INTERPOL Function

Standard Library function that performs a linear interpolation of a vector using either a regular or irregular grid.

result = INTERPOL(v, n)

This form is used with a regular grid.

result = INTERPOL(v, x, u)

This form is used with an irregular grid.

For a regular grid:

v The dependent values of the vector that is to be interpolated. Must be one-dimensional. Can be of any data type except string.

n The number of interpolated points.

For an irregular grid:

v The dependent values of the vector that is to be interpolated. Must be one-dimensional. Can be of any data type except string.

x The independent values of the vector that is to be interpolated. Must have the same number of values as v, and must be monotonic, either increasing or decreasing.

u The independent values at which interpolation is to occur. Is not necessarily monotonic.

For a regular grid:

result A vector containing n points interpolated from vector v.

For an irregular grid:

result A vector containing the same number of values as u.

None.

The result returned by INTERPOL differs depending on whether a regular or an irregular grid was used, as described below.

• Regularly-gridded vectors. The vector resulting from INTERPOL used with a regular grid is calculated in the following way, using the FIX function:

result(i) = v(j) + (j - FIX(j)) (v(j + 1) - v(j))

where

j = i(m-1)/(n-1)

i is in the range 0 i (n-1)

m is the number of points in the input vector v.

The output grid horizontal coordinates (abscissae values) are calculated in the following way, using the FLOAT function:

abscissa_value(i) = FLOAT(i) / m

where i is in the range 0 i (n - 1).

• Irregularly-gridded vectors. The vector resulting from INTERPOL used with an irregular grid has the same number of elements as j and is calculated in the following way, using the FIX function:

result(i) = v(j) + (j - FIX(j)) (v(j + 1) - v(j))

where j = u(i).

INTERPOL can be used in signal processing to reconstruct the signal between original samples of data. For example, suppose you have 5 sample data readings, [0, 5, 10, 5, 0], but you need 15 samples.

To get these additional samples, enter the following command:

out_vector = INTERPOL(in_vector, 15)

where in_vector has a value of [0, 5, 10, 5, 0] andout_vector yields the following values:

[0, 1.42857, 2.85714, 4.28571, 5.71429, 7.14286, 8.57143, 10.0000, 
8.57143, 7.14286, 5.71429, 4.28571, 2.85714, 1.42857, 0]

The data still starts and ends with zero, and the maximum is still ten, but all the points in between have been recalculated.

BILINEAR, SPLINE