What is a signal in Signal Processing - Practice Questions & Exercises

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the basic definition of a signal

Which of the following best describes what a signal is in signal processing?

A A signal is a function that conveys information about the behavior or attributes of some phenomenon.

B A signal is a random noise that cannot be analyzed or processed.

C A signal is a programming language used for data analysis.

D A signal is a type of database used to store large amounts of data.

💡 Hint

Think about what carries information in communication systems.

A signal is any function that carries information. It can be electrical, sound, or other types of data that represent real-world phenomena.

❓ Predict Output

intermediate

Output of a simple discrete signal array

What is the output of the following Python code that represents a discrete signal?

Signal Processing

import numpy as np
signal = np.array([0, 1, 2, 3, 4])
print(signal * 2)

A TypeError: unsupported operand type(s) for *: 'list' and 'int'

B [0 2 4 6 8]

C [0 4 8 12 16]

D [0 1 2 3 4]

💡 Hint

Multiplying a numpy array by 2 doubles each element.

The numpy array elements are multiplied by 2 element-wise, resulting in [0, 2, 4, 6, 8].

❓ data_output

advanced

Resulting frequency components after Fourier Transform

Given a discrete signal sampled as [1, 0, -1, 0], what is the output of its discrete Fourier transform (DFT)?

Signal Processing

import numpy as np
signal = np.array([1, 0, -1, 0])
dft = np.fft.fft(signal)
print(np.round(dft, decimals=1))

A [0.+0.j 2.+0.j 0.+0.j 2.+0.j]

B [0.+0.j 0.+0.j 0.+0.j 0.+0.j]

C [0.+0.j 1.+0.j 0.+0.j 1.+0.j]

D [0.+0.j 2.+0.j 0.+0.j -2.+0.j]

💡 Hint

Recall that the DFT of a real-valued signal can have complex conjugate symmetry.

The DFT of [1, 0, -1, 0] results in [0, 2, 0, -2] with zero imaginary parts, showing frequency components at indices 1 and 3.

❓ visualization

advanced

Plotting a continuous sine wave signal

Which option correctly plots a continuous sine wave signal using matplotlib in Python?

Signal Processing

import numpy as np
import matplotlib.pyplot as plt
t = np.linspace(0, 1, 500)
signal = np.sin(2 * np.pi * 5 * t)
plt.plot(t, signal)
plt.xlabel('Time (seconds)')
plt.ylabel('Amplitude')
plt.title('5 Hz Sine Wave')
plt.show()

A A smooth sine wave oscillating 5 times between 0 and 1 second.

B A sine wave with random noise added.

C A flat line at zero amplitude.

D A sine wave oscillating only once between 0 and 1 second.

💡 Hint

Frequency of 5 Hz means 5 cycles per second.

The plot shows a sine wave oscillating 5 times over the 1-second interval, matching the 5 Hz frequency.

🔧 Debug

expert

Identify the error in signal normalization code

What error will the following code produce when normalizing a signal array, and why?

Signal Processing

import numpy as np
signal = np.array([0, 2, 4, 6, 8])
normalized = (signal - np.min(signal)) / (np.max(signal) - np.min(signal))
print(normalized)

# Now normalize again incorrectly
normalized_again = (signal - np.min(signal)) / np.max(signal - np.min(signal))
print(normalized_again)

A TypeError because np.max(signal - np.min(signal)) is invalid operation.

B Wrong normalization result because np.max(signal - np.min(signal)) computes max of array minus scalar, not the range.

C No error; both normalizations produce the same correct output.

D ValueError due to division by zero in normalization.

💡 Hint

Check the difference between np.max(signal - np.min(signal)) and np.max(signal) - np.min(signal).

No error occurs; both normalizations produce the same correct output because np.max(signal - np.min(signal)) equals np.max(signal) - np.min(signal), which is the range of the signal.

Practice

1. What is a signal in simple terms?

easy

A. A fixed number that never changes

B. A type of computer program

C. A way to carry information about changes over time or space

D. A random noise with no meaning

Solution

1. Step 1: Understand the definition of a signal

   A signal is something that carries information about changes, like sound or temperature over time.

2. Step 2: Compare options to the definition

   Only A way to carry information about changes over time or space describes a signal as carrying information about changes over time or space.

3. Final Answer:

   A way to carry information about changes over time or space -> Option C

4. Quick Check:

   Signal = Information carrier [OK]

Hint: Signals carry info about change, not fixed values [OK]

Common Mistakes:

• Thinking a signal is a fixed number
• Confusing signal with software
• Assuming signals have no meaning

2. Which of the following is the correct way to represent a simple signal in code?

easy

A. signal = [1, 2, 3, 4, 5]

B. signal = 'hello world'

C. signal = 42

D. signal = True

Solution

1. Step 1: Identify what a signal looks like in code

   A signal is often a list or array of numbers representing values over time or space.

2. Step 2: Check each option

   signal = [1, 2, 3, 4, 5] is a list of numbers, which fits the signal concept. Others are a string, a single number, or a boolean, which do not represent signals well.

3. Final Answer:

   signal = [1, 2, 3, 4, 5] -> Option A

4. Quick Check:

   Signal = list of numbers [OK]

Hint: Signals are lists or arrays of numbers [OK]

Common Mistakes:

• Using strings or single values as signals
• Confusing booleans with signals
• Not using a sequence for signal data

3. Given the code below, what is the output?

signal = [10, 20, 30, 40]
average = sum(signal) / len(signal)
print(average)

medium

A. 40

B. 20

C. 30

D. 25.0

Solution

1. Step 1: Calculate the sum of the signal values

   Sum = 10 + 20 + 30 + 40 = 100

2. Step 2: Calculate the average by dividing sum by number of elements

   Average = 100 / 4 = 25.0

3. Final Answer:

   25.0 -> Option D

4. Quick Check:

   Average = 25.0 [OK]

Hint: Average = sum of values ÷ count [OK]

Common Mistakes:

• Forgetting to divide by length
• Using sum without parentheses
• Mixing sum and max functions

4. Find the error in the code below that tries to calculate the average of a signal:

signal = [5, 15, 25]
average = sum(signal) / signal.length
print(average)

medium

A. signal should be a string, not a list

B. Using signal.length instead of len(signal)

C. Missing parentheses in print statement

D. Using sum() instead of average()

Solution

1. Step 1: Identify how to get list length in Python

   Python uses len(list) to get length, not list.length.

2. Step 2: Check the code for length usage

   The code uses signal.length which is invalid in Python and causes an error.

3. Final Answer:

   Using signal.length instead of len(signal) -> Option B

4. Quick Check:

   List length = len(list) [OK]

Hint: Use len() for list length in Python [OK]

Common Mistakes:

• Using .length like in other languages
• Confusing sum() with average()
• Forgetting parentheses in print

5. You have a signal representing temperature readings every hour: temps = [22, 21, 23, 22, 24, 23]. How would you create a new signal that shows the change in temperature between each hour?

hard

A. changes = [temps[i+1] - temps[i] for i in range(len(temps)-1)]

B. changes = [temps[i] + temps[i+1] for i in range(len(temps))]

C. changes = [temps[i] * 2 for i in range(len(temps))]

D. changes = [temps[i] / temps[i+1] for i in range(len(temps)-1)]

Solution

1. Step 1: Understand the goal to find temperature changes between hours

   We want the difference between each consecutive temperature reading.

2. Step 2: Check each option for correct difference calculation

   changes = [temps[i+1] - temps[i] for i in range(len(temps)-1)] correctly subtracts temps[i] from temps[i+1] for all valid indices.

3. Final Answer:

   changes = [temps[i+1] - temps[i] for i in range(len(temps)-1)] -> Option A

4. Quick Check:

   Difference = next - current [OK]

Hint: Subtract consecutive values to find changes [OK]

Common Mistakes:

• Adding instead of subtracting
• Using wrong range causing index error
• Multiplying or dividing instead of subtracting