SNS Re-Exam 2018-19

The trigonometric fourier series of an even function of time does not contain

• (a) sine term

• (b) odd harmonics term

• (c) cosine term

• (d) DC term

Fourier series uses which domain representation of signals?

• a) Time domain representation

• b) Frequency domain representation

• c) Both combined

• d) Neither depends on the situation

What are the values of an and bn when the signal is even?

• a) an=0 and bn=0

• b) $a_n\ =0\ and\ b_{n\ }=\frac{4}{T}\int_{\ }x\left(t\right)\cos\left(nwt\right)dt$

• c) $b_n\ =0\ and\ a_{n\ }=\frac{4}{T}\int_{\ }x\left(t\right)\cos\left(nwt\right)dt$

• d) $b_n\ =\frac{4}{T}\int_{\ }x\left(t\right)\cos\left(nwt\right)dt\ \ ;\ \ a_{n\ }=\frac{4}{T}\int_{\ }x\left(t\right)\sin\left(nwt\right)dt$

What are fourier coefficients?

• a) The terms that are present in a fourier series

• b) The terms that are obtained through fourier series

• c) The terms which consist of the fourier series along with their sine or cosine values

• d) The terms which are of resemblance to fourier transform in a fourier series are called fourier series coefficients

Calculate the value of a0 for the periodic exponential signal

Write all the dirichlets condition for the existence of fourier series

Find the fourier transform of an exponential signal
 $x\left(t\right)=e^{-at\ }u\left(t\right)\ for\ a>0$  

Determine system function of a system having impulse response given by h(t) =e^-3t u(t). If the input to this system is given by x(t) = e^-2t u(t), the output of the system using fourier transform can be given by

• $H\left(jw\right)=\frac{1}{3+jw}\ \ and\ y\left(t\right)\ =e^{-2t\ }u\left(t\right)-e^{-3t\ }u\left(t\right)$

• $H\left(jw\right)=\frac{1}{3-jw}\ \ and\ y\left(t\right)\ =e^{2t\ }u\left(t\right)-e^{3t\ }u\left(t\right)$

• $H\left(jw\right)=\frac{1}{3+jw}\ \ and\ y\left(t\right)\ =e^{-2t\ }u\left(-t\right)-e^{-3t\ }u\left(t\right)$

• $H\left(jw\right)=\frac{1}{3+jw}\ \ and\ y\left(t\right)\ =e^{-2t\ }u\left(t\right)+e^{-3t\ }u\left(t\right)$

The Fourier transform of f(t)=te^-at u(t) is given by

• $\frac{1}{\left(a-jw\right)^2}$

• $\frac{1}{\left(a+jw\right)^2}$

• $\frac{a}{\left(a-jw\right)^2}$

• $\frac{w}{\left(a-jw\right)^2}$

Find the inverse Fourier transform of X(ω)
 $X\left(jw\right)=\frac{6+4jw\ }{jw^{2\ }+6jw\ +8}$  

•  $e^{-2t}u\left(t\right)-5e^{-4t}u\left(t\right)$  

•  $e^{-2t}u\left(t\right)+\ 5e^{-4t}u\left(t\right)$  

•  $-e^{-2t}u\left(t\right)-5e^{-4t}u\left(t\right)$  

•  $-e^{-2t}u\left(t\right)+\ 5e^{-4t}u\left(t\right)$