Correlation with np.correlate() in NumPy - Step-by-Step Execution

Concept Flow - Correlation with np.correlate()

Start with two arrays x, y

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Call np.correlate(x, y, mode='full')

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Slide y over x, multiply overlapping elements

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Sum products for each overlap position

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Collect sums into result array

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Return correlation array showing similarity at each lag

np.correlate slides one array over another, multiplies overlapping values, sums them, and returns these sums to show similarity at different shifts.

Execution Sample

NumPy

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

Calculate full correlation of x and y arrays, showing similarity at all shifts.

Execution Table

Step	Overlap Position (Lag)	Overlapping Elements (x, y)	Products	Sum of Products	Result Array Value
1	-2	(3, 0.5)	3*0.5=1.5	1.5	1.5
2	-1	(2, 0.5), (3, 1)	2*0.5=1, 3*1=3	4	4
3	0	(1, 0), (2, 1), (3, 0.5)	1*0=0, 2*1=2, 3*0.5=1.5	3.5	3.5
4	1	(1, 1), (2, 0.5)	1*1=1, 2*0.5=1	2	2
5	2	(1, 0)	1*0=0	0	0

💡 All overlap positions processed, correlation array complete with length 5 (2*len(x)-1).

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	Final
result	[]	[1.5]	[1.5, 4]	[1.5, 4, 3.5]	[1.5, 4, 3.5, 2]	[1.5, 4, 3.5, 2, 0]	[1.5, 4, 3.5, 2, 0]

Key Moments - 3 Insights

Why does the result array have length 5 when input arrays have lengths 3?

np.correlate with mode='full' returns an array of length 2*N-1 where N is length of input arrays, because it computes correlation at all possible overlaps including partial ones (see execution_table rows 1 to 5).

Why do some overlap positions have fewer elements multiplied?

At edges, arrays partially overlap, so fewer elements multiply (see execution_table rows 1 and 5), unlike the full overlap in the middle (row 3).

What does a higher sum of products mean in the result?

A higher sum means stronger similarity at that lag position, indicating the arrays align better there (see step 3 with sum 3.5).

Visual Quiz - 3 Questions

Look at the execution table, what is the sum of products at overlap position 0?

A 3.5

B 3

C 2

D 0.5

💡 Hint

Check the row with Overlap Position (Lag) 0 in the execution_table.

At which overlap position does the correlation result first become non-zero?

A -1

B 0

C -2

D 1

💡 Hint

Look at the Sum of Products column in execution_table rows from top to bottom.

If the input arrays were longer, how would the length of the result array change?

A It would stay the same length

B It would be twice the length of the longer array minus one

C It would be the sum of lengths of both arrays

D It would be the product of the lengths

💡 Hint

Recall the exit_note and how result length is calculated as 2*N-1 for arrays of length N.

Concept Snapshot

np.correlate(x, y, mode='full') slides y over x,
multiplies overlapping elements,
sums these products for each shift,
and returns an array showing similarity at each lag.
Result length = 2*len(x) - 1.
Useful for finding where two signals match.

Full Transcript

This visual execution shows how np.correlate computes the correlation of two arrays by sliding one over the other. At each overlap position, it multiplies the overlapping elements and sums these products. The result array collects these sums for all possible overlaps, including partial ones at the edges. The length of the result is 2*N-1 for input arrays of length N. Higher sums indicate stronger similarity at that lag. The step-by-step table traces each overlap position, the elements multiplied, and the sum computed, helping beginners see exactly how the correlation is built.