# Why is the Second to Last Sample Off Scale in My Cubic Spline Boundary Problem?

• bwhitejr
In summary: The last sample in the new arrays may still be off scale, so you may need to adjust for that. In summary, the conversation discusses the problem of converting a file with three arrays of 528 samples into three arrays of 301 samples. The solution proposed is to use the interpolation method to calculate the values for the points in between the existing samples. This method may need to be adjusted for the last sample in the new arrays that may still be off scale.
bwhitejr
Hi All,
I am trying to convert a file that has three arrays of 528 samples into three arrays of 301.
The first is log spaced frequency points the second is the impedance values at each frequency and the last is phase values. I have the routines spline and splint. My problem is the the second to last sample [299] is off scale. The last sample [300] is correct. I know it is some kind of boundary problem, but it is beyond me to figure it out.

fr,re,ph are arrays[1..528] of float

Spline(fr,re,528,re[1],re[528],y2);
Spline(fr,ph,528,ph[1],ph[528],y4);
fm:=Power((20000.0/10.0),1.0/300);
For i:=1 to 301 do
begin
tempARRF:=10.0*Power(fm,i-1);
end;
For i:=1 to 301 do
begin
splint(fr,re,y2,528,tempARRF,tempARRR);
splint(fr,ph,y4,528,tempARRF,tempARRP);
end;
CloseFile(impFile);
For i:=0 to 300 do
begin
impARR.Freq:=tempARRF[i+1];
impARR.Res:=tempARRR[i+1];
impARR.Phs:=tempARRP[i+1];
end;

You could try using the interpolation method to convert the 528 samples into 301. Interpolation works by taking the two closest points and then using a formula to calculate the values for the points in between. For example, if you have two points (x1,y1) and (x2,y2), and you want to calculate the value of y at x, you can use the following formula: y = y1 + (x - x1)(y2 - y1)/(x2 - x1)You can apply this formula to the three arrays of 528 samples to calculate the three arrays of 301 samples.

## What is a Cubic Spline Boundary Problem?

A Cubic Spline Boundary Problem is a mathematical problem in which a curve is defined by a set of points, and the goal is to find a smooth curve that passes through each of these points. It involves using cubic polynomials to create a continuous curve with specific boundary conditions.

## What are some real-world applications of Cubic Spline Boundary Problems?

Cubic Spline Boundary Problems have a wide range of practical applications, such as in computer graphics, where they are used to create smooth curves and surfaces in 3D models. They are also commonly used in engineering and physics to model and solve problems involving curves and surfaces, such as in fluid dynamics and structural analysis.

## How is a Cubic Spline Boundary Problem solved?

To solve a Cubic Spline Boundary Problem, the curve is broken down into smaller segments, and cubic polynomials are used to create a smooth curve within each segment. The polynomials are then joined together at the points where they meet, ensuring that the curve is continuous. The coefficients of the polynomials are determined using the given boundary conditions.

## What are the benefits of using Cubic Spline Boundary Problems?

One of the main benefits of using Cubic Spline Boundary Problems is that they provide a smooth and continuous curve that accurately represents the given data points. They also allow for easy manipulation and control of the curve, making them useful in various applications. Additionally, they can handle complex boundary conditions and provide a more accurate solution than other curve-fitting methods.

## Are there any limitations to using Cubic Spline Boundary Problems?

While Cubic Spline Boundary Problems have many benefits, they also have some limitations. One of the main limitations is that they require a large number of data points to accurately represent the curve. They also may not perform well in cases where the curve has sharp corners or discontinuities. Additionally, the solutions may be sensitive to changes in the given data points.