3. Signals and Systems

Fourier Analysis — Quiz

Test your understanding of fourier analysis with 5 practice questions.

Practice Questions

Question 1

For the periodic function $x(t)=t$ defined on $-\pi<t<\pi$ and extended with period $2\pi$, what is the complex Fourier series coefficient $C_k$ for $k\neq0$?

Question 2

If $x(t)$ has complex Fourier series coefficients $C_k$ with fundamental angular frequency $\omega_0$, what is the coefficient $D_k$ of $\dfrac{d}{dt}x(t)$?

Question 3

For a periodic signal with jump discontinuities, its complex Fourier series coefficients $C_k$ decay asymptotically as which of the following as $|k|\to\infty$?

Question 4

What is the continuous-time Fourier transform $X(\omega)$ of the triangular pulse $x(t)=\begin{cases}1-\tfrac{|t|}{T},&|t|\le T,\\\\0,&|t|>T\,,\end{cases}$ using $\mathrm{sinc}(y)=\tfrac{\sin y}{y}$?

Question 5

For a discrete-time signal sampled at $f_s=48\,\mathrm{kHz}$ and zero-padded to length $N=1024$ before computing its DFT, what is the frequency spacing $\Delta f$ between bins?