a period of $2 \pi$, is represented as its Fourier series, $$f(t) = a_0 + \sum_{n=1}^{\infty }a_n \cos nt + \sum_{n=1}^{\infty} b_n \sin ...

Let the signal$x(t)=\sum_{k=-\infty }^{+\infty } (-1)^{k} \delta (t-\frac{k}{2000})$be passed through an LTI system with frequency response $H(\omega )$, as given in the ...

Consider $g(t)= \begin{cases} t-\lfloor t \rfloor, & t \geq 0 \\ t-\lceil t \rceil, & \text{otherwise }\end{cases}$, where $t \in \mathbb{R}$.Here, $\lfloor t \rfloor$ r...

Let $f(x)$ be a real, periodic function satisfying $f(-x)=-f(x)$. The general form of its Fourier series representation would be$f(x)=a_{0}+\sum_{k=1}^{\infty}a_{k}\cos(k...