Analog vs digital signals in Signal Processing - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define an analog signal as a continuous sine wave.

Signal Processing

import numpy as np
import matplotlib.pyplot as plt

time = np.linspace(0, 1, 500)
frequency = 5
analog_signal = np.sin(2 * np.pi * frequency * [1])
plt.plot(time, analog_signal)
plt.title('Analog Signal')
plt.show()

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

Afrequency

Btime

Cnp.pi

Dnp.linspace

Attempts:

3 left

💡 Hint

Common Mistakes

Using frequency instead of time inside the sine function.

Using constants like np.pi instead of a variable.

The analog signal is a sine wave that varies continuously with time.

2fill in blank

medium

Complete the code to create a digital signal by sampling the analog signal.

Signal Processing

sample_rate = 50
sample_points = np.arange(0, 1, 1/[1])
digital_signal = np.sin(2 * np.pi * frequency * sample_points)
plt.stem(sample_points, digital_signal)
plt.title('Digital Signal')
plt.show()

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

Afrequency

Btime

Csample_rate

Dnp.linspace

Attempts:

3 left

💡 Hint

Common Mistakes

Using frequency instead of sample_rate for sampling intervals.

Using continuous time variable instead of discrete sample points.

The digital signal samples the analog signal at intervals defined by the sample_rate.

3fill in blank

hard

Fix the error in the code to correctly quantize the digital signal into discrete levels.

Signal Processing

quantization_levels = 8
quantized_signal = np.round(digital_signal * ([1] - 1)) / (quantization_levels - 1)
plt.stem(sample_points, quantized_signal)
plt.title('Quantized Digital Signal')
plt.show()

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

Aquantization_levels

Btime

Csample_rate

Dfrequency

Attempts:

3 left

💡 Hint

Common Mistakes

Using frequency or sample_rate instead of quantization_levels.

Not subtracting 1 from quantization_levels in scaling.

The signal is scaled by the number of quantization_levels minus one to map values correctly.

4fill in blank

hard

Fill both blanks to create a dictionary mapping signal types to their characteristics.

Signal Processing

signal_characteristics = {
    'Analog': '[1]',
    'Digital': '[2]'
}

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

AContinuous waveform

BDiscrete levels

CInfinite precision

DBinary values

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up continuous and discrete descriptions.

Using 'Binary values' for analog signals.

Analog signals have continuous waveform, while digital signals have discrete levels.

5fill in blank

hard

Fill all three blanks to complete the code that compares analog and digital signals in a DataFrame.

Signal Processing

import pandas as pd

signals = pd.DataFrame({
    'Type': ['Analog', 'Digital'],
    'Representation': ['[1]', '[2]'],
    'Precision': ['[3]', 'Finite']
})
print(signals)

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

AContinuous waveform

BDiscrete levels

CInfinite

DBinary code

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping analog and digital descriptions.

Using 'Discrete levels' for analog representation.

Analog signals have continuous waveform and infinite precision. Digital signals use binary code and have finite precision.

Practice

1. Which of the following best describes an analog signal?

easy

A. A signal that changes smoothly and continuously over time

B. A signal that only has two fixed levels, 0 and 1

C. A signal that is always digital

D. A signal that cannot be measured

Solution

1. Step 1: Understand the nature of analog signals

   Analog signals vary smoothly and continuously, representing information in a flowing manner.

2. Step 2: Compare with digital signals

   Digital signals use fixed steps, usually two levels (0 and 1), unlike analog signals.

3. Final Answer:

   A signal that changes smoothly and continuously over time -> Option A

4. Quick Check:

   Analog = continuous signal [OK]

Hint: Analog means continuous change, not fixed steps [OK]

Common Mistakes:

• Confusing analog with digital signals
• Thinking analog signals have only two levels
• Assuming analog signals cannot be measured

2. Which of the following is the correct way to represent a digital signal?

easy

A. A smooth curve that varies continuously

B. A signal that changes randomly without pattern

C. A signal that cannot be converted to numbers

D. A signal with only two levels, such as 0 and 1

Solution

1. Step 1: Identify digital signal characteristics

   Digital signals use fixed levels, typically two: 0 and 1, representing discrete steps.

2. Step 2: Eliminate incorrect options

   Smooth curves describe analog signals, not digital. Digital signals can be converted to numbers and are not random.

3. Final Answer:

   A signal with only two levels, such as 0 and 1 -> Option D

4. Quick Check:

   Digital = two-level signal [OK]

Hint: Digital signals have two fixed levels: 0 and 1 [OK]

Common Mistakes:

• Choosing smooth continuous signals for digital
• Thinking digital signals cannot be numeric
• Confusing randomness with digital signals

3. Consider this Python code simulating signal values:

import numpy as np

# Analog signal: sine wave
analog_signal = np.sin(np.linspace(0, np.pi, 5))

# Digital signal: threshold at 0

digital_signal = (analog_signal > 0).astype(int)

print(digital_signal)

What is the output of print(digital_signal)?

medium

A. [0 1 1 1 0]

B. [1 1 1 1 1]

C. [0 0 0 0 0]

D. [1 0 0 0 1]

Solution

1. Step 1: Calculate analog signal values

   Using np.linspace(0, π, 5), the sine values are [0, ~0.707, 1, ~0.707, 0].

2. Step 2: Apply threshold to create digital signal

   Values > 0 become 1, else 0. So digital_signal = [0, 1, 1, 1, 0].

3. Final Answer:

   [0 1 1 1 0] -> Option A

4. Quick Check:

   Threshold > 0 converts sine to binary [OK]

Hint: Threshold analog > 0 to get digital 0 or 1 [OK]

Common Mistakes:

• Misunderstanding np.linspace endpoints
• Confusing >0 with >=0 condition
• Forgetting to convert boolean to int

4. The following code attempts to convert an analog signal to digital but has an error:

import numpy as np

analog = np.array([0.1, -0.5, 0.3, -0.2])
digital = analog > 0
print(digital)

What is the error and how to fix it?

medium

A. No error; code works correctly

B. digital is boolean, convert to int with digital = (analog > 0).astype(int)

C. Use analog >= 0 instead of > 0

D. Use np.sign(analog) instead of > 0

Solution

1. Step 1: Identify output type of comparison

   analog > 0 returns a boolean array, not integers 0 or 1.

2. Step 2: Convert boolean to integer

   Use .astype(int) to convert True/False to 1/0 for digital signal representation.

3. Final Answer:

   digital is boolean, convert to int with digital = (analog > 0).astype(int) -> Option B

4. Quick Check:

   Boolean to int conversion needed [OK]

Hint: Convert boolean array to int for digital signals [OK]

Common Mistakes:

• Assuming boolean array is digital signal
• Changing threshold condition unnecessarily
• Using np.sign without reason

5. You have a noisy analog signal that fluctuates between -0.1 and 0.1 around zero. Which method best converts it to a stable digital signal?

hard

A. Use a simple threshold at 0 to convert to 0 or 1

B. Convert directly to integers without filtering

C. Apply a smoothing filter before thresholding at 0

D. Ignore noise and use raw analog values

Solution

1. Step 1: Understand noise impact on thresholding

   Noise near zero causes unstable digital output if thresholded directly.

2. Step 2: Apply smoothing filter before threshold

   Smoothing reduces noise fluctuations, producing stable digital signals after thresholding.

3. Final Answer:

   Apply a smoothing filter before thresholding at 0 -> Option C

4. Quick Check:

   Smoothing stabilizes noisy analog signals [OK]

Hint: Smooth noisy signals before thresholding [OK]

Common Mistakes:

• Thresholding noisy signal directly
• Ignoring noise effects
• Using raw analog values as digital