Complex number Inerpolation

In summary: If you are working with Fourier Transformation and collecting values based on some formula, then the correct approach would be to first convert the complex numbers into (R,Theta) coordinates and then interpolate on R and Theta before converting back to (x,y) coordinates. This is because it is more accurate and preserves the original form of the data. However, if you are only using linear interpolation and not concerned with accuracy or preserving the original form, then the first approach would be sufficient. Ultimately, the choice between the two approaches depends on your specific needs and the nature of your data.
  • #1
sansty
1
0
Hi,
I need to do Interpolation of complex numbers let say
z1=x1+i*y1
and
z2=x2+i*y2
now I have two approaches:
1) interpolate real and imaginary parts separately and have the result

or

2) First change the complex numbers into (R,Theta) co-ordinate and then do the interpolation on R and Theta, and then transform it back to (x,y) co-ordinates...

so which of my appraoch is right, as I have seen different results..
Please reply ASAP
__________________________________________________________________________________________________

thanks to @mathman and @hamster143 for reply...

I want to further clear my problem...
I am doing Fourier Transformation of a 2D data, and then in Fourier domain, based on some formula, I am collecting values, and in some cases required values comes in between the spacing of two samples in Fourier domain. So to get those values I need to do interpolation, and for time being, I am using "linear interpolation" .
and my problem is my two approaches gives me two different results, and my prof. wants to know why am I using particular approach, with some proof...
 
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  • #2
If by interpolation, you mean linear interpolation, then the first approach (interpolate in x and y) is correct.
 
  • #3
Depends on the reason why you need to interpolate them.
 

1. What are complex numbers?

Complex numbers are numbers that consist of a real part and an imaginary part. The imaginary part is represented by the square root of -1, often denoted as "i". Complex numbers are written in the form a + bi, where a is the real part and bi is the imaginary part.

2. What is interpolation?

Interpolation is a mathematical method used to estimate values between known data points. It involves finding a function that passes through the given data points and using that function to calculate intermediate values.

3. How does complex number interpolation work?

Complex number interpolation works by finding a complex-valued function that passes through a set of given complex numbers. This function is used to estimate intermediate values between the known complex numbers.

4. What are some applications of complex number interpolation?

Complex number interpolation has various applications in mathematics and engineering. It is used in signal processing, image processing, and numerical analysis to estimate values between known data points. It is also used in circuit design, fluid dynamics, and computer graphics, among others.

5. Are there different methods for complex number interpolation?

Yes, there are various methods for complex number interpolation, including linear interpolation, polynomial interpolation, and spline interpolation. The choice of method depends on the given data and the desired accuracy of the estimated values.

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