Questions & Answers of Continuous-time and discrete-time Fourier series

Weightage of Continuous-time and discrete-time Fourier series

Total 5 Questions have been asked from Continuous-time and discrete-time Fourier series topic of Signals and Systems subject in previous GATE papers. Average marks 1.20.

The magnitude and phase of the complex Fourier series coefficients ak of a periodic signal x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation C is the set of complex numbers, R is the set of purely real numbers, and P is the set of purely imaginary numbers.

Let $\stackrel{~}{x}\left[n\right]=1+\mathrm{cos}\left(\frac{\mathrm{\pi n}}{8}\right)$ be a periodic signal with period 16. Its DFS coefficients are defined by $a_k=\frac1{16}\sum\limits_{n=0}^{15}\widetilde x\left[n\right]exp\left(-j\frac{\mathrm\pi}8kn\right)$ for all $k$. The value of the coefficients a31 is_____.

Let $g\left(t\right)={e}^{-\pi {t}^{2}}$ , and h(t) is a filter matched to g(t) . If g(t) is applied as input to h(t) , then the Fourier transform of the output is

The trigonometric Fourier series of an even function does not have the