Exam 1 Practice

Question 1

What is the Unit Step Function?

Answer 1

A function that is zero for negative arguments and one for positive arguments

Often denoted as u(t), it is used in signal processing to represent signals that turn on at a specific time.

Question 2

What does waveform synthesis involve?

Answer 2

The process of creating complex waveforms from simpler waveforms

It often involves adding or multiplying basic functions like sine and cosine waves.

Question 3

What is the purpose of signal transforms?

Answer 3

To convert signals from one domain to another, typically from time domain to frequency domain

Common transforms include the Fourier Transform and Laplace Transform.

Question 4

How is total energy of a waveform determined?

Answer 4

By integrating the square of the signal over time

The formula is E = ∫|x(t)|^2 dt.

Question 5

What is the rect function?

Answer 5

A rectangular pulse function defined by its width and height

It is often used to represent signals that are ‘on’ for a certain duration.

Question 6

What is the sinc function?

Answer 6

Defined as sinc(t) = sin(πt)/(πt), it is used in signal processing

It arises in the context of Fourier transforms and is important in sampling theory.

Question 7

What does time scaling of a signal involve?

Answer 7

Changing the time axis of the signal, which can compress or expand its duration

For example, g(at) scales the function g(t) by a factor of ‘a’.

Question 8

What does time shifting of a signal involve?

Answer 8

Shifting the signal in time without changing its shape

For example, g(t + b) shifts the function to the left if b is positive and to the right if b is negative.

Question 9

How is the Root-Mean-Square (RMS) value of a waveform calculated?

Answer 9

By taking the square root of the average of the squares of the waveform’s values

The root-mean-square (RMS) value of a waveform is calculated by first squaring each instantaneous value, then finding the mean (average) of those squared values over one period, and finally taking the square root of that mean. For a continuous waveform, this is represented by the formula: (V_{RMS}=\sqrt{\frac{1}{T}\int _{0}^{T}v(t)^{2}dt}).

Question 10

What does the energy of a signal represent?

Answer 10

The total power contained within the signal over time

Calculated as E = ∫|x(t)|^2 dt from -∞ to +∞.

Question 11

What is convolution in signal processing?

Answer 11

A mathematical operation that combines two signals to form a third signal

It represents the way in which one signal modifies another.

Question 12

Fill in the blank: The total energy of a waveform can be expressed as E = ∫________.

Answer 12

|x(t)|^2 dt

This integral is evaluated over the entire time range of the signal.

Question 13

True or False: The overlap of two signals during convolution is constant over time.

Answer 13

False

The overlap changes as the signals are shifted relative to each other.

Question 14

What are the steps to sketch y(t) = x(t) * h(t)?

Answer 14

1. Flip h(t)
2. Shift h(t)
3. Integrate the product over time

This process visually represents the convolution of two signals.