1A signal defined for all values of time over a continuous interval is called a:
Continuous time and discrete time signals : energy and power signals
Easy
A.Discrete-time signal
B.Quantized signal
C.Digital signal
D.Continuous-time signal
Correct Answer: Continuous-time signal
Explanation:
A continuous-time signal is defined for every instant of time over a continuous range, denoted as .
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2A discrete-time signal is usually represented as:
Continuous time and discrete time signals : energy and power signals
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
Discrete-time signals are defined only at integer values of the index and are written as .
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3A signal with finite energy and zero average power is classified as a(n):
Continuous time and discrete time signals : energy and power signals
Easy
A.Power signal
B.Periodic signal
C.Energy signal
D.Random signal
Correct Answer: Energy signal
Explanation:
An energy signal has finite, non-zero energy () and its average power is zero.
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4A signal with finite non-zero average power is called a(n):
Continuous time and discrete time signals : energy and power signals
Easy
A.Aperiodic signal
B.Power signal
C.Impulse signal
D.Energy signal
Correct Answer: Power signal
Explanation:
A power signal has finite, non-zero average power () and infinite energy.
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5The energy of a continuous-time signal is defined as:
Continuous time and discrete time signals : energy and power signals
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
Signal energy is the integral of the squared magnitude of the signal over all time.
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6A signal is periodic if there exists a period such that:
Transformations of the independent variable : periodic signals, even and odd signals
Easy
A. for all
B. for all
C. for all
D. for all
Correct Answer: for all
Explanation:
A periodic signal repeats itself after a fixed period , satisfying .
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7A signal that satisfies is said to be:
Transformations of the independent variable : periodic signals, even and odd signals
Easy
A.Causal
B.Odd
C.Periodic
D.Even
Correct Answer: Even
Explanation:
An even signal is symmetric about the vertical axis, satisfying .
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8A signal that satisfies is said to be:
Transformations of the independent variable : periodic signals, even and odd signals
Easy
A.Bounded
B.Even
C.Odd
D.Deterministic
Correct Answer: Odd
Explanation:
An odd signal is antisymmetric about the origin, satisfying .
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9The operation represents a:
Transformations of the independent variable : periodic signals, even and odd signals
Easy
A.Amplitude scaling
B.Time shift (delay)
C.Time reversal
D.Time scaling
Correct Answer: Time shift (delay)
Explanation:
Replacing with shifts the signal to the right by 2 units, which is a time delay.
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10The signal is an example of a(n):
Transformations of the independent variable : periodic signals, even and odd signals
Easy
A.Even signal
B.Aperiodic signal
C.Odd signal
D.Neither even nor odd
Correct Answer: Even signal
Explanation:
Since , the cosine function is an even signal.
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11The general form of a continuous-time real exponential signal is:
Exponential and sinusoidal signals
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
A real exponential signal has the form , where and are real constants.
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12For the exponential with , the signal is:
Exponential and sinusoidal signals
Easy
A.Oscillating
B.Growing
C.Constant
D.Decaying
Correct Answer: Decaying
Explanation:
When , the exponential decreases with time, producing a decaying signal.
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13Euler's relation expresses as:
Exponential and sinusoidal signals
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
Euler's formula states .
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14The fundamental period of the sinusoid is:
Exponential and sinusoidal signals
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The period of a sinusoid with angular frequency is .
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15The continuous-time unit step function is equal to:
The unit impulse and unit step functions
Easy
A. for all
B. for
C. for and for
D. for and for
Correct Answer: for and for
Explanation:
The unit step function is for non-negative time and for negative time.
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16The area under the continuous-time unit impulse is:
The unit impulse and unit step functions
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The unit impulse has unit area: .
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17The discrete-time unit impulse equals when:
The unit impulse and unit step functions
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The discrete-time unit impulse is at and everywhere else.
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18The unit impulse is related to the unit step by which operation?
The unit impulse and unit step functions
Easy
A.
B.
C.
D.
Correct Answer:
Explanation:
The unit impulse is the derivative of the unit step function: .
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19The operation performed on a signal is called:
Operations on signals
Easy
A.Time reversal
B.Time delay
C.Time scaling
D.Amplitude scaling
Correct Answer: Time reversal
Explanation:
Replacing with reflects the signal about the vertical axis, which is time reversal (folding).
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20In MATLAB, which function is commonly used to plot a discrete-time signal as stems?
Software Simulation of Basic Operations on Elementary Signals
Easy
A.surf
B.bar
C.plot
D.stem
Correct Answer: stem
Explanation:
The stem function displays discrete-time sequences as stems, ideal for plotting .
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21For the signal , what is the total energy?
Continuous time and discrete time signals : energy and power signals
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
Energy . Since energy is finite, it is an energy signal.
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22A signal is classified as which type?
Continuous time and discrete time signals : energy and power signals
Medium
A.Energy signal with energy
B.Power signal with power
C.Power signal with power
D.Neither energy nor power signal
Correct Answer: Power signal with power
Explanation:
A sinusoid has infinite energy but finite average power , so it is a power signal.
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23The energy of the discrete-time signal is:
Continuous time and discrete time signals : energy and power signals
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
.
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24The fundamental period of is:
Transformations of the independent variable : periodic signals
Medium
A. s
B. s
C. s
D. s
Correct Answer: s
Explanation:
Periods are and . The fundamental period is the LCM: s.
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25For the discrete-time signal to be periodic, its fundamental period is:
Transformations of the independent variable : periodic signals
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
For periodicity, must be rational. The fundamental period is (numerator and denominator in lowest terms give , ).
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26The signal is periodic with fundamental period:
Transformations of the independent variable : periodic signals
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
A complex exponential is periodic with .
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27The even part of the signal is:
even and odd signals
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
Even part .
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28If is an odd signal, then the value of must be:
even and odd signals
Medium
A.
B.Any nonzero constant
C.
D.
Correct Answer:
Explanation:
For an odd signal . Setting gives , hence .
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29The odd part of is:
even and odd signals
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
Odd part .
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30The complex exponential represents which behavior?
Exponential and sinusoidal signals
Medium
A.A constant DC signal
B.A pure undamped sinusoid
C.A sinusoid with exponentially decaying amplitude
D.A sinusoid with exponentially growing amplitude
Correct Answer: A sinusoid with exponentially decaying amplitude
Explanation:
. The real part of the exponent is negative, giving a decaying envelope.
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31For the discrete-time signal , as the signal:
Exponential and sinusoidal signals
Medium
A.Oscillates with constant amplitude
B.Grows without bound
C.Remains constant at
D.Decays toward zero
Correct Answer: Decays toward zero
Explanation:
Since , the geometric sequence monotonically decreases toward as increases.
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32The signal has an angular frequency of:
Exponential and sinusoidal signals
Medium
A. rad/s
B. rad/s
C. rad/s
D. rad/s
Correct Answer: rad/s
Explanation:
In , the angular frequency is the coefficient of , so rad/s.
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33The value of the integral is:
The unit impulse and unit step functions
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
By the sifting property, .
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34The relationship between the continuous-time unit step and unit impulse is:
The unit impulse and unit step functions
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The unit impulse is the derivative of the unit step; equivalently .
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35In discrete time, the unit step can be expressed in terms of the unit impulse as:
The unit impulse and unit step functions
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
The step is a running sum of impulses: , equivalently .
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36Given defined for , the signal is defined over which interval?
Operations on signals
Medium
A.
B.
C.
D.
Correct Answer:
Explanation:
Set . Adding 4: , dividing by 2: .
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37To obtain from , the correct order of operations is:
Operations on signals
Medium
A.Shift right by 3, then scaling
B.Time reversal, then shift right by 3
C.Time scaling by 3, then reversal
D.Shift left by 3, then time reversal
Correct Answer: Time reversal, then shift right by 3
Explanation:
Write . Reflect to get , then replace with (shift right by 3).
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38The operation applied to a signal represents:
Operations on signals
Medium
A.Time expansion by a factor of 3
B.Amplitude scaling by 3
C.Time compression by a factor of 3
D.A time shift by 3 units
Correct Answer: Time expansion by a factor of 3
Explanation:
Replacing with stretches the signal along the time axis, expanding it by a factor of 3.
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39In MATLAB, to generate a discrete unit impulse over the range , which approach is correct?
Software Simulation of Basic Operations on Elementary Signals
Medium
A.n=-5:5; x=ones(size(n));
B.n=-5:5; x=(n==0);
C.n=-5:5; x=(n~=0);
D.n=-5:5; x=(n>=0);
Correct Answer: n=-5:5; x=(n==0);
Explanation:
The logical expression (n==0) returns 1 only where and 0 elsewhere, exactly matching .
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40When simulating signal addition of two discrete sequences with different index ranges, the essential first step is to:
Software Simulation of Basic Operations on Elementary Signals
Medium
A.Multiply the sequences element by element
B.Reverse one of the sequences
C.Convolve the two sequences
D.Align both sequences over a common index range using zero padding
Correct Answer: Align both sequences over a common index range using zero padding
Explanation:
Element-wise addition requires both sequences to share the same index vector; zero padding extends each over the common range before summing.
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41Consider the signal . Classify the signal based on energy and power.
Continuous time and discrete time signals : energy and power signals
Hard
A.Neither energy nor power signal
B.Energy signal with
C.Energy signal with
D.Power signal with
Correct Answer: Energy signal with
Explanation:
, which is finite. Since is finite and nonzero, it is an energy signal and its average power is zero.
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42For the discrete-time signal , the total energy is:
Continuous time and discrete time signals : energy and power signals
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
.
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43The signal is:
Continuous time and discrete time signals : energy and power signals
Hard
A.A power signal with
B.An energy signal with
C.An energy signal with infinite energy
D.A power signal with
Correct Answer: A power signal with
Explanation:
A sinusoid has infinite energy but finite average power , so it is a power signal.
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44For (discrete unit step), the average power is:
Continuous time and discrete time signals : energy and power signals
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
.
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45The signal is periodic with fundamental period:
Transformations of the independent variable : periodic signals
Hard
A.
B.
C.Not periodic
D.
Correct Answer:
Explanation:
For periodicity, must be rational, which it is. The fundamental period is (smallest integer making an integer).
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46The sum of two periodic continuous-time signals with periods and has fundamental period:
Transformations of the independent variable : periodic signals
Hard
A.
B.Not periodic
C.
D.
Correct Answer:
Explanation:
The sum is periodic with period equal to the LCM of and . .
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47The signal is periodic with fundamental period:
Transformations of the independent variable : periodic signals
Hard
A.Not periodic
B.
C.
D.
Correct Answer:
Explanation:
Periods are and . The overall period is the LCM, which corresponds to the GCD of frequencies , giving .
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48The discrete signal (argument in radians) is:
Transformations of the independent variable : periodic signals
Hard
A.Periodic with period
B.Aperiodic because is irrational
C.Periodic with period
D.Periodic with period
Correct Answer: Aperiodic because is irrational
Explanation:
For to be periodic, must be rational. Since it is irrational, the signal is aperiodic.
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49The odd part of is:
even and odd signals
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
.
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50If is real and odd, then equals:
even and odd signals
Hard
A.
B.
C.
D.Cannot be determined
Correct Answer:
Explanation:
For odd signals , so and terms cancel pairwise. Hence the sum is .
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51The even part of (unit step) is:
even and odd signals
Hard
A.
B.
C. for all
D.
Correct Answer: for all
Explanation:
. For and , one of the terms is 1, giving ; at it is by convention.
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52For the complex exponential , the signal is:
Exponential and sinusoidal signals
Hard
A.A real decaying exponential
B.A growing oscillation
C.A decaying oscillation (damped sinusoid)
D.A pure sinusoid of constant amplitude
Correct Answer: A decaying oscillation (damped sinusoid)
Explanation:
. The real part gives exponential decay and the imaginary part gives oscillation, producing a damped sinusoid.
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53Two discrete-time sinusoids and are identical if and differ by:
Exponential and sinusoidal signals
Hard
A.An integer multiple of
B.An integer multiple of
C.An integer multiple of
D.Any rational number
Correct Answer: An integer multiple of
Explanation:
Discrete-time sinusoids are identical when frequencies differ by , since for integer . This is the frequency aliasing property.
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54The highest rate of oscillation for a discrete-time sinusoid occurs at:
Exponential and sinusoidal signals
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Unlike continuous time, in discrete time the oscillation rate increases as goes from to , then decreases. Maximum oscillation occurs at .
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55Evaluate .
The unit impulse and unit step functions
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Using , the integral evaluates to .
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56The relationship between the discrete unit impulse and unit step is:
The unit impulse and unit step functions
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
The unit impulse is the first difference of the unit step: . Equivalently, .
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57The derivative of the ramp function is:
The unit impulse and unit step functions
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
. Since (sifting at gives ), the derivative reduces to .
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58Given defined for , the signal is nonzero over:
Operations on signals
Hard
A.
B.
C.
D.
Correct Answer:
Explanation:
Nonzero when . Solving: .
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59To obtain from , the correct order of operations is:
Operations on signals
Hard
A.Compress by 2, then shift left by 4
B.Shift right by 4, then compress by 2
C.Shift right by 2, then compress by 2
D.Compress by 2, then shift right by 2
Correct Answer: Shift right by 4, then compress by 2
Explanation:
Write . Shifting first by 4 (i.e. ) then compressing gives . Alternatively, compress then shift right by 2 — but per shift-first convention, shift by 4 then compress by 2 is correct.
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60In MATLAB, to generate a time-reversed and shifted signal from a vector x defined over n = -2:2, the correct approach is:
Software Simulation of Basic Operations on Elementary Signals
Hard
A.Flip the vector x and adjust the time index to -(n)+2
B.Use circshift(x,2) only
C.Simply use fliplr(x) without changing the index range
D.Multiply x by and shift by 2
Correct Answer: Flip the vector x and adjust the time index to -(n)+2
Explanation:
Time reversal maps (flip the array), and the shift requires recomputing the corresponding time index vector as . Both the amplitude order and the index axis must be updated together.
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