Why communication relies on signal modulation in Signal Processing - Test Your Understanding

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a simple sine wave signal.

Signal Processing

import numpy as np
import matplotlib.pyplot as plt

t = np.linspace(0, 1, 500)
signal = np.sin(2 * np.pi * [1] * t)
plt.plot(t, signal)
plt.title('Sine Wave Signal')
plt.show()

Drag options to blanks, or click blank then click option'

A5

B0.5

C50

D500

Attempts:

3 left

💡 Hint

Common Mistakes

Using a frequency too high causes the wave to look like noise.

Using zero frequency results in a flat line.

The frequency of the sine wave is set to 50 Hz to create a clear signal for modulation.

2fill in blank

medium

Complete the code to modulate the sine wave signal by multiplying with a carrier wave.

Signal Processing

carrier_freq = 100
carrier = np.sin(2 * np.pi * [1] * t)
modulated_signal = signal * carrier
plt.plot(t, modulated_signal)
plt.title('Amplitude Modulated Signal')
plt.show()

Drag options to blanks, or click blank then click option'

A5

B50

C10

D100

Attempts:

3 left

💡 Hint

Common Mistakes

Using a carrier frequency lower than the signal frequency.

Using the same frequency for both signal and carrier.

The carrier frequency is set to 100 Hz to modulate the original 50 Hz signal.

3fill in blank

hard

Fix the error in the code to correctly demodulate the signal by multiplying with the carrier again.

Signal Processing

demodulated = modulated_signal * np.sin(2 * np.pi * [1] * t)
plt.plot(t, demodulated)
plt.title('Demodulated Signal')
plt.show()

Drag options to blanks, or click blank then click option'

A50

B100

C5

D10

Attempts:

3 left

💡 Hint

Common Mistakes

Using the original signal frequency instead of the carrier frequency.

Using a frequency not used before.

Demodulation requires multiplying by the same carrier frequency used in modulation, which is 100 Hz.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps words to their lengths only if length is greater than 3.

Signal Processing

words = ['data', 'science', 'ai', 'ml', 'python']
lengths = {word: [1] for word in words if [2] > 3}
print(lengths)

Drag options to blanks, or click blank then click option'

Alen(word)

Cword

Attempts:

3 left

💡 Hint

Common Mistakes

Using the word itself as the value instead of its length.

Filtering by the word instead of its length.

We use len(word) to get the length and filter words with length greater than 3.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps uppercase words to their lengths if length is greater than 2.

Signal Processing

words = ['cat', 'dog', 'a', 'elephant']
result = { [1]: [2] for w in words if [3] > 2 }
print(result)

Drag options to blanks, or click blank then click option'

Aw.upper()

Blen(w)

Dw

Attempts:

3 left

💡 Hint

Common Mistakes

Using the original word as key instead of uppercase.

Filtering by word instead of length.

The dictionary keys are uppercase words, values are their lengths, filtered by length greater than 2.

Practice

1. Why is signal modulation important in communication systems?

easy

A. It allows information to be transmitted over long distances clearly.

B. It increases the size of the signal.

C. It removes noise from the signal completely.

D. It changes the signal into a digital format only.

Solution

1. Step 1: Understand the role of modulation

   Modulation changes a carrier wave to carry information clearly over distances.

2. Step 2: Identify the main benefit

   This helps signals travel far and avoid interference, making communication clear.

3. Final Answer:

   It allows information to be transmitted over long distances clearly. -> Option A

4. Quick Check:

   Modulation improves signal clarity and distance [OK]

Hint: Modulation helps signals travel far and clear [OK]

Common Mistakes:

• Thinking modulation removes all noise
• Believing modulation only changes signal size
• Confusing modulation with digitization

2. Which of the following is the correct way to describe amplitude modulation (AM)?

easy

A. Changing the frequency of the carrier wave to carry information.

B. Changing the amplitude of the carrier wave to carry information.

C. Changing the phase of the carrier wave to carry information.

D. Changing the speed of the carrier wave to carry information.

Solution

1. Step 1: Recall modulation types

   Amplitude modulation changes the amplitude of the carrier wave.

2. Step 2: Match description to AM

   Only Changing the amplitude of the carrier wave to carry information correctly describes amplitude modulation.

3. Final Answer:

   Changing the amplitude of the carrier wave to carry information. -> Option B

4. Quick Check:

   Amplitude modulation = amplitude change [OK]

Hint: Amplitude modulation changes wave height [OK]

Common Mistakes:

• Confusing amplitude with frequency or phase
• Thinking speed changes in modulation
• Mixing up modulation types

3. Consider this Python code simulating a simple amplitude modulation signal:

import numpy as np
import matplotlib.pyplot as plt

carrier_freq = 5  # Hz
modulating_freq = 1  # Hz
time = np.linspace(0, 1, 500)

carrier = np.sin(2 * np.pi * carrier_freq * time)
modulating = 0.5 * np.sin(2 * np.pi * modulating_freq * time) + 1
am_signal = modulating * carrier

plt.plot(time, am_signal)
plt.title('Amplitude Modulated Signal')
plt.xlabel('Time (seconds)')
plt.ylabel('Amplitude')
plt.show()

What does the plot show?

medium

A. A carrier wave whose amplitude changes over time.

B. A carrier wave with constant amplitude.

C. A modulating wave with constant frequency.

D. A frequency modulated signal.

Solution

1. Step 1: Analyze the code signals

   The carrier is a sine wave at 5 Hz. The modulating signal varies amplitude between 0.5 and 1.5.

2. Step 2: Understand the multiplication effect

   Multiplying carrier by modulating changes the carrier's amplitude over time.

3. Final Answer:

   A carrier wave whose amplitude changes over time. -> Option A

4. Quick Check:

   Amplitude modulation changes amplitude [OK]

Hint: Multiplying carrier by modulating changes amplitude [OK]

Common Mistakes:

• Thinking amplitude stays constant
• Confusing amplitude modulation with frequency modulation
• Ignoring the modulating signal effect

4. The following code attempts to create a frequency modulated signal but has an error:

import numpy as np
import matplotlib.pyplot as plt

carrier_freq = 5
modulating_freq = 1

time = np.linspace(0, 1, 500)

carrier = np.sin(2 * np.pi * carrier_freq * time)
modulating = np.sin(2 * np.pi * modulating_freq * time)

fm_signal = np.sin(2 * np.pi * (carrier_freq + modulating) * time)

plt.plot(time, fm_signal)
plt.title('Frequency Modulated Signal')
plt.show()

What is the error in this code?

medium

A. The modulating signal should be multiplied, not added, to the carrier frequency.

B. The time array is not defined correctly.

C. The carrier frequency should be a vector, not a scalar.

D. The modulating signal should be integrated before adding to the carrier frequency.

Solution

1. Step 1: Understand frequency modulation basics

   Frequency modulation requires integrating the modulating signal before adding to carrier frequency.

2. Step 2: Identify code mistake

   The code adds modulating signal directly without integration, which is incorrect.

3. Final Answer:

   The modulating signal should be integrated before adding to the carrier frequency. -> Option D

4. Quick Check:

   FM needs integrated modulating signal [OK]

Hint: FM requires integrating modulating signal first [OK]

Common Mistakes:

• Adding modulating signal directly without integration
• Confusing multiplication with addition
• Incorrect time array assumptions

5. You want to send a message signal over a noisy channel. Which modulation method helps reduce noise impact and allows the signal to travel farther?

hard

A. Amplitude Modulation (AM)

B. Pulse Width Modulation (PWM)

C. Frequency Modulation (FM)

D. No modulation, send raw signal

Solution

1. Step 1: Compare modulation types for noise resistance

   Frequency modulation is known to resist noise better than amplitude modulation.

2. Step 2: Consider signal travel distance

   FM signals can travel farther with less interference, improving communication quality.

3. Final Answer:

   Frequency Modulation (FM) -> Option C

4. Quick Check:

   FM reduces noise and extends range [OK]

Hint: FM reduces noise better than AM [OK]

Common Mistakes:

• Choosing AM for noise resistance
• Thinking raw signals travel farther
• Confusing PWM with noise reduction