fft_upsample

Upsamples a complex series to form time domain interpolation for a fixed spaced grid.

Description

One cannot interpolate a complex number in the form of Real + j*imaginary.
The only way to do interpolation is on the complex representation of an amplitude + phase. But sometimes the phase is not continuous, and given in the modulo(2*pi) representation (such as the result from the "FFT" function).

Using "unwrap" function does not always manage to restore the phase to be continuous, thus interpolation in the Fourier plane is probably the only answer.

This function works on a single or 2 dimensional arrays.

• Acknowledgements: This submission has inspired the following:; updownsample
• MATLAB release: MATLAB 6.1 (R12.1)

[karri srinivas]

Respected sir,
i, srinivas, am student from university of applied sciences offenburg. i am doing master thesis on visualization of 3d electromagnetic fileds using animation. in this topic i have to interpolate two complex numbers. i did that taking real and imaginary parts seperately and also using magnitude and phase but i am not able to get interpolation correctly please do help me in calcualating interpolation using complex numbers
my email is [e-mail]

Thanking you sir,
srinivas

[Spam A. Lope]

Straight forward approach. I was hoping for a faster method that forward and backward transforms, possibly a short term transform or approximation. I am curious if there is a good prediction routine for complex numbers to predict values outside the bounds of known samples.

[Adam Wyatt]

I found the output of this function to be VASTLY incorrect (e.g. for a spiral, even when the spiral was well sampled).

"One cannot interpolate a complex number in the form of Real + j*imaginary. "
I do not believe this statement!!

One can interpolate the real and imaginary numbers instead of amp and phase. Such an approach would only fail if the data is badly sampled, in which case the results are EVEN WORSE when performing an FFT (the data is incorrectly sampled).

Try:
zi = spline(x, real(y), xi) + i*spline(x, imag(y), yi);

Remember that what you are doing is interpolating a contour on 2D data!