Digital modulation (ASK, FSK, PSK) in Signal Processing - Step-by-Step Execution

Concept Flow - Digital modulation (ASK, FSK, PSK)

Input: Digital bits

↓

Choose modulation type

↓

ASK

↓

Modulate signal

↓

Output: Modulated waveform

Digital bits are taken as input, a modulation type is chosen (ASK, FSK, or PSK), then the signal is modulated accordingly to produce the output waveform.

Execution Sample

Signal Processing

bits = [1,0,1,1]
mod_type = 'ASK'
carrier_amplitude = 1  # Define carrier amplitude
for bit in bits:
  if mod_type == 'ASK':
    signal = bit * carrier_amplitude
    print(signal)

This code modulates a digital bit stream using ASK by multiplying each bit with a carrier amplitude.

Execution Table

Step	bit	Condition (mod_type=='ASK')	signal calculation	Output signal
1	1	True	1 * carrier_amplitude	carrier_amplitude
2	0	True	0 * carrier_amplitude	0
3	1	True	1 * carrier_amplitude	carrier_amplitude
4	1	True	1 * carrier_amplitude	carrier_amplitude
End	-	-	-	All bits modulated, loop ends

💡 All bits processed, loop ends after step 4

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	Final
bit	-	1	0	1	1	-
signal	-	carrier_amplitude	0	carrier_amplitude	carrier_amplitude	-

Key Moments - 2 Insights

Why does the signal become zero when the bit is 0 in ASK?

Because in ASK, the signal amplitude is multiplied by the bit value. When bit is 0, amplitude times 0 equals 0, so no signal is transmitted (see execution_table step 2).

How does the modulation type affect the signal calculation?

The modulation type decides how bits change the carrier. ASK changes amplitude, FSK changes frequency, PSK changes phase. The example only shows ASK, so condition mod_type=='ASK' is always True (execution_table column Condition).

Visual Quiz - 3 Questions

Look at the execution table, what is the output signal at step 2?

A carrier_amplitude

B 0

C bit value

D frequency shift

💡 Hint

Check the Output signal column at step 2 in the execution_table

At which step does the bit value equal 1 and the output signal equals carrier_amplitude?

A Step 2

B Step 3

C Both Step 3 and Step 4

D Step 4

💡 Hint

Look at bit and Output signal columns in execution_table for steps 3 and 4

If modulation type changed to FSK, which part of the signal would change?

A Frequency

B Amplitude

C Phase

D Bit value

💡 Hint

Recall that FSK changes frequency, not amplitude or phase

Concept Snapshot

Digital modulation converts bits into signals.
ASK changes amplitude based on bit (0 or 1).
FSK changes frequency for each bit.
PSK changes phase for each bit.
Choose modulation type to encode data on carrier wave.

Full Transcript

Digital modulation takes digital bits and changes a carrier wave to represent them. ASK changes the wave's amplitude depending on the bit value. FSK changes the frequency, and PSK changes the phase. In the example, bits are modulated using ASK by multiplying each bit with the carrier amplitude. When the bit is 0, the output signal is zero amplitude, meaning no signal. When the bit is 1, the output signal equals the carrier amplitude. This process repeats for all bits, producing a modulated waveform that carries the digital data.

Practice

1. Which digital modulation technique changes the amplitude of the carrier wave to represent data bits?

easy

A. Phase Shift Keying (PSK)

B. Amplitude Shift Keying (ASK)

C. Frequency Shift Keying (FSK)

D. Pulse Code Modulation (PCM)

Solution

1. Step 1: Understand modulation types

   ASK changes the amplitude of the carrier wave to represent data bits, while FSK changes frequency and PSK changes phase.

2. Step 2: Match modulation to description

   The question asks for the technique that changes amplitude, which is ASK.

3. Final Answer:

   Amplitude Shift Keying (ASK) -> Option B

4. Quick Check:

   Amplitude change = ASK [OK]

Hint: ASK changes amplitude, FSK frequency, PSK phase [OK]

Common Mistakes:

• Confusing ASK with FSK or PSK
• Choosing PCM which is not a modulation technique
• Mixing phase and amplitude changes

2. Which of the following is the correct Python syntax to generate a Frequency Shift Keying (FSK) signal using numpy arrays for two frequencies f1 and f2?

easy

A. signal = np.sin(2 * np.pi * f1 * t) + np.sin(2 * np.pi * f2 * t)

B. signal = np.cos(2 * np.pi * f1 * t) + np.cos(2 * np.pi * f2 * t)

C. signal = np.sin(2 * np.pi * f1 * t) * np.sin(2 * np.pi * f2 * t)

D. signal = np.sin(2 * np.pi * (f1 if bit == 0 else f2) * t)

Solution

1. Step 1: Understand FSK signal generation

   FSK uses one frequency for bit 0 and another for bit 1, so the signal switches frequency based on the bit.

2. Step 2: Check syntax for conditional frequency

   signal = np.sin(2 * np.pi * (f1 if bit == 0 else f2) * t) uses a conditional expression to select frequency based on bit, which is correct for FSK.

3. Final Answer:

   signal = np.sin(2 * np.pi * (f1 if bit == 0 else f2) * t) -> Option D

4. Quick Check:

   Conditional frequency selection = signal = np.sin(2 * np.pi * (f1 if bit == 0 else f2) * t) [OK]

Hint: FSK switches frequency based on bit using conditional [OK]

Common Mistakes:

• Adding two sine waves instead of switching frequency
• Multiplying sine waves which is incorrect
• Using cosine instead of sine without reason

3. Given the following Python code snippet for Phase Shift Keying (PSK), what will be the output signal array for bits = [0, 1] and phase0 = 0, phase1 = pi?

import numpy as np
t = np.linspace(0, 1, 5)
bits = [0, 1]
phase0 = 0
phase1 = np.pi
signal = np.array([np.cos(2 * np.pi * 1 * t + (phase0 if bit == 0 else phase1)) for bit in bits])
print(signal)

medium

A. [[ 1. 0. -1. 0. 1.]
[-1. 0. 1. 0. -1.]]

B. [[ 0. 0. 0. 0. 0.]
[ 1. 1. 1. 1. 1.]]

C. [[ 1. 0. -1. 0. 1.]
[ 1. 0. -1. 0. 1.]]

D. [[ 1. 1. 1. 1. 1.]
[ 1. 1. 1. 1. 1.]]

Solution

1. Step 1: Calculate cosine values for bit 0

   For bit 0, phase = 0, t = np.linspace(0,1,5) = [0, 0.25, 0.5, 0.75, 1], angles = 2πt = [0, π/2, π, 3π/2, 2π], cos = [1, 0, -1, 0, 1].

2. Step 2: Calculate cosine values for bit 1

   For bit 1, phase = π, angles = 2πt + π, cos(θ + π) = -cos(θ) = [-1, 0, 1, 0, -1].

3. Final Answer:

   [[ 1. 0. -1. 0. 1.] [-1. 0. 1. 0. -1.]] -> Option A

4. Quick Check:

   PSK phase shift: cos(θ + π) = -cos(θ) [OK]

Hint: PSK phase π: cos(θ + π) = -cos(θ) [OK]

Common Mistakes:

• Confusing phase shift effect on cosine
• Misinterpreting array shape or values
• Ignoring phase addition in cosine

4. The following code attempts to generate an ASK signal but produces an error. What is the error and how to fix it?

import numpy as np
bit = 0
t = np.linspace(0, 1, 100)
f = 5
signal = np.sin(2 * np.pi * f * t) if bit == 1 else 0
print(signal)

medium

A. Error: signal is assigned a scalar 0 instead of an array; fix by replacing 0 with np.zeros_like(t)

B. Error: np.sin requires integer input; fix by casting t to int

C. Error: Missing parentheses in np.sin; fix by adding parentheses

D. No error; code runs correctly

Solution

1. Step 1: Identify the error in conditional assignment

   If bit == 1, signal is an array from np.sin, else signal is scalar 0, causing inconsistent types.

2. Step 2: Fix by using array of zeros

   Replace 0 with np.zeros_like(t) to keep signal as an array in both cases.

3. Final Answer:

   Error: signal is assigned a scalar 0 instead of an array; fix by replacing 0 with np.zeros_like(t) -> Option A

4. Quick Check:

   Consistent array types needed = Error: signal is assigned a scalar 0 instead of an array; fix by replacing 0 with np.zeros_like(t) [OK]

Hint: Use np.zeros_like(t) for zero arrays, not scalar 0 [OK]

Common Mistakes:

• Using scalar 0 causing type mismatch
• Casting t to int which is unnecessary
• Ignoring conditional expression structure

5. You want to design a digital communication system that must be robust to amplitude noise but can tolerate frequency variations. Which modulation technique should you choose and why?

hard

A. ASK, because it changes amplitude which is sensitive to noise

B. ASK, because it changes phase which is robust to amplitude noise

C. FSK, because it changes frequency which is less affected by amplitude noise

D. PSK, because it changes phase which is sensitive to frequency noise

Solution

1. Step 1: Analyze noise tolerance requirements

   The system must be robust to amplitude noise, so modulation should not rely on amplitude changes.

2. Step 2: Match modulation to noise tolerance

   FSK changes frequency, which is less affected by amplitude noise, making it suitable. ASK changes amplitude and is sensitive to amplitude noise. PSK changes phase and can be sensitive to frequency noise.

3. Final Answer:

   FSK, because it changes frequency which is less affected by amplitude noise -> Option C

4. Quick Check:

   Amplitude noise robustness = FSK [OK]

Hint: Choose FSK to avoid amplitude noise sensitivity [OK]

Common Mistakes:

• Choosing ASK despite amplitude noise sensitivity
• Confusing phase noise sensitivity with frequency noise
• Misunderstanding modulation noise robustness