The Laplace transform of unit ramp function starting at t = a is
The Laplace transform of the waveform shown in the below figure is
The function x(t) is shown in the given figure. Even and odd parts of a unit step function ∪ (t) are respectively,
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 isi = 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.
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
If Laplace transform of f(t) is F(s), then £ f(t - a) u (t - a)= 0
A signal is sampled at Nyquist rate fs = 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?
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