Signals & Systems

Two systems with impulse responses h1(t) and h2(t) are connected in a cascade. Then the overall impulse response of the cascaded system is given by __

• Product of h1(t) and h2(t)

• Sum of h1(t) and h2(t)

• Convolution of h1(t) and h2(t)

Given the signal x (t) = cos t, if t<0 and x(t) = sin t, if t≥0. The correct statement among the following is?

• Periodic with fundamental period 2π

• Periodic but with no fundamental period

• Non-periodic and discontinuous

• Non-periodic but continuous

What is the frequency shifting property of continuous time fourier series?

• Multiplication in the time domain by a real sinusoid

• Multiplication in the time domain by a complex sinusoid

• Multiplication in the time domain by a sinusoid

• Addition in the time domain by a complex sinusoid

Find the Fourier transform of x(t) = f(t – 2) + f(t + 2).

• 2F(ω)cos⁡2ω

• F(ω)cos⁡2ω

• 2F(ω)sin⁡2ω

• F(ω)sin⁡2ω

In discrete signal, if y [n] = x [k*n] and k>1 then ______

• Some samples are lost from x [n]

• Some samples are added to x [n]

• It has no effect on samples

• Samples will be increased with factor k

The system characterized by the equation y (t) = ax (t) + b is ____________

• Linear for any value of b

• Linear if b>0

• Linear if b<0

• Non-linear

The impulse response of an LTI system can be obtained by ________

• Differentiating the unit ramp response

• Differentiating the unit step response

• Integrating the unit ramp response

• Integrating the unit step response

If a signal f(t) has energy E, the energy of the signal f(100t) is equal to _______

• E

• 100E

• E/100

• 400E

• sin(10)

• -sin(10)

• 0

• 1

Choose the condition from below that is not a part of Dirichlet’s conditions?

• If it is continuous then there are a finite number of discontinuities in the period T

• It has a finite average value over the period T

• It has a finite number of positive and negative maxima in the period T

• It is a periodic signal