Interpolation (interp1) in MATLAB - Step-by-Step Execution

Concept Flow - Interpolation (interp1)

Define known points x, y

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Choose query points xi

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Call interp1(x, y, xi)

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interp1 finds position of xi in x

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Calculate interpolated yi values

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Return yi as output

This flow shows how interp1 takes known data points and query points, then calculates interpolated values step-by-step.

Execution Sample

MATLAB

x = [1 2 3 4];
y = [10 20 30 40];
xi = 2.5;
yi = interp1(x, y, xi);

This code finds the interpolated y value at x=2.5 using linear interpolation.

Execution Table

Step	Action	Input/Condition	Result/Output
1	Define x and y	x=[1 2 3 4], y=[10 20 30 40]	Known data points set
2	Define xi	xi=2.5	Query point set
3	Find interval for xi	2 <= 2.5 <= 3	xi lies between x(2)=2 and x(3)=3
4	Calculate interpolation fraction	fraction = (2.5-2)/(3-2) = 0.5	fraction=0.5
5	Calculate yi	yi = y(2) + fraction*(y(3)-y(2))	yi = 20 + 0.5*(30-20) = 25
6	Return yi	yi=25	Interpolated value at xi=2.5 is 25

💡 Interpolation complete for xi=2.5 within x range

Variable Tracker

Variable	Start	After Step 2	After Step 4	Final
x	[1 2 3 4]	[1 2 3 4]	[1 2 3 4]	[1 2 3 4]
y	[10 20 30 40]	[10 20 30 40]	[10 20 30 40]	[10 20 30 40]
xi	undefined	2.5	2.5	2.5
fraction	undefined	undefined	0.5	0.5
yi	undefined	undefined	undefined	25

Key Moments - 3 Insights

Why does interp1 look for the interval where xi fits between x values?

Because interpolation estimates yi by using the two known points around xi, as shown in step 3 of the execution_table.

What happens if xi is exactly one of the x points?

interp1 returns the corresponding y value directly without interpolation, since the point is known exactly.

Why do we calculate the fraction (step 4) before finding yi?

The fraction tells us how far xi is between the two x points, so we can scale the difference in y values accordingly.

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of 'fraction' at step 4?

A 25

B 2.5

C 0.5

D 1

💡 Hint

Check the 'fraction' value in the 'Result/Output' column at step 4.

At which step does interp1 find the interval where xi fits between x values?

A Step 2

B Step 3

C Step 5

D Step 6

💡 Hint

Look for the step describing 'Find interval for xi' in the execution_table.

If xi was 3 instead of 2.5, what would yi be according to the variable_tracker?

A 30

B 20

C 25

D 35

💡 Hint

Recall that if xi matches an x point exactly, yi equals the corresponding y value.

Concept Snapshot

interp1(x, y, xi) finds yi by linear interpolation.
It locates xi between two x points,
calculates fraction of distance,
and scales y difference accordingly.
Returns yi as interpolated value.

Full Transcript

This visual execution traces MATLAB's interp1 function. First, known points x and y are defined. Then, a query point xi is chosen. interp1 finds where xi fits between x values, calculates how far xi is between those points as a fraction, and uses that fraction to interpolate yi between the corresponding y values. The final yi is returned as the estimated value at xi. This step-by-step shows how interpolation works by estimating values between known data points.