Modulation concept (AM, FM, PM) in Signal Processing - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is modulation in signal processing?

Modulation is the process of changing a carrier signal's properties like amplitude, frequency, or phase to carry information.

beginner

What does AM stand for and what changes in the carrier signal?

AM stands for Amplitude Modulation. It changes the amplitude (height) of the carrier signal to carry information.

beginner

How does Frequency Modulation (FM) work?

FM changes the frequency (how fast the wave oscillates) of the carrier signal to carry information, while keeping amplitude constant.

intermediate

What is Phase Modulation (PM)?

PM changes the phase (the position of the wave in time) of the carrier signal to carry information, without changing amplitude or frequency.

beginner

Why do we use modulation in communication systems?

Modulation helps send signals over long distances, allows multiple signals on the same channel, and adapts signals for different transmission media.

Which property of the carrier wave changes in Amplitude Modulation (AM)?

A Phase

B Frequency

C Amplitude

D Wavelength

In AM, the amplitude of the carrier wave changes to carry the information.

In Frequency Modulation (FM), what remains constant?

A Frequency

B Signal power

C Phase

D Amplitude

FM changes frequency but keeps amplitude constant.

Phase Modulation (PM) changes which aspect of the carrier signal?

A Phase

B Frequency

C Speed

D Amplitude

PM changes the phase of the carrier signal to encode information.

Which modulation type is most affected by noise in amplitude?

A AM

B FM

C PM

D None

AM is more sensitive to noise because noise often affects amplitude.

Why is modulation important in radio communication?

A To increase signal power only

B To allow multiple signals on one channel

C To reduce signal frequency

D To eliminate noise completely

Modulation allows multiple signals to share the same channel by using different carrier frequencies.

Explain the differences between AM, FM, and PM in simple terms.

Think about what part of the wave changes to carry information.

Why do communication systems use modulation instead of sending raw signals?

Consider practical reasons for changing the signal before sending.

Practice

1. Which type of modulation changes the amplitude of the carrier wave to transmit information?

easy

A. Frequency Modulation (FM)

B. Amplitude Modulation (AM)

C. Phase Modulation (PM)

D. Pulse Modulation

Solution

1. Step 1: Understand modulation types

   Amplitude Modulation (AM) changes the amplitude of the carrier wave to carry information.

2. Step 2: Compare with other modulation types

   Frequency Modulation changes frequency, Phase Modulation changes phase, so they are not correct here.

3. Final Answer:

   Amplitude Modulation (AM) -> Option B

4. Quick Check:

   Amplitude change = AM [OK]

Hint: Amplitude change means AM modulation [OK]

Common Mistakes:

• Confusing amplitude change with frequency or phase
• Choosing FM or PM instead of AM
• Thinking pulse modulation is amplitude modulation

2. Which of the following is the correct way to represent Frequency Modulation (FM) mathematically for a carrier wave c(t) = A_c cos(2πf_c t) with message signal m(t)?

easy

A. s(t) = A_c cos(2πf_c t + k_f m(t))

B. s(t) = A_c (1 + k_a m(t)) cos(2πf_c t)

C. s(t) = A_c cos(2π(f_c + k_f m(t)) t)

D. s(t) = A_c cos(2πf_c t) + m(t)

Solution

1. Step 1: Recall FM formula

   Frequency Modulation changes the frequency of the carrier. The instantaneous frequency is f_c + k_f m(t).

2. Step 2: Match formula to options

   s(t) = A_c cos(2π(f_c + k_f m(t)) t) shows s(t) = A_c cos(2π(f_c + k_f m(t)) t), which correctly represents FM.

3. Final Answer:

   s(t) = A_c cos(2π(f_c + k_f m(t)) t) -> Option C

4. Quick Check:

   Frequency inside cosine = FM [OK]

Hint: FM changes frequency inside cosine argument [OK]

Common Mistakes:

• Choosing amplitude modulation formula instead
• Ignoring the time variable in frequency term
• Adding message signal outside cosine

3. Given the Python code below simulating a simple AM signal, what will be the output array values?

import numpy as np

A_c = 1
k_a = 0.5
f_c = 5
fs = 50
t = np.arange(0, 1, 1/fs)
m_t = np.sin(2 * np.pi * 1 * t)
s_t = A_c * (1 + k_a * m_t) * np.cos(2 * np.pi * f_c * t)
print(np.round(s_t[:5], 3))

medium

A. [1.0, 0.309, -0.809, -1.191, -0.691]

B. [1.0, 0.809, -0.309, -1.191, -0.691]

C. [1.0, 0.309, 0.809, 1.191, 0.691]

D. [0.0, 0.309, -0.809, -1.191, -0.691]

Solution

1. Step 1: Calculate message and carrier values

   Message m_t is a 1 Hz sine wave sampled at 50 Hz. Carrier frequency is 5 Hz. Calculate first 5 samples of s_t using AM formula.

2. Step 2: Compute first 5 samples

   Using formula: s_t = 1 * (1 + 0.5 * m_t) * cos(2π * 5 * t), the first 5 rounded values are approximately [1.0, 0.309, -0.809, -1.191, -0.691].

3. Final Answer:

   [1.0, 0.309, -0.809, -1.191, -0.691] -> Option A

4. Quick Check:

   AM signal first samples = [1.0, 0.309, -0.809, -1.191, -0.691] [OK]

Hint: AM output = carrier * (1 + k_a * message) [OK]

Common Mistakes:

• Mixing up frequency and amplitude terms
• Not rounding values correctly
• Using wrong sampling frequency

4. The following code attempts to generate a Phase Modulated (PM) signal but has an error. What is the error?

import numpy as np

A_c = 1
k_p = 0.5
f_c = 10
fs = 100

t = np.arange(0, 1, 1/fs)
m_t = np.sin(2 * np.pi * 2 * t)
s_t = A_c * np.cos(2 * np.pi * f_c * t + k_p * np.sin(m_t))
print(np.round(s_t[:5], 3))

medium

A. The time vector t is incorrectly defined

B. The carrier frequency f_c is too high for sampling frequency fs

C. The amplitude A_c should be multiplied inside the cosine argument

D. The modulation term should be k_p * m_t, not k_p * np.sin(m_t)

Solution

1. Step 1: Analyze modulation term in PM formula

   Phase modulation uses k_p * m_t inside the cosine argument, not k_p * np.sin(m_t).

2. Step 2: Identify the error in code

   The code incorrectly applies np.sin(m_t) instead of directly using m_t as the phase modulation signal.

3. Final Answer:

   The modulation term should be k_p * m_t, not k_p * np.sin(m_t) -> Option D

4. Quick Check:

   PM uses message signal directly in phase [OK]

Hint: PM uses message signal directly inside cosine phase [OK]

Common Mistakes:

• Applying sine twice on message signal
• Confusing amplitude with phase modulation
• Incorrect time vector or sampling frequency

5. You want to transmit a message signal m(t) that has sudden jumps (discontinuities). Which modulation technique among AM, FM, and PM is best to minimize distortion caused by these jumps, and why?

hard

A. FM, because frequency changes are less affected by amplitude noise

B. PM, because phase changes handle discontinuities smoothly

C. AM, because amplitude changes are less sensitive to sudden jumps

D. None, all modulation types distort sudden jumps equally

Solution

1. Step 1: Understand effect of sudden jumps on modulation

   Sudden jumps cause rapid changes in signal. AM changes amplitude, which is sensitive to noise and distortion.

2. Step 2: Compare FM and PM for handling jumps

   FM changes frequency, which is more robust to amplitude noise and sudden jumps than AM. PM also changes phase but can be more sensitive to rapid phase shifts.

3. Final Answer:

   FM, because frequency changes are less affected by amplitude noise -> Option A

4. Quick Check:

   FM resists distortion from sudden jumps [OK]

Hint: FM resists noise and sudden jumps better than AM or PM [OK]

Common Mistakes:

• Choosing AM thinking amplitude is always best
• Assuming PM handles jumps better than FM
• Ignoring noise sensitivity differences