Miscellaneous · Signals and Systems · GATE ECE

The waveform of a periodic signal x(t) is shown in the figure. A signal g(t) is defined by $$g(t) = x\left( {{{t - 1} \over 2}} \right)$$. The ...

Consider the function $$g(t) = {e^{ - t}}\,\,\,\sin (2\pi t)\,u(t)$$ where u(t) is the unit step function. The area under g(t) is_______________.

The phase response of a passband waveform at receiver is given by $$\varphi \,(f) = - 2\,\pi \,\alpha \,(f - {f_c}) - \,2\pi \beta \,{f_c}$$ where $...

A discrete - time signal x[n] = $${\rm{sin(}}\,{\pi ^2}n)$$, n being an integer is

For a periodic signal v(t) = 30 sin 100t + 10cos 300t + 6sin $${\rm{(500t + }}\,\pi /4)$$, the fundamental frequency in rad/s is

Consider an angle modutated signal $$x(t) = 6\,\,\cos \,[2\,\pi \, \times {10^6}t + 2\sin (8000\pi t)\,4\cos (8000\pi t)]$$ V. The average power of ...

The Dirac delta function $$\delta (t)$$ is defined as

A solution for the differential equation $$\mathop x\limits^. $$(t) + 2 x (t) = $$\delta (t)$$ with intial condition $$x({0^ - }) = 0$$ is

The function x(t) is shown in Fig. Even and odd parts of a unit-step function u(t) are respectively. ...

Let $$\delta (t)$$ denote the delta function. The value of the the integral $$\int\limits_{ - \infty }^\infty {\delta (t)} \,\,\cos \left( {{{3\,\,t}...

The ACF of a rectangular pulse of duration T is

The complex envelope of the bandpass signal $$x(t) = - \sqrt 2 \left( {{{\sin \,(\pi t/5)} \over {\pi t/5}}} \right)\,\sin \,\left( {\pi t - {\pi \o...

An LTI system having transfer function $${{{s^2} + 1} \over {{s^2} + 2s + 1}}$$ and input x(t) = sin (t + 1) is in steady state. The output is sampled...

A Hilbert transformer is a

In the following scheme, if the spectrum M(f) of m(t) is as shown, then the spectrum Y(f) of y(t) will be: ...

As x is increased from $$ - \infty \,\,to\,\infty $$, the function $$f(x) = {{{e^x}} \over {1 + {e^x}}}$$

Match the following and choose the correct combination. GROUP 1 E- continuous and aperiodic signal F- continuous and periodic signal G- discr...

The value of the integral $$\,I = {1 \over {\sqrt {2\,\,\pi } }}\int\limits_0^\infty {\exp \left( { - {{{x^2}} \over 8}} \right)dx} $$ is

The derivative of the symmetric function drawn in Fig .1 will look like ...

Consider the sequence $$x[n] = [ - \,4 - \,j5,\,\mathop {1 + j2}\limits_ \uparrow ,\,\,4]$$ The conjugate anti-symmetric part of the sequence is ...

Match each of the items, A, B and C, with an appropriate item from 1, 2, 3, 4 and 5 A. Fourier transform of a Gaussian function B. Convolution of ...