Signal addition and multiplication in Signal Processing - Mini Project: Build & Apply

Signal Addition and Multiplication

📖 Scenario: You are working with simple digital signals represented as lists of numbers. Each number is a signal value at a time point. You want to combine two signals by adding and multiplying their values point by point.

🎯 Goal: Build a program that takes two signals (lists of numbers), adds them together point by point, multiplies them point by point, and shows the results.

📋 What You'll Learn

Create two lists called signal1 and signal2 with exact values

Create a variable length to store the length of the signals

Use a for loop with index i to add and multiply signal values point by point

Store the added values in a list called added_signal

Store the multiplied values in a list called multiplied_signal

Print the added_signal and multiplied_signal lists

💡 Why This Matters

🌍 Real World

Combining signals is common in audio processing, sensor data analysis, and communications to create new signals or analyze interactions.

💼 Career

Understanding how to manipulate signals point by point is a foundational skill for roles in signal processing, data analysis, and engineering.

1

Create the two signals

Create two lists called signal1 and signal2 with these exact values: signal1 = [1, 3, 5, 7, 9] and signal2 = [2, 4, 6, 8, 10].

Signal Processing

# Create the two signals
# Your code here

Hint

Use square brackets to create lists with the exact numbers given.

2

Set the length of the signals

Create a variable called length and set it to the length of signal1 using the len() function.

Signal Processing

signal1 = [1, 3, 5, 7, 9]
signal2 = [2, 4, 6, 8, 10]
# Create a variable length for the signals
# Your code here

Hint

Use len(signal1) to get the number of elements in the list.

3

Add and multiply the signals point by point

Create two empty lists called added_signal and multiplied_signal. Use a for loop with index i from 0 to length - 1. Inside the loop, add signal1[i] and signal2[i] and append the result to added_signal. Also multiply signal1[i] and signal2[i] and append the result to multiplied_signal.

Signal Processing

signal1 = [1, 3, 5, 7, 9]
signal2 = [2, 4, 6, 8, 10]
length = len(signal1)
# Create empty lists for added and multiplied signals
# Use a for loop with i from 0 to length - 1
# Add and multiply signal values and append to lists
# Your code here

Hint

Use range(length) to loop over indexes. Use append() to add values to lists.

4

Print the results

Print the added_signal list and then print the multiplied_signal list.

Signal Processing

signal1 = [1, 3, 5, 7, 9]
signal2 = [2, 4, 6, 8, 10]
length = len(signal1)
added_signal = []
multiplied_signal = []
for i in range(length):
    added_signal.append(signal1[i] + signal2[i])
    multiplied_signal.append(signal1[i] * signal2[i])
# Print the added_signal list
# Print the multiplied_signal list
# Your code here

Hint

Use two print() statements to show the two lists.

Practice

1. What happens when you add two signals of the same length point by point?

easy

A. The signals are concatenated end to end.

B. You get a new signal where each value is the product of the corresponding values.

C. You get a new signal where each value is the sum of the corresponding values.

D. The signals are subtracted from each other point by point.

Solution

1. Step 1: Understand signal addition

   Signal addition means adding each value of one signal to the corresponding value of the other signal.

2. Step 2: Apply point-by-point addition

   For signals of the same length, each position's values are summed to form the new signal.

3. Final Answer:

   You get a new signal where each value is the sum of the corresponding values. -> Option C

4. Quick Check:

   Signal addition = sum of values [OK]

Hint: Addition means sum values at each point [OK]

Common Mistakes:

• Confusing addition with multiplication
• Thinking signals concatenate instead of adding
• Assuming subtraction instead of addition

2. Which of the following is the correct Python syntax to multiply two signals stored as lists a and b element-wise?

easy

A. result = a + b

B. result = [a[i] * b[i] for i in range(len(a))]

C. result = multiply(a, b)

D. result = a * b

Solution

1. Step 1: Understand element-wise multiplication

   We multiply each element of list a by the corresponding element of list b.

2. Step 2: Use list comprehension with index

   The syntax [a[i] * b[i] for i in range(len(a))] correctly multiplies elements point by point.

3. Final Answer:

   result = [a[i] * b[i] for i in range(len(a))] -> Option B

4. Quick Check:

   Element-wise multiply = list comprehension [OK]

Hint: Use list comprehension with index for element-wise multiply [OK]

Common Mistakes:

• Using a * b which repeats list instead of multiply
• Using undefined function multiply
• Using addition instead of multiplication

3. Given two signals a = [1, 3, 5] and b = [2, 4, 6], what is the result of their element-wise addition?

medium

A. [3, 7, 11]

B. [2, 7, 11]

C. [2, 4, 6]

D. [1, 3, 5, 2, 4, 6]

Solution

1. Step 1: Add corresponding elements of signals

   Calculate 1+2=3, 3+4=7, 5+6=11 for each position.

2. Step 2: Form the new signal list

   The resulting list is [3, 7, 11].

3. Final Answer:

   [3, 7, 11] -> Option A

4. Quick Check:

   Sum each pair = [3, 7, 11] [OK]

Hint: Add each pair of values in order [OK]

Common Mistakes:

• Adding all values together instead of point-wise
• Confusing addition with multiplication
• Concatenating lists instead of adding

4. Consider the code below that tries to multiply two signals element-wise:

signal1 = [1, 2, 3]
signal2 = [4, 5]
result = [signal1[i] * signal2[i] for i in range(len(signal1))]

What is the main problem with this code?

medium

A. The signals have different lengths causing an index error.

B. The multiplication operator is incorrect.

C. The range should be based on signal2 length.

D. List comprehension syntax is invalid.

Solution

1. Step 1: Check signal lengths

   signal1 has length 3, signal2 has length 2, so they differ.

2. Step 2: Identify index error cause

   Loop runs 3 times, but signal2[2] does not exist, causing an error.

3. Final Answer:

   The signals have different lengths causing an index error. -> Option A

4. Quick Check:

   Different lengths cause index error [OK]

Hint: Check signal lengths before element-wise operations [OK]

Common Mistakes:

• Ignoring length mismatch
• Blaming operator instead of index range
• Assuming list comprehension syntax is wrong

5. You have two signals representing sensor readings:
temp = [20, 22, 21, 23] and humidity = [0.5, 0.6, 0.55, 0.65].
You want to create a new signal that represents the heat index by multiplying temperature and humidity point by point.
What is the correct Python code to do this?

hard

A. heat_index = [temp[i] + humidity[i] for i in range(len(temp))]

B. heat_index = temp * humidity

C. heat_index = multiply(temp, humidity)

D. heat_index = [temp[i] * humidity[i] for i in range(len(temp))]

Solution

1. Step 1: Confirm signals have same length

   Both temp and humidity have length 4, so element-wise operations are valid.

2. Step 2: Use list comprehension for multiplication

   Multiply each temperature by corresponding humidity using [temp[i] * humidity[i] for i in range(len(temp))].

3. Final Answer:

   heat_index = [temp[i] * humidity[i] for i in range(len(temp))] -> Option D

4. Quick Check:

   Element-wise multiply with list comprehension [OK]

Hint: Multiply matching elements with list comprehension [OK]

Common Mistakes:

• Using temp * humidity which repeats list
• Adding instead of multiplying signals
• Using undefined function multiply