The magnitude and phase of the complex Fourier series coefficients a_{k} 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 a_{31} is_____.
Let $g(t)={e}^{-\pi {t}^{2}}$ , 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
The Fourier series of a real periodic function has only
P. Cosine terms if it is even Q. Sine terms if it is even R. Cosine terms if it is odd S. Sine terms if it is odd
Which of the above statements are correct?