Signal Properties

The radian frequency value(s) for which the discrete time sinusoidal signal $x[n] = A \cos(\Omega n + \pi/3)$ has a period of 40 is/are __.

A causal and stable LTI system with impulse response h(t) produces an output y(t) for an input signal x(t) . A signal x(0.5t) is applied to another causal and stable LTI system with impulse response h(0.5t) . The resulti...

Let $$m(t)$$ be a strictly band-limited signal with bandwidth B and energy E. Assuming $${\omega _0} = 10B$$, the energy in the signal $$m(t)\cos {\omega _0}t$$ is

In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics (i) Continuous, aperiodic (a) Continuous, aperiodic (ii) Continuous, periodic (b) Continuous, period...

Consider a system with input $$x(t)$$ and output $$y(t) = x({e^t})$$. The system is

Let x 1 (t) = e $$-$$t u(t) and x 2 (t) = u(t) $$-$$ u(t $$-$$ 2), where u( . ) denotes the unit step function. If y(t) denotes the convolution of x 1 (t) and x 2 (t), then $$\mathop {\lim }\limits_{t \to \infty } y(t)$$...

For a unit step input $u[n]$, a discreate-time $L T I$ system produces an output signal $(2 \delta[n+1]+\delta[n]+\delta[n-1])$. Let $y[n]$ be the output of the system for an input $\left(\left(\frac{1}{2}\right)^n u[n]\...

The output $y[n]$ of a discrete - time system for an input $x[n]$ is $$ y[n]=\max\limits_{-\infty \leq k \leq n}|x[k]| $$ The unit impulse response of the system is

Let the input be u and the output be y of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:

The input x(t) and the output y(t) of a continuous time system are related as $$y\left( t \right) = \int\limits_{t - T}^t {x\left( u \right)du.} $$. The system is

Consider a single input single output discrete-time system with $$h\left[ n \right]\,$$ as input and $$y\left[ n \right]\,$$ as output, where the two are related as $$y\left[ n \right]\, = \left\{ {\matrix{ {n\left| {x\l...

Consider an LTI system with magnitude response $$$\left| {H(f)} \right| = \left\{ {\matrix{ {1 - \,{{\left| f \right|} \over {20}},} & {\left| f \right| \le 20} \cr {0,} & {\left| f \right| > 20} \cr } } \right.$$$ and p...

Two discrete-time signals x [n] and h [n] are both non-zero only for n = 0, 1, 2 and are zero otherwise. It is given that x(0)=1, x[1] = 2, x [2] =1, h[0] = 1, let y [n] be the linear convolution of x[n] and h [n]. Given...

Which one of the following is an eight function of the class of all continuous-time, linear, time- invariant systems u(t) denotes the unit-step function?

The energy of the signal x(t) =$${{\sin (4\pi t)} \over {4\pi t}}$$ is ___________.

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 excitation signals X, Y, Z with the corresponding time responses for $$t\, \g...

The impulse response of an LTI system can be obtained by

The result of the convolution $$x\left( { - t} \right) * \delta \left( { - t - {t_0}} \right)$$ is

Two sequence $${x_1}\left[ n \right]$$ and $${x_2}\left[ n \right]$$ have the same energy. Suppose $${x_1}\left[ n \right]$$ $$ = \alpha \,{0.5^n}\,u\left[ n \right],$$ where $$\alpha $$ is a positive real number and $$u...

The impulse response of an LTI system can be obtained by

A discrete - time signal x[n] = $${\rm{sin(}}\,{\pi ^2}n)$$, n being an integer 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 $${f_c}$$ is the centre frequency, and $$\alpha $$ and $$\beta $$ are pos...

Consider a discrete-time signal $$x\left[ n \right] = \left\{ {\matrix{ {n\,\,for\,\,0 \le n \le 10} \cr {0\,\,otherwise} \cr } } \right.$$ If $$y\left[ n \right]$$ is the convolution of $$x\left[ n \right]$$ with itself...

A continuous, linear time - invariant fiilter has an impulse response h(t) described by $$h\left( t \right) = \left\{ {\matrix{ {3\,for\,0 \le t \le 3} \cr {0\,otherwise} \cr } } \right.$$ Whjen a constant input of value...

The impulse response of a continuous time system is given by $$h(t) = \delta (t - 1) + \delta (t - 3)$$. The value of the step response at t = 2 is

The impulse response of a system is h(t) = t u(t). For an input u(t - 1), the output is

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

Two system with impulse responses h 1 (t) and h 2 (t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

Let $$y\left[ n \right]$$ denote the convolution of $$h\left[ n \right]$$ and $$g\left[ n \right]$$, where $$h\left[ n \right]$$ $$ = \,{\left( {1/2} \right)^2}\,\,u\left[ n \right]$$ and $$g\left[ n \right]\,$$ is a cau...

The input x(t) and output y(t) of a system are related as y(t) = $$\int\limits_{ - \infty }^t x (\tau )\cos (3\tau )d\tau $$. The system is

An input x(t) = exp( -2t) u(t) + $$\delta $$(t-6) is applied to an LTI system with impulse response h(t) = u(t). The output is

A system is defined by its impulse response $$h\left( n \right) = {2^n}\,u\left( {n - 2} \right).$$ The system is

Two discrete time systems with impulse responses $${h_1}\left[ n \right]\, = \delta \left[ {n - 1} \right]$$ and $${h_2}\left[ n \right]\, = \delta \left[ {n - 2} \right]$$ are connected in cascade. The overall impulse r...

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 x(t) is

The input and output of a continuous system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a causal system?

A discrete time linear shift - invariant system has an impulse response $$h\left[ n \right]$$ with $$h\left[ 0 \right]$$ $$ = 1,\,\,h\left[ 1 \right]\,\, = - 1,\,\,h\left[ 2 \right]\,\, = \,2$$, and zero otherwise. The s...

Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with system relations R1, R2, R3, R4. Properties P1 : Linear but NOT time-invariant P2: Time-invariant b...

The impulse response h(t) of a linear time-invariant continuous time system is described by $$h\left( t \right) = \,\,\exp \left( {\alpha t} \right)u\left( t \right)\,\,\, + \,\,\exp \left( {\beta t} \right)u\left( { - t...

Let g(t) = p(t) * p(t), where * denotes convolution and p(t) = u(t) - (t-1) with u(t) being the unit step function. The impulse response of filter matched to the singal s(t) = g(t) - $$[\delta (t - 2)*g(t)]$$ is given as

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

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 system with input $$x\left( n \right)$$ and output $$y\left( n \right)$$ is given as $$y\left( n \right)$$ $$ = \left( {\sin {5 \over 6}\,\pi \,n} \right)x\left( n \right).$$ The system is

Which of the following can be impulse response of a causal system?

Choose the function f (t );−$$\infty$$ < 1 < +$$\infty$$, for which a Fourier series cannot be defined.

A signal x(n)$$ = \sin ({\omega _0}\,n + \phi )$$ is the input to a linear time-invariant system having a frequency response $$H({e^{j\omega }})$$.If the output of the system is $$Ax(n - {n_0})$$, then the most general f...

The impulse response $$h\left[ n \right]$$ of a linear time-invariant system is given by $$h\left[ n \right]$$ $$ = u\left[ {n + 3} \right] + u\left[ {n - 2} \right] - 2\,u\left[ {n - 7} \right],$$ where $$u\left[ n \rig...

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

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 delay function of the given RC-LPF and $${f_2}$$ = 100 Hz. Then $${t_g}$$$...

Let P be linearity, Q be time-invariance, R be causality and S be stability. A discrete time system has the input-output relationship, $$y\left( n \right) = \left\{ {\matrix{ {x\left( n \right),} & {n \ge 1} \cr {0,} & {...

Which of the following cannot be the Fourier series expansion of a periodic signal?

A linear phase channel with phase delay $${\tau _p}$$ and group delay $${\tau _g}$$ must have

Convolution of x(t + 5) with impulse function $$\delta \left( {t\, - \,7} \right)$$ is equal to

Let $$\delta (t)$$ denote the delta function. The value of the the integral $$\int\limits_{ - \infty }^\infty {\delta (t)} \,\,\cos \left( {{{3\,\,t} \over 2}} \right)dt$$ is

The impulse response function of four linear system S1, S2, S3, S4 are given respectively by $${h_1}$$(t), = 1; $${h_2}$$(t), = U(t); $${h_3}(t)\, = \,{{U(t)} \over {t + 1}}$$; $${h_4}(t)\, = {e^{ - 3t}}U(t)$$ , where U...

The PSD and the power of a signal g(t) are, respectively, S g ($$\omega$$) and P g . The PSD and the power of the signal ag(t) are, respectively

If a signal f(t) has energy E, the energy of the signal f(2t) is equal to

A linear time invariant system has an impulse response e 2t , t > 0. If the initial conditions are zero and the input is e 3t , the output for t > 0 is

A system with an input x(t) and an output y(t) is described by the relation: y(t) = t x(t). This system is

A system has a phase response given by $$\phi \,(\omega )$$ where $$\omega $$ is the angular frequency. The phase delay and group delay at $$\omega $$ = $${\omega _0}$$ are respectively given by

A linear time invariant system has an impulse response $${e^{2t}},\,\,t\, > \,0.$$ If the initial conditions are zero and the input is $${e^{3t}}$$, the output for $$t\, > \,0$$ is

Let u(t) be the unit step function. Which of the waveforms in Fig.(a) -(d) corresponds to the convolution of $$\left[ {u\left( t \right)\, - \,u\left( {t\, - \,1} \right)} \right]$$ with $$\left[ {u\left( t \right)\, - \...

The input to a matched filter is given by $$s(t) = \left\{ {\matrix{ {10\sin (2\pi \times {{10}^6}t),} & {0 < \left| t \right| < {{10}^{ - 4}}\sec } \cr 0 & {Otherwise} \cr } } \right.$$ The peak amplitude of the filter...

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 channel due to this input is given by y(t) = (1/100) cos$$(100t - {10...

The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system ot an excitation e -at u(t), a > 0 will be

The unit impulse response of a linear time invariant system is the unit step function u(t). For t>0, the response of the system to an excitation e -at u(t), a>0 will be

The ACF of a rectangular pulse of duration T is

Match each of the items 1, 2 on the left with the most appropriate item A, B, C or D on the right. In the case of a linear time invariant system List - 1 (1) Poles in the right half plane implies. (2) Impulse response ze...

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 exp $$\,( - \alpha \,\,t)$$. Determine the filter output, sketch it as a...

A system having a unit impulse response $$h\left( n \right)$$ = $$u\left( n \right)$$ is excited by a signal $$x\left( n \right)$$ $$ = \,{\alpha ^n}\,\,u\left( n \right).\,$$ Determine the output $$y\left( n \right)$$

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 $${f_0}$$. Determine and plot the output power spectrum and aslo calcu...

A rectangular pulse of duration T is applied to a filter matched to this input. The output of the filter is a

The autocorrelation function of an energy signal has

Let h(t) be the impulse response of a linear time invariant system. Then the response of the system for any input u(t) is

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\{ {\matrix{ {A\,\,\,\,for} & {0 \le t < {2 \over 3}T} \cr {0\,\,\,\,\,\,...

Which of the following signals is/are periodic?

An excitation is applied to a system at $$t = T$$ and its response is zero for $$ - \infty < t < T$$. Such a system is a

The response of an initially relaxed linear constant parameter network to a unit impulse applied at $$t = 0$$ is $$4{e^{ - 2t}}u\left( t \right).$$ The response of this network to a unit step function will be:

The magnitude and phase transfer functions for a distortionless filter should respectively be: