1 $Which of the following completely characterizes the behavior of a Linear Time-Invariant (LTI) system?$

A.

Step response

B.

Ramp response

C.

Frequency response magnitude only

D.

Impulse response

2 $The mathematical operation used to determine the output of a discrete-time LTI system given its input and impulse response is called:$

A.

Modulation

B.

The convolution sum

C.

Correlation

D.

The convolution integral

3 $Which equation represents the continuous-time convolution integral of two signals and ?$

A.

B.

C.

D.

4 $The commutative property of convolution implies that:$

A.

B.

C.

D.

5 $What is the result of convolving a signal with the unit impulse function ?$

A.

B.

C.

D.

0

6 $If an LTI system has an impulse response, which condition must be met for the system to be causal ?$

A.

for

B.

C.

must be even

D.

for

7 $For a discrete-time LTI system to be BIBO (Bounded Input, Bounded Output) stable, the impulse response must satisfy:$

A.

B.

C.

D.

for

8 $What is the convolution of with a shifted impulse ?$

A.

B.

C.

D.

9 $If two finite-length discrete-time sequences (length) and (length) are convolved, what is the length of the resulting sequence ?$

A.

B.

C.

D.

10 $The distributive property of convolution allows us to analyze the interconnection of two LTI systems connected in:$

A.

Parallel

B.

Cascade (Series)

C.

Feedback

D.

Loop

11 $Which of the following represents the step response of an LTI system in terms of its impulse response ?$

A.

B.

C.

D.

12 $An LTI system is memoryless if and only if its impulse response has the form:$

A.

B.

C.

D.

13 $Given and, what is ?$

A.

B.

C.

D.

14 $The associative property of convolution,, implies that:$

A.

Systems must be causal

B.

Feedback loops are stable

C.

Parallel systems can be swapped

D.

The order of systems in a cascade does not affect the final output

15 $In software simulation, the operation 'Correlation' differs from 'Convolution' primarily in that:$

A.

Convolution involves folding (time-reversal) of one signal, whereas correlation does not

B.

Correlation is only for complex numbers

C.

There is no difference

D.

Correlation requires infinite signals

16 $A discrete-time LTI system is described by the difference equation . This is an example of a:$

A.

Finite Impulse Response (FIR) system

B.

Non-causal system

C.

Memoryless system

D.

Infinite Impulse Response (IIR) system

17 $The impulse response of an ideal delay system with delay is:$

A.

B.

C.

D.

$1$ for

18 $If an LTI system is invertible, there exists an inverse system with impulse response such that ?$

A.

$1$

B.

$0$

C.

D.

19 $Which of the following signals is an eigenfunction of an LTI system?$

A.

B.

C.

D.

20 $Given a discrete signal starting at and starting at . Calculate using convolution.$

A.

4

B.

5

C.

2

D.

1

21 $A system described by the linear constant-coefficient differential equation is LTI only if:$

A.

The coefficients are functions of time

B.

The system is initially at rest (zero initial conditions)

C.

The input is periodic

D.

The system is unstable

22 $Calculate the convolution sum .$

A.

B.

C.

D.

23 $Which property states that ?$

A.

Scaling Property

B.

Distributive Property

C.

Commutative Property

D.

Associative Property

24 $If is of duration and is of duration, the duration of their convolution is generally:$

A.

B.

C.

D.

25 $The discrete unit impulse is defined as:$

A.

undefined at n=0

B.

1 for all n

C.

1 for n=0, 0 otherwise

D.

0 for n<0, 1 for n>=0

26 $For a continuous-time LTI system to be stable, the region of convergence (ROC) of its Laplace transform must include:$

A.

The origin

B.

Positive real numbers

C.

The axis

D.

The real axis

27 $If, then is equal to:$

A.

B.

C.

Neither A nor B

D.

Both A and B

28 $The cross-correlation of two signals and is denoted as . If, it is called:$

A.

Cross-covariance

B.

Auto-correlation

C.

Energy density

D.

Auto-convolution

29 $In a software simulation using MATLAB, which command computes the convolution of vectors u and v ?$

A.

impulse(u, v)

B.

convolve(u, v)

C.

filter(u, v)

D.

conv(u, v)

30 $The system described by is an LTI system. Its impulse response is:$

A.

B.

C.

D.

31 $Is the system with impulse response stable?$

A.

No, it is unstable

B.

Depends on the input

C.

Yes, always

D.

Marginally stable

32 $What is the result of (convolution with the unit doublet)?$

A.

B.

C.

(first derivative)

D.

33 $A Moving Average (MA) filter is a discrete-time LTI system that is:$

A.

Unstable

B.

Usually FIR

C.

Usually IIR

D.

Non-linear

34 $Which of the following is NOT a property of convolution?$

A.

Multiplicative ()

B.

Commutative

C.

Associative

D.

Distributive

35 $The area under the curve of the convolution result is equal to:$

A.

0

B.

(Area of) / (Area of)

C.

(Area of) (Area of)

D.

(Area of) + (Area of)

36 $For a causal discrete-time LTI system defined by a linear constant coefficient difference equation, the order of the difference equation refers to:$

A.

The amplitude of the input

B.

The number of coefficients

C.

The highest power of input

D.

The maximum delay (lag) in the output

37 $The zero-state response of a system is exclusively due to:$

A.

The input signal

B.

Initial conditions

C.

System noise

D.

The DC offset

38 $If is periodic with period, and is finite length, the convolution is:$

A.

Aperiodic

B.

Periodic with period length of

C.

Zero

D.

Periodic with period

39 $The autocorrelation function at zero lag,, represents:$

A.

The phase shift

B.

The bandwidth

C.

The DC value

D.

The total energy (or average power) of the signal

40 $Which mathematical property explains why we can synthesize the output of an LTI system by decomposing the input into shifted impulses?$

A.

Invertibility

B.

Stability

C.

Causality

D.

Linearity and Time-Invariance

41 $Convolution in the time domain corresponds to what in the frequency domain?$

A.

Subtraction

B.

Convolution

C.

Multiplication

D.

Addition

42 $Consider the discrete impulse response . For what values of is the system stable?$

A.

B.

C.

only

D.

43 $Two LTI systems with impulse responses and are connected in parallel. The equivalent impulse response is:$

A.

B.

C.

D.

44 $When computing convolution graphically, the 'folding' step refers to:$

A.

B.

C.

D.

45 $Which of the following describes a 'Static' system?$

A.

System with zero input

B.

System without memory

C.

System that does not change with time

D.

System with memory

46 $For a CT system defined by, the impulse response is of the form:$

A.

B.

C.

D.

47 $In discrete convolution, if indices of are $0$ to and are $0$ to, the lower limit of the non-zero output indices is:$

A.

M

B.

1

C.

0

D.

N

48 $The property is known as:$

A.

Associative Property

B.

Shift Property

C.

Commutative Property

D.

Distributive Property

49 $What is the result of convolving a rectangular pulse of width with itself?$

A.

A triangular pulse of width

B.

An impulse

C.

A rectangular pulse of width

D.

A Gaussian pulse

50 $In the context of correlation, if for all, the signals are said to be:$

A.

Causal

B.

Uncorrelated (Orthogonal)

C.

Identical

D.

Periodic

Unit 2 - Practice Quiz