Interpolation (interp1) in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the purpose of the interp1 function in MATLAB?

The interp1 function is used to find intermediate values between known data points in one dimension. It helps estimate values at points where data is not explicitly given.

beginner

What are the basic inputs required for interp1?

You need three inputs:
1. x: known data points on the x-axis,
2. v: known values at points x,
3. xq: query points where you want to estimate values.

beginner

Name two common interpolation methods used with interp1.

Two common methods are:
1. 'linear': connects points with straight lines.
2. 'nearest': uses the value of the closest known point.

intermediate

What happens if the query points xq are outside the range of known points x in interp1?

By default, interp1 returns NaN for query points outside the known range. You can change this behavior by specifying an extrapolation method.

beginner

How do you specify the interpolation method in interp1?

You add the method as the fourth argument, for example: interp1(x, v, xq, 'spline') uses spline interpolation.

What does interp1(x, v, xq, 'nearest') do?

A Connects points with straight lines to estimate values.

B Returns NaN for all query points.

C Uses polynomial fitting for interpolation.

D Returns the value of the closest known point to each query point.

The 'nearest' method picks the value of the closest known point to each query point.

If xq is outside the range of x, what is the default output of interp1?

A NaN (Not a Number).

B Extrapolated value based on nearest point.

C Zero.

D Error message.

By default, interp1 returns NaN for query points outside the known data range.

Which input to interp1 represents the known values at data points?

A <code>x</code>

B <code>xq</code>

C <code>v</code>

D <code>method</code>

v holds the known values corresponding to points x.

What interpolation method connects points with straight lines?

A 'nearest'

B 'linear'

C 'pchip'

D 'spline'

The 'linear' method connects known points with straight lines.

How do you ask interp1 to use spline interpolation?

A interp1(x, v, xq, 'spline')

B interp1(x, v, xq, 'nearest')

C interp1(x, v, xq, 'linear')

D interp1(x, v, xq)

Passing 'spline' as the method argument uses spline interpolation.

Explain how interp1 works and when you would use it.

Think about filling gaps between known points.

Describe the difference between 'nearest' and 'linear' interpolation methods in interp1.

Consider how the estimated values change between points.

Practice

1. What does the MATLAB function interp1 do?

easy

A. It calculates the derivative of a function.

B. It sorts a vector in ascending order.

C. It estimates intermediate values between known data points.

D. It plots data points on a graph.

Solution

1. Step 1: Understand the purpose of interpolation

   Interpolation is used to estimate values between known data points.

2. Step 2: Identify the role of interp1

   interp1 in MATLAB performs 1D interpolation to find intermediate values.

3. Final Answer:

   It estimates intermediate values between known data points. -> Option C

4. Quick Check:

   Interpolation = estimating values [OK]

Hint: Remember: interp1 fills gaps between points [OK]

Common Mistakes:

• Confusing interpolation with sorting
• Thinking interp1 calculates derivatives
• Assuming interp1 creates plots

2. Which of the following is the correct syntax to interpolate the value at x = 2.5 using vectors x and y in MATLAB?

easy

A. interp1(x, y, 2.5)

B. interp1(y, x, 2.5)

C. interp1(2.5, x, y)

D. interp1(x, 2.5, y)

Solution

1. Step 1: Recall interp1 function syntax

   The syntax is interp1(x, y, xi) where x and y are known points, xi is query point.

2. Step 2: Match the correct order of arguments

   interp1(x, y, 2.5) uses interp1(x, y, 2.5), which matches the syntax correctly.

3. Final Answer:

   interp1(x, y, 2.5) -> Option A

4. Quick Check:

   interp1(x, y, xi) = correct syntax [OK]

Hint: Remember: interp1(x, y, xi) order matters [OK]

Common Mistakes:

• Swapping x and y vectors
• Putting query point before vectors
• Using wrong argument order

3. Given x = [1 2 3 4] and y = [10 20 30 40], what is the output of interp1(x, y, 2.5) in MATLAB?

medium

A. Error

B. 20

C. 30

D. 25

Solution

1. Step 1: Understand linear interpolation between points

   At x=2, y=20 and at x=3, y=30. For x=2.5, interpolate linearly.

2. Step 2: Calculate interpolated value

   Value = 20 + (2.5-2)*(30-20)/(3-2) = 20 + 0.5*10 = 25.

3. Final Answer:

   25 -> Option D

4. Quick Check:

   Linear interp at 2.5 = 25 [OK]

Hint: Linear interp averages between neighbors [OK]

Common Mistakes:

• Choosing nearest point value instead of interpolating
• Confusing x and y values
• Expecting an error for valid input

4. What is wrong with this MATLAB code snippet?

x = [1 2 3];
y = [10 20];
interp1(x, y, 2)

medium

A. Vectors x and y have different lengths causing an error.

B. The query point 2 is outside the range of x.

C. interp1 requires y to be a matrix, not a vector.

D. The syntax of interp1 is incorrect.

Solution

1. Step 1: Check vector lengths

   Vector x has length 3, y has length 2; they must be equal for interp1.

2. Step 2: Identify error cause

   Different lengths cause MATLAB to throw an error when calling interp1.

3. Final Answer:

   Vectors x and y have different lengths causing an error. -> Option A

4. Quick Check:

   Equal vector lengths needed [OK]

Hint: Check x and y lengths match before interp1 [OK]

Common Mistakes:

• Ignoring vector length mismatch
• Thinking query point must be outside range
• Assuming interp1 needs matrix y

5. You have temperature data temp = [15 18 21 24] measured at times time = [0 3 6 9] hours. How would you find the temperature at 4.5 hours using cubic interpolation in MATLAB?

hard

A. interp1(time, temp, 4.5)

B. interp1(time, temp, 4.5, 'cubic')

C. interp1(time, temp, 4.5, 'linear')

D. interp1(temp, time, 4.5, 'cubic')

Solution

1. Step 1: Identify correct argument order and method

   Syntax is interp1(x, y, xi, method). Here x=time, y=temp, xi=4.5, method='cubic'.

2. Step 2: Choose cubic interpolation

   interp1(time, temp, 4.5, 'cubic') uses 'cubic' method correctly for smooth interpolation.

3. Final Answer:

   interp1(time, temp, 4.5, 'cubic') -> Option B

4. Quick Check:

   Use 'cubic' for smooth interp [OK]

Hint: Use 'cubic' as 4th argument for smooth interp [OK]

Common Mistakes:

• Swapping time and temp vectors
• Using default linear instead of cubic
• Omitting interpolation method argument