Signals & Systems

An example of a discrete set of information/system is

• the trajectory of the Sun

• data on a CD

• universe time scale

• movement of water through a pipe

Which one of the following systems is causal?

• y(t) = x(t) + x(t-3) + x(t²)

• y[n] = x[n+2]

• y(t)=x(t-1)+x(t-2)

• y[n] = x[2n²]

Which among the following is a Time Invariant system?

• dy(t)/dt + ty(t) = x(t)

• y(t) = x(t) cosπt

• y[n] = x[n] + n x[n-1]

• y[n] = x³ [n+1]

Find the convolution sum of sequences x¹[n] = [1, 2, 3] and x₂[n] = [2, 1, 4].

• {2, 5, 12, 11, 12}

• {2, 12, 5, 11, 12}

• {2, 11, 5, 12, 12}

• {-2, 5,-12, 11, 12}

If a function f(t) u(t) is shifted to right side by t₀,then the function can be expressed as

• f(t – t₀) u(t)

• f(t) u(t –t₀)

• f(t – t₀) u(t – t₀)

• f(t +t₀) u(t + t₀)

What does the term y(-1) indicate especially in an equation that represents the behavior of the causal system?

• initial condition of the system

• negative initial condition of the system

• negative feedback condition of the system

• response of the system to its initial input

Under which conditions does an initially relaxed system become unstable?

• only if bounded input generates unbounded output

• only if bounded input generates bounded output

• only if unbounded input generates unbounded output

• only if unbounded input generates bounded output

Which mathematical notation specifies the condition of periodicity for a continuous time signal?

• x(t) = x(t +T₀)

• x[n] = x[n+ N]

• x(t) = e-αt

• None of these

If two LTI systems with impulse response h1 (t) and h2 (t) and are connected in parallel then output is given by ______

• y(t) = x(t) *(h1(t) + h2(t))

• y(t) = x(t) + (h1(t) + h2(t))

• y(t) = x(t) * (h1(t) h2(t))

• y(t) = (x(t) * h1(t)) + h2(t)

The signal defined by the equations f(t) = 0 for t < 0, f(t) = E for 0 ≤ t ≤ a and f(t) = 0 for t > a is

• a step function

• a pulse function

• a shifted step function originating at t=a

• none of the above