Correlation (correlate) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of 1D correlation using scipy.correlate

What is the output of the following code snippet using scipy.signal.correlate on two 1D arrays?

SciPy

import numpy as np
from scipy.signal import correlate

x = np.array([1, 2, 3])
y = np.array([0, 1, 0.5])
result = correlate(x, y, mode='full')
print(result)

A [0. 1. 2.5 4. 1.5]

B [0. 1. 2.5 3. 1.5]

C [0. 1. 2. 3. 1.5]

D [0. 1. 2.5 4. 3. ]

💡 Hint

Remember that correlation flips the second array before sliding it over the first.

The correlation flips y and slides it over x, computing sums of products at each shift. The output length is len(x)+len(y)-1 = 5. The values correspond to the sums at each shift.

❓ data_output

intermediate

Length of correlation output with different modes

Given two arrays a and b of lengths 4 and 3 respectively, what is the length of the output from scipy.signal.correlate(a, b, mode='valid')?

SciPy

import numpy as np
from scipy.signal import correlate

a = np.array([1, 2, 3, 4])
b = np.array([0, 1, 0.5])
result = correlate(a, b, mode='valid')
print(len(result))

A 3

B 2

C 4

D 6

💡 Hint

For 'valid' mode, output length is max(len(a), len(b)) - min(len(a), len(b)) + 1.

The 'valid' mode returns only points where the arrays fully overlap. So length is 4 - 3 + 1 = 2.

🔧 Debug

advanced

Identify the error in correlation code

What error will this code raise when run, and why?

SciPy

from scipy.signal import correlate

x = [1, 2, 3]
y = [0, 1, 'a']
result = correlate(x, y)
print(result)

A SyntaxError: invalid syntax

B ValueError: operands could not be broadcast together

C No error, outputs a numeric array

D TypeError: unsupported operand type(s) for *: 'int' and 'str'

💡 Hint

Check the data types in the input arrays.

The list y contains a string 'a', which cannot be multiplied by integers during correlation, causing a TypeError.

🚀 Application

advanced

Using correlation to find a pattern in a signal

You have a signal array signal = [1, 3, 2, 1, 0, 1, 3, 2] and a pattern pattern = [1, 3, 2]. Using scipy.signal.correlate with mode='valid', which index in the correlation output corresponds to the best match of the pattern in the signal?

SciPy

import numpy as np
from scipy.signal import correlate

signal = np.array([1, 3, 2, 1, 0, 1, 3, 2])
pattern = np.array([1, 3, 2])
correlation = correlate(signal, pattern, mode='valid')
best_match_index = np.argmax(correlation)
print(best_match_index)

A 5

B 0

C 1

D 6

💡 Hint

Look for where the pattern aligns best with the signal by highest correlation value.

The highest correlation value occurs at index 5, where the pattern matches the last three elements of the signal exactly.

🧠 Conceptual

expert

Effect of correlation mode on output length

Given two arrays of lengths 7 and 5, which mode of scipy.signal.correlate will produce an output array of length 5?

A 'full'

B 'valid'

C None of the above

D 'same'

💡 Hint

The 'same' mode returns output length equal to the first input array.

The 'same' mode returns an output with the same length as the first input array (7). 'valid' returns length 3, 'full' returns length 11. None produce length 5 except 'same' if the first array length is 5.