Signal addition and multiplication in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to add two signals element-wise.

Signal Processing

result = signal1 [1] signal2

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

A+

B/

C-

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using * instead of + causes multiplication, not addition.

Using - subtracts signals instead of adding.

Adding two signals means adding their values at each point, which is done using the + operator.

2fill in blank

medium

Complete the code to multiply two signals element-wise.

Signal Processing

result = signal1 [1] signal2

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

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using + adds signals instead of multiplying.

Using / divides signals instead of multiplying.

Multiplying two signals element-wise uses the * operator to multiply each pair of values.

3fill in blank

hard

Fix the error in the code to correctly add two signals stored as numpy arrays.

Signal Processing

import numpy as np
signal1 = np.array([1, 2, 3])
signal2 = np.array([4, 5, 6])
result = signal1 [1] signal2

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

A+

B*

C-

D//

Attempts:

3 left

💡 Hint

Common Mistakes

Using * multiplies arrays instead of adding.

Using // causes floor division, which is not addition.

To add numpy arrays element-wise, use the + operator.

4fill in blank

hard

Fill both blanks to create a new signal by multiplying signal1 by 2 and then adding signal2.

Signal Processing

new_signal = (signal1 [1] 2) [2] signal2

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

A*

B+

C-

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using - instead of + changes the operation to subtraction.

Using / instead of * causes division, not scaling.

First multiply signal1 by 2 using *, then add signal2 using +.

5fill in blank

hard

Fill all three blanks to create a signal dictionary with keys as signal names and values as signals multiplied by 3 if their length is greater than 2.

Signal Processing

signals = {'a': [1, 2, 3], 'b': [4, 5], 'c': [6, 7, 8, 9]}
result = {k[1]: [x[2] 3 for x in v] for k, v in signals.items() if len(v) [3] 2}

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

A.upper()

B*

C>

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using + instead of * changes multiplication to addition.

Using < instead of > filters the wrong signals.

Use k.upper() to capitalize keys, multiply each element by 3, and filter signals with length greater than 2.

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