GATE ECE
Signals and Systems
Transmission of Signal Through Continuous Time LTI Systems
Previous Years Questions

## Marks 1

Let x1(t) = e$$-$$t u(t) and x2(t) = u(t) $$-$$ u(t $$-$$ 2), where u( . ) denotes the unit step function. If y(t) denotes the convolution of x1(t) an...
The outputs of four systems (S1, S2, S3 and S4) corresponding to the input signal sin(t), for all time t, are shown in the figure. Based on the given ...
A continuous-time sinusoid of frequency 33 Hz is multiplied with a periodic Dirac impulse train of frequency 46 Hz. The resulting signal is passed thr...
A real - values signal x(t) limited to the frequency band $$\left| f \right| \le {W \over 2}$$ is passed through a linear time invariant system whose ...
Assuming zero initial condition, the response y (t) of the system given below to a unit step input u(t) 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 outpu...
Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is ...
A system with the transfer function $${{Y(s)} \over {X(s)}} = {s \over {s + p}}\,\,$$ has an output $$y(t) = \cos \left( {2t - {\pi \over 3}} \righ... In the system shown below, x(t) = (sint)u(t). In steady-state, the response y(t) will be ... A low-pass filter having a frequency response$$H(j\omega )$$=$$A(\omega ){e^{j\Phi (\omega )}}$$, does not product any phase distortion if A linear phase channel with phase delay$${\tau _p}$$and group delay$${\tau _g}$$must have The input to a channel is a band pass signal. It is obtained by linearly modulating a sinusoidal carrier with a signal- tone signal. The output of the... A rectangular pulse of duration T is applied to a filter matched to this input. The output of the filter is a ## Marks 2 A continuous-time filter with transfer function$$\,H(S) = {{2s + 6} \over {{s^2} + 6s + 8}}$$is converted to a discrete time filter with transfer fu... A first-order low-pass filter of time constant T is excited with different input signals (with zero initial conditions up to t = 0). Match the excitat... In the system shown in Figure (a), m(t) is a low-pass signal with bandwidth W Hz. The frequency response of the band-pass filter H(f) is shown in Figu... The 3 - dB bandwidth of the low - pass signal$${e^{ - 1}}$$u(t), where u(t) is the unit step function, is given by A system has poles at 0.01 Hz, 1 Hz and 80 Hz; zeros at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is Consider the signal x(t) shown in Fig. Let h(t) denote the impulse response of the filter matched to x(t), with h(t) being non-zero only in the interv... The system under consideration is an RC low -pass filter (RC-LPF) with R = 1.0$$k\Omega $$and C = 1.0$$\mu F$$. Let$${t_g}$$(f) be the group del... The system under consideration is an RC low -pass filter (RC-LPF) with R = 1.0$$k\Omega $$and C = 1.0$$\mu F$$. Let H(t) denote the frequency resp... In Fig. m(t) =$$ = {{2\sin 2\pi t} \over t}$$,$$s(t) = \cos \,200\pi t\,\,andn(t) = {{\sin 199\pi t} \over t}$$. The output y(t) will be ... A system has a phase response given by$$\phi \,(\omega )$$where$$\omega $$is the angular frequency. The phase delay and group delay at$$\omega $$... The input to a matched filter is given by$$s(t) = \left\{ {\matrix{ {10\sin (2\pi \times {{10}^6}t),} & {0 < \left| t \right| < {{10}^{...
Sketch the waveform (with properly marked axes) at the output of a matched filter matched for a signal s(t), of duration T, given by $$s(t) = \left\{ ... The pole-zero pattern of a certain filter is shown in the Fig. The filter must be of the following type. ... The magnitude and phase transfer functions for a distortionless filter should respectively be: Specify the filter type if its voltage transfer function H(s) is given by H(s) =$${{K({s^2} + {\omega _0}^2)} \over {{s^2} + ({\omega _0}/Q)s + {\o...

## Marks 5

A base band signal g(t) band limited to 100 Hz modulates a carrier of frequency $${{f_0}}$$ Hz. The modulated signal g(t) $$\cos 2\,\pi \,{f_0}t$$ is ...
A signal 3 sin $$\left( {\pi \,\,{f_0}t} \right) + \,5\,\,\cos \,\,\,(3\pi \,\,{f_0}t)$$ is applied to an RC low pass filter of 3 dB cutoff frequency ...
An input signal A exp $$\left( { - \alpha \,t} \right)$$ u(t) with $$\alpha > 0$$ is applied to a causal filter, the impulse response of which is ...
A signal, f(t) = $${e^{ - at}}$$ u(t), where u(t) is the unit step function, is applied to the input of a low-pass filter having $$\left| {H(\omega )}... Obtain an expression for the signal in figure, for the signal$${v_3}(t)$$in Fig for$${v_1}(t) = 100\cos (2000\pi t) + 4\sin (200\pi t). Assume ...
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