Convolution operation in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to compute the convolution of two 1D signals using numpy.

Signal Processing

import numpy as np
signal = np.array([1, 2, 3])
kernel = np.array([0, 1, 0.5])
result = np.[1](signal, kernel)
print(result)

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

Aconvolve

Bdot

Cmultiply

Dadd

Attempts:

3 left

💡 Hint

Common Mistakes

Using dot product instead of convolution

Trying to multiply arrays directly

Using addition instead of convolution

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

2fill in blank

medium

Complete the code to perform convolution with 'valid' mode to avoid zero-padding.

Signal Processing

import numpy as np
signal = np.array([1, 2, 3, 4])
kernel = np.array([1, 0])
result = np.convolve(signal, kernel, mode='[1]')
print(result)

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

Avalid

Bsame

Cfull

Dextend

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'full' mode which includes zero-padding

Using 'same' mode which pads to keep size

Using an invalid mode string

The 'valid' mode returns only positions where the signals fully overlap, avoiding zero-padding.

3fill in blank

hard

Fix the error in the code to compute convolution of two lists by converting them to numpy arrays first.

Signal Processing

import numpy as np
signal = [1, 2, 3]
kernel = [0, 1, 0.5]
result = np.convolve([1], kernel)
print(result)

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

Asignal.tolist()

Bsignal

Clist(signal)

Dnp.array(signal)

Attempts:

3 left

💡 Hint

Common Mistakes

Passing a Python list directly to np.convolve

Using list() or tolist() which do not convert to numpy array

Convolution requires numpy arrays, so convert the list to an array first.

4fill in blank

hard

Fill both blanks to create a dictionary of convolution results for signals longer than 2 elements.

Signal Processing

signals = {'a': [1, 2, 3], 'b': [0, 1], 'c': [2, 3, 4, 5]}
kernel = [1, 0]
results = {key: np.convolve(np.array(value), kernel) for key, value in signals.items() if len(value) [1] 2}
print(results)

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

A!=

B==

C>

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' or '==' which exclude longer signals

Using '!=' which includes unwanted lengths

We want to include only signals longer than 2 elements, so use '>' operator.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that convolves signals with kernel only if signal length is greater than 2.

Signal Processing

signals = {'x': [1, 2, 3], 'y': [4, 5], 'z': [6, 7, 8, 9]}
kernel = [1, 0]
results = { [1]: np.convolve(np.array([2]), kernel) for [3], [2] in signals.items() if len([2]) > 2 }
print(results)

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

Akey

Bvalue

Ck

Dv

Attempts:

3 left

💡 Hint

Common Mistakes

Using inconsistent variable names

Using the value as the key in the dictionary

The dictionary comprehension uses key and value to iterate and build results.

Practice

1. What does the convolution operation do in signal processing?

easy

A. It adds two signals point by point

B. It multiplies two signals element-wise without shifting

C. It combines two signals to see how one modifies the other

D. It reverses a signal in time

Solution

1. Step 1: Understand convolution purpose

   Convolution combines two signals by flipping one and sliding it over the other to measure overlap.

2. Step 2: Compare with other operations

   Multiplying element-wise or adding signals do not capture the shifting and overlap aspect of convolution.

3. Final Answer:

   It combines two signals to see how one modifies the other -> Option C

4. Quick Check:

   Convolution = combine and shift signals [OK]

Hint: Convolution slides and multiplies signals to combine effects [OK]

Common Mistakes:

• Confusing convolution with element-wise multiplication
• Thinking convolution just adds signals
• Believing convolution reverses signals without overlap

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

easy

A. numpy.convolve(a, b)

B. numpy.conv(a, b)

C. numpy.convolution(a, b)

D. numpy.convolve_arrays(a, b)

Solution

1. Step 1: Recall numpy convolution function

   The correct numpy function to compute convolution is numpy.convolve().

2. Step 2: Check other options

   Functions like conv, convolution, or convolve_arrays do not exist in numpy.

3. Final Answer:

   numpy.convolve(a, b) -> Option A

4. Quick Check:

   Use numpy.convolve() for convolution [OK]

Hint: Remember numpy.convolve() is the standard convolution function [OK]

Common Mistakes:

• Using incorrect function names like conv or convolution
• Forgetting to import numpy before calling the function
• Confusing convolution with other numpy functions

3. What is the output of the following Python code?

import numpy as np
x = np.array([1, 2, 3])
h = np.array([0, 1, 0.5])
result = np.convolve(x, h)
print(result)

medium

A. [0. 1. 2. 3. 0.5]

B. [0. 1. 2.5 4. 1.5]

C. [1. 2. 3.]

D. [0.5 1. 1.5 2. 3. ]

Solution

1. Step 1: Understand convolution calculation

   Convolution flips and slides h over x, multiplying and summing overlapping elements.

2. Step 2: Calculate each element of result

   Result length = len(x)+len(h)-1 = 5.
   Calculations:
   Index 0: 1*0 = 0
   Index 1: 1*1 + 2*0 = 1
   Index 2: 1*0.5 + 2*1 + 3*0 = 0.5 + 2 = 2.5
   Index 3: 2*0.5 + 3*1 = 1 + 3 = 4
   Index 4: 3*0.5 = 1.5

3. Final Answer:

   [0. 1. 2.5 4. 1.5] -> Option B

4. Quick Check:

   Convolution sums = [0,1,2.5,4,1.5] [OK]

Hint: Result length = len(a)+len(b)-1; calculate stepwise [OK]

Common Mistakes:

• Confusing element-wise multiplication with convolution
• Ignoring the length increase after convolution
• Miscomputing sums at each step

4. The following code attempts to compute the convolution of two lists but produces an error. What is the error?

import numpy as np
x = [1, 2, 3]
h = [0, 1, 0.5]
result = np.convolve(x, h, mode='same')
print(result)

medium

A. AttributeError because np.convolve does not accept lists

B. TypeError because lists are not converted to numpy arrays

C. ValueError due to invalid mode parameter

D. No error; code runs correctly

Solution

1. Step 1: Check numpy.convolve input types

   numpy.convolve accepts lists or arrays as inputs by converting lists internally.

2. Step 2: Verify mode parameter

   Mode 'same' is valid and returns output of same length as first input.

3. Final Answer:

   No error; code runs correctly -> Option D

4. Quick Check:

   np.convolve accepts lists and mode='same' is valid [OK]

Hint: np.convolve works with lists; mode='same' is valid [OK]

Common Mistakes:

• Assuming lists cause TypeError in np.convolve
• Thinking mode='same' is invalid
• Expecting numpy arrays are mandatory

5. You have two signals: signal = [1, 3, 2, 1] and kernel = [0.5, 0.5]. You want to smooth the signal by averaging each point with its neighbor using convolution. Which code snippet correctly performs this smoothing and returns the smoothed signal of the same length as the original?

hard

A. np.convolve(signal, kernel, mode='same')

B. np.convolve(signal, kernel, mode='full')

C. np.convolve(signal, kernel, mode='valid')

D. np.convolve(kernel, signal, mode='same')

Solution

1. Step 1: Understand smoothing with convolution

   Smoothing averages each point with neighbors using a kernel like [0.5, 0.5].

2. Step 2: Choose convolution mode for output length

   Mode 'same' returns output same length as input, preserving signal size.

3. Step 3: Check argument order

   The first argument is the signal, the second is the kernel. Swapping produces output length of the kernel.

4. Final Answer:

   np.convolve(signal, kernel, mode='same') -> Option A

5. Quick Check:

   Smoothing = convolution with kernel, mode='same' [OK]

Hint: Use mode='same' to keep output length equal to input [OK]

Common Mistakes:

• Using mode='full' which increases output length
• Using mode='valid' which shortens output
• Swapping the signal and kernel arguments