The function x(t) is shown in the given figure. Even and odd parts of a unit step function ∪ (t) are respectively,

The Laplace transform of unit ramp function starting at t = a is

If , then x(n) series has

If , then x(n) series has

The trignometric Fourier series of an even function of time does not have

The impulse response of discrete time system is x[n] = (4)ⁿ ∪[3 - n], the system is

An ac wave with superimposed dc is symmetrical about x - axis.

Assertion (A): L[e^-at f(t)] = F(s + a)

Reason (R): In use of Laplace transform method, initial conditions may be neglected.

An ac sinusoidal wave has an rms value ofV. The peak to peak value is

The z transform of sequence x[n] = {2}

Assertion (A): If a wave v = A₁ + A₂ sin ωt is applied to a pure capacitor the current wave is
i = A₃ sin(ωt + 90°)

Reason (R): A capacitor presents infinite impedance to dc.

A complex wave is 5 + 5 sin ωt. Its rms value is

State variables which describe a system are a unique set.

A complex wave is 5 + 5 sin ωt. Its rms value is

For the function u(t - a) = 0 for t < a and u(t - a) = 1 fort ≥ a, the Laplace transform is

A complex wave is 5 + 5 sin ωt. Its rms value is

For the function u(t - a) = 0 for t < a and u(t - a) = 1 fort ≥ a, the Laplace transform is

For the function u(t - a) = 0 for t < a and u(t - a) = 1 fort ≥ a, the Laplace transform is

State variables which describe a system are a unique set.

For the function u(t - a) = 0 for t < a and u(t - a) = 1 fort ≥ a, the Laplace transform is

The inverse Laplace transform of is

The inverse Laplace transform of is

The inverse Laplace transform of is

If Laplace transform of f(t) is F(s), then £ f(t - a) u (t - a)= 0

A signal is sampled at Nyquist rate f_s = 2f₀. The function can be recovered from its samples only. If it is a

Assertion (A): L[af₁(t) + bf₂(t)] = aF₁(s) - bF₂(s)

Reason (R): Initial value theroem enables us to find the value of f(t) at t = 0 directly from F(s)

The energy of constant amplitude complex valued exponential sequence is ...

A voltage wave is v =sin ωt. Its average value calculated over full one cycle is

Laplace transform of unit doublet is

If f(t) = - f(- t) satisfies Drichlet conditions, then f(t) can be expanded in Fourier series containing

The Laplace transform of impulse δ(t) is

The function δ(t - b) is

A rectangular pulse is passed through an L.P.F. The response is a

If f₁ (t) and f₂ (f) are two functions of time and a and b are constants, then

In terms of signum function sgn(t), unit step function u(t) =

The integral of a unit step function is

An ac network has a power factor of 0.8 lagging for fundamental frequency. If the applied voltage contains thrid and fifth harmonics, the overall power factor will be

Assertion (A): The number ∈ such that the probability that an error is between -∈ and + ∈ is 1 is called probable error of single obserevation.

Reason (R): The standard deviation is the arms value of the deviation from the arithmetic mean.

Fourier transform of f(t) =

Choose correct option

FIR filter Passes __________ Phase.

A pulse function having magnitude E and duration from t = 0 to t = a can be represented as

If a number of even functions are added, the resultant sum is

If f₁(t)<< F₁(jω) and f₂(t)↔ F₂(jω), then [a₁ f₁(t) + a₂f₂(t)]↔

Highest value of autocorrelation functionsinpt is

For an ac sinusoidal wave, the rms value isA. For the same wave delayed byin each half cycle, the rms value is likely to be

If a linear time invartant system is exicited by a pure random signal like white noise, the output of the linear system will have which of the following properties?

In the state equation x = AX + Bu is a n x m matrix.

A 1 kHz sinusoidal signal is ideally sampled atsamples/sec and the sampled signal is passed through an ideal low pass filter with cut off frequencyHz. The output signal has the frequency.

Principle of superposition is applicable to