Convolution with np.convolve() in NumPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to perform convolution of two arrays using numpy.

NumPy

import numpy as np

result = np.[1](a, b)
print(result)

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

Adot

Bconvolve

Cmultiply

Dadd

Attempts:

3 left

💡 Hint

Common Mistakes

Using np.dot instead of np.convolve

Using np.multiply which does element-wise multiplication

Using np.add which sums arrays element-wise

The np.convolve() function computes the convolution of two arrays.

2fill in blank

medium

Complete the code to specify the convolution mode as 'valid'.

NumPy

import numpy as np

result = np.convolve(a, b, mode=[1])
print(result)

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

A'valid'

B'same'

C'full'

D'extend'

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'full' mode which returns the complete convolution

Using 'same' mode which returns output the same size as first array

Using an invalid mode string

The mode='valid' returns output only where the signals fully overlap.

3fill in blank

hard

Fix the error in the code to correctly perform convolution.

NumPy

import numpy as np

a = [1, 2, 3]
b = [0, 1, 0.5]

result = np.convolve([1], b)
print(result)

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

Aa

Bb

Cresult

Dnp

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping the order of arrays

Passing the result variable instead of input arrays

Passing the numpy module instead of arrays

The first argument to np.convolve() should be the first array a.

4fill in blank

hard

Fill both blanks to create a dictionary with words as keys and their lengths as values for words longer than 3 characters.

NumPy

words = ['data', 'science', 'ai', 'ml', 'python']
lengths = { [1]: [2] for word in words if len(word) > 3 }
print(lengths)

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

Aword

Blen(word)

Cword.upper()

Dlen

Attempts:

3 left

💡 Hint

Common Mistakes

Using the length as key instead of value

Using word.upper() as key which changes the word

Using len function object instead of calling it

The dictionary comprehension uses the word as key and its length as value.

5fill in blank

hard

Fill all three blanks to create a dictionary with uppercase words as keys, their lengths as values, only for words longer than 3 characters.

NumPy

words = ['data', 'science', 'ai', 'ml', 'python']
lengths = { [1]: [2] for word in words if len(word) [3] 3 }
print(lengths)

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

Aword.upper()

Blen(word)

C>

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using lowercase words as keys

Using '<' instead of '>' in condition

Using the function len without parentheses

The dictionary comprehension uses uppercase words as keys, their lengths as values, and filters words longer than 3 characters.

Practice

1. What does the np.convolve() function do in numpy?

easy

A. It combines two arrays to produce a third array showing how one affects the other.

B. It sorts an array in ascending order.

C. It finds the maximum value in an array.

D. It reshapes an array into a different dimension.

Solution

1. Step 1: Understand the purpose of convolution

   Convolution combines two arrays to analyze how one array modifies or overlaps with the other.

2. Step 2: Match this with np.convolve() function

   In numpy, np.convolve() performs this combination and returns the resulting array.

3. Final Answer:

   It combines two arrays to produce a third array showing how one affects the other. -> Option A

4. Quick Check:

   np.convolve() = combine arrays [OK]

Hint: Convolution means combining arrays to see overlap effects [OK]

Common Mistakes:

• Confusing convolution with sorting or reshaping
• Thinking it finds max or min values
• Assuming it changes array shape without combining

2. Which of the following is the correct syntax to convolve two arrays a and b using numpy?

easy

A. np.convolve(a, b, mode='sum')

B. np.convolve(a + b)

C. np.convolve(a * b)

D. np.convolve(a, b)

Solution

1. Step 1: Recall the np.convolve() function signature

   The function requires two arrays as separate arguments: np.convolve(a, b).

2. Step 2: Check each option

   np.convolve(a, b) correctly passes two arrays. Options B and D use invalid expressions inside convolve. np.convolve(a, b, mode='sum') uses an invalid mode value.

3. Final Answer:

   np.convolve(a, b) -> Option D

4. Quick Check:

   Correct syntax = np.convolve(a, b) [OK]

Hint: np.convolve takes two arrays as separate arguments [OK]

Common Mistakes:

• Passing combined arrays instead of two separate arguments
• Using invalid mode values
• Using operators inside np.convolve() argument

3. What is the output of the following code?

import numpy as np
x = np.array([1, 2, 3])
k = np.array([0, 1])
result = np.convolve(x, k)
print(result)

medium

A. [0 1 2]

B. [1 2 3 0]

C. [0 1 2 3]

D. [1 2 3]

Solution

1. Step 1: Understand convolution of x and k

   Convolution slides kernel k over x, multiplying and summing overlapping elements. Here, x=[1,2,3], k=[0,1].

2. Step 2: Calculate convolution manually

   Output length = len(x)+len(k)-1 = 3+2-1=4.
   Values:
   Index 0: 1*0=0
   Index 1: 1*1 + 2*0=1
   Index 2: 2*1 + 3*0=2
   Index 3: 3*1=3
   Result: [0, 1, 2, 3]

3. Final Answer:

   [0 1 2 3] -> Option C

4. Quick Check:

   Convolution length = 4, values match [OK]

Hint: Output length = len(a)+len(b)-1 for default mode [OK]

Common Mistakes:

• Forgetting output length formula
• Mixing up order of multiplication
• Assuming output length equals input length

4. The following code throws an error. What is the mistake?

import numpy as np
x = np.array([1, 2, 3])
k = np.array([1, 0])
result = np.convolve(x, k, mode='middle')
print(result)

medium

A. Missing import statement for np.convolve()

B. 'middle' is not a valid mode for np.convolve()

C. np.convolve() requires integer arrays only

D. Arrays x and k must be the same length

Solution

1. Step 1: Check valid modes for np.convolve()

   Valid modes are 'full', 'valid', and 'same'. 'middle' is not valid.

2. Step 2: Identify error cause

   Using mode='middle' causes a ValueError because it's unsupported.

3. Final Answer:

   'middle' is not a valid mode for np.convolve() -> Option B

4. Quick Check:

   Valid modes = full, valid, same [OK]

Hint: Use only 'full', 'valid', or 'same' modes in np.convolve() [OK]

Common Mistakes:

• Using unsupported mode strings
• Assuming arrays must be same length
• Thinking np.convolve needs special imports

5. You want to smooth a noisy signal stored in array signal using a simple moving average kernel of length 3. Which code correctly applies convolution to achieve this smoothing?

hard

A. kernel = np.array([1, 1, 1])
smoothed = np.convolve(signal, kernel, mode='valid') / 3

B. kernel = np.array([1, 1, 1])
smoothed = np.convolve(signal, kernel, mode='full') * 3

C. kernel = np.array([1, 0, 1])
smoothed = np.convolve(signal, kernel, mode='same') / 2

D. kernel = np.array([1, 1, 1])
smoothed = np.convolve(signal, kernel, mode='valid') * 3

Solution

1. Step 1: Define the moving average kernel

   A simple moving average kernel of length 3 is [1, 1, 1].

2. Step 2: Apply convolution and normalize

   Convolve signal with kernel using mode='valid' to avoid edge effects, then divide by 3 to average.

3. Final Answer:

   kernel = np.array([1, 1, 1]) smoothed = np.convolve(signal, kernel, mode='valid') / 3 -> Option A

4. Quick Check:

   Moving average = sum/3 with valid mode [OK]

Hint: Use kernel of ones and divide by length for moving average [OK]

Common Mistakes:

• Forgetting to divide by kernel length
• Using wrong kernel values
• Using mode='full' causing longer output
• Multiplying instead of dividing for average