WorksheetsSignals and Systems Quiz
Total questions: 50
Worksheet time: 25mins
Which of the following is not a continuous-time signal?
Sin(t)
exp(-t)
δ[n]
t²
The unit step function u(t) is:
1 for t > 0
0 for t > 0
0 for t < 0
-1 for t < 0
A system is said to be time-invariant if:
It produces the same output for all inputs
Its output does not change with time
Time shift in input causes a corresponding shift in output
It works only in the time domain
An energy signal has:
Infinite energy
Finite energy and zero average power
Infinite power
Zero energy
Which signal is both even and periodic?
sin(t)
cos(t)
exp(t)
t
δ(t) is called:
Unit ramp
Unit impulse
Step function
Sine function
A system with memory:
Depends only on current input
Depends on future input
Depends on past input
B and C
Which operation reflects a signal about the vertical axis?
Time scaling
Time shifting
Time reversal
None
A causal system is one where:
Output depends on future input
Output depends only on past and present input
Output is independent of input
None
Even part of a signal x(t) is given by:
x(t) - x(-t)
[x(t) + x(-t)]/2
[x(t) - x(-t)]/2
x(-t)
Fourier series represents a signal as:
Sum of step functions
Product of impulses
Sum of sinusoids
Convolution of signals
The CT Fourier Transform of δ(t) is:
1
0
∞
jω
The condition for existence of Fourier Transform is:
Signal must be periodic
Signal must be finite energy
Signal must be zero mean
Signal must be real
Which of the following is NOT a property of the Fourier Transform?
Linearity
Differentiation in frequency domain
Time shifting
Multiplication
The inverse Fourier Transform is used to:
Convert signals from time to frequency domain
Convert signals from frequency to time domain
Remove noise
Compress signals
Laplace Transform is defined for:
Periodic signals only
Non-periodic signals only
Both periodic and non-periodic signals
Discrete signals only
Laplace Transform exists if the signal is:
Absolutely integrable
Power limited
Non-causal
Even
The region of convergence (ROC) in Laplace Transform defines:
Energy of the signal
Frequency content
Stability and existence
None of the above
Final value theorem is applicable when:
All poles are on jω axis
System is unstable
Poles are in left half-plane
Poles are in right half-plane
The Laplace transform of the unit step function u(t) is:
1
1/s
s
δ(t)
Convolution in time domain corresponds to what in frequency domain?
Addition
Convolution
Multiplication
Division
The response of a system to δ(t) is called:
Step response
Ramp response
Impulse response
Frequency response
A linear system satisfies:
Time invariance
Causality
Superposition
Memorylessness
The Laplace transform of the impulse response gives:
Output
Fourier Transform
Transfer Function
Input
If all poles of transfer function lie in left half of s-plane, the system is:
Unstable
Marginally stable
Stable
Causal
Time invariance implies:
Output depends on time explicitly
Output is constant
Shift in input shifts output similarly
None
Transfer function is defined as:
Output/Input in time domain
Output/Input in s-domain
Product of input and output
Impulse function
A system is BIBO stable if:
Output is zero
Output is infinite
Bounded input gives bounded output
None
Laplace transform is useful to analyze:
Only periodic signals
Random signals
Transient and steady states
Noise only
If h(t) = 0 for t < 0, the system is:
Anti-causal
Non-causal
Causal
Time variant
Which is a discrete-time signal?
sin(t)
exp(jωt)
x[n]
δ(t)
The DTFT of a real even signal is:
Imaginary
Odd
Real and even
Zero
DTFT is defined over which interval?
[0, π]
[0, 2π]
[−π, π]
[−∞, ∞]
Which of these is periodic in DT domain?
sin(2πn)
exp(n)
sin(πn/4)
exp(jπn)
The Z-transform is generalization of:
Fourier Transform
Laplace Transform
DTFT
Impulse Transform
Z-transform exists if signal is:
Finite energy
Causal
Absolutely summable
Periodic
ROC of Z-transform helps in:
Power calculation
Plotting graphs
Stability analysis
Energy estimation
Inverse Z-transform gives:
Frequency domain signal
Original time domain signal
Laplace domain signal
None
The initial value theorem applies when:
Pole at origin
System unstable
System is causal
ROC includes origin
If X(z) is Z-transform, then x[n−1] is:
zX(z)
z⁻¹X(z)
X(z)/z
zX(z)−x[−1]
Impulse response of discrete system is denoted by:
δ[n]
h[n]
x[n]
y[n]
Convolution sum is used to compute:
Step response
Power
Output of LTI system
Frequency response
An LTI system is causal if h[n] =
0 for n > 0
1 for n < 0
0 for n < 0
Any value
For BIBO stability in discrete domain:
h[n] must be even
h[n] must be odd
|h[n]| must be summable
x[n] must be periodic
Difference equation relates:
Only input
Only output
Input and output
Frequency
Frequency response of a system is H (푒푗푤) obtained from:
Laplace transform
Z-transform
Inverse Z-transform
DTFT of h[n]
A system is time-invariant if:
y[n] = x[n+1]
y[n] = x[n−1]
y[n] = x[n]
Output changes with time
Zero input response is due to:
Initial conditions
External input
Noise
Convolution
Which of these systems is memoryless?
y[n] = x[n] + x[n−1]
y[n] = x[n]
y[n] = ∑x[k]
y[n] = x[n+2]
Z-domain analysis helps in analyzing:
Non-linear systems
Time variant systems
LTI systems
Memoryless systems
