Quizzes

Question 1

Answer 1

x(t) = 10u(t) - 20u(t-2) + 10u(t-4)

Question 2

What is a System?

Answer 2

A system is a process or device that transforms an input signal into an output signal according to a specific rule or function.

It can be described mathematically as a mapping or operator, often represented as y(t) = T{x(t)}

where
- x(t) is the input signal
- y(t) is the output signal
- T is the system transformation.

Examples include amplifiers, filters, or communication channels.

Question 3

Answer 3

Even Symmetry

Question 4

If x(t) = t^3 and y(t)=8t^3 : what type of transformation relates x(t) to y(t)?

Answer 4

Time scaling with a factor of 2

Question 5

Analog Signal

Answer 5

Amplitude assumes any value within a continuous range

Question 6

Digital Signal

Answer 6

Amplitude has been quantized

Question 7

Discrete Signal

Answer 7

Defined only for certain moments in time

Question 8

Continuous Signal

Answer 8

Defined for every instance in time

Question 9

Causal Signal

Answer 9

Only depends on present and past values

Question 10

Non-causal Signal

Answer 10

Not only depends on past and present values, but also future values

Question 11

• Noncausal
• Digital Signal
• Continuous-time
• Analog
• Unidimensional
• Causal
• Energy
• Power
• Period=10s
• Period=(2*pi)/10
• Multidimensional
• Discrete-time

Answer 11

• Noncausal
• Continuous-time
• Analog
• Unidimensional
• Power
• Period=10s

Question 12

If x(t)=t^2 and y(t)=16t^2 : What type of transformation relates x(t) to y(t)?

Answer 12

Time scaling with a factor of 4

Question 13

True/False: Periodic signals are always energy signals.

Answer 13

False

Question 14

Compute the Integral:

Answer 14

4

Question 15

True/False: An arbitrary signal x(t) can be both an energy signal and a power signal.

Answer 15

False

Question 16

True/False: A signal can be classified as linear and time-invariant.

Answer 16

False

These are terms for a system not a signal

Question 17

__________ allows us to breakdown a complex input into a sum of simple ones, find the output to each simple input and then add all the outputs.

Answer 17

An LTI System

LTI= Linear and Time-Invariant

Question 18

Using the impulse response of an LTI system, the output y(t) may be determined in response to an arbitrary input by applying the __________.

Answer 18

convolution

Question 19

Given the impulse response of a system, to find the step response, you need to ___________________.

Answer 19

Integrate the impulse response

Question 20

What is the impulse response of a system?

Answer 20

The output signal from a system was when an Impulse function is the input signal.

Question 21

Fourier Analysis helps us decompose an input signal as:

Answer 21

The sum of complex exponentials

Question 22

True/False: Fourier Series are used to represent periodic signals of any form.

Answer 22

True

Question 23

Answer 23

DC component

Question 24

True/False: Fourier analysis can be used for all types of input signals, including signals that grow.

Answer 24

False

Question 25

If the input to an LTI system is, x(t)=2cos(3t), explain how can we find out the output of this LTI system (without computing the convolution integral)?

Answer 25

Find the frequency domain equivalent of the signal and multiply it by the frequency domain equivalent of the signal h(t) into H(w) and x(t) into X(w). h(t) is not a signal, it is the impulse response of the system. If you are multiplying in the frequency domain, you need to bring that back to the time domain. However, for the type of input signal given, it is only necessary to find the frequency response of the system.

Question 26

True/False: The sine/cosine (Full series) and the amplitude/phase (Compact series) representation of the Fourier series are used only if x(t) is real-valued.

Answer 26

True

Question 27

If the input to an LTI system is, x(t)=2cos(3t), explain how can we find out the output of this LTI system (without computing the convolution integral)?

Answer 27

* Use the frequency response (H(omega)). * For input (x(t) = 2cos(3t) = e^{i3t} + e^{-i3t} ), the output is (y(t) = H(3)e^{i3t} + H^*(3)e^{-i3t} = 2|H(3)|cos(3t + angle H(3))). * Evaluate (H(3) \) to find the magnitude and phase.

Question 28

The Fourier series reveals how an LTI system reshapes each harmonic by:

Answer 28

* scaling the amplitudes of the harmonics * shifting the phases of the harmonics

Question 29

True/False: Parseval's relations for the Fourier series illustrate that the energy of an aperiodic signal can be computed from its Fourier coefficients.

Answer 29

False

Question 30

The __________ representation of the Fourier Series is characterized by a two-sided line spectra.

Answer 30

Exponential

Question 31

True/False: Signals that are neither energy nor power signals do not have a Fourier Transform.

Answer 31

True

Question 32

Explain one advantage of calculating the energy of a signal in the frequency domain rather than the time domain.

Answer 32

The math can be much simpler than in the time domain.

Question 33

True/False: The magnitude spectrum |X(f)| alone is sufficient to completely reconstruct the original signal x(t) from its Fourier Transform.

Answer 33

False

Question 34

The _________ property allows us to derive new Fourier transform pairs from known pairs by swapping the time and frequency variables.

Answer 34

duality

Question 35

If a signal is absolutely integrable and square integrable, it guarantees that the signal has a

Answer 35

Fourier transform