What is the main edge of using a spectral method (Spectral Intp/Trigonometric Intp) for upsampling or downsampling a signal in comparison to using a linear (Trilinear Intp) method to do the same?
I understand that spectral methods are more accurate than linear ones. But how and why? Please negate my statement if I am wrong.
Shannon Nyquist suggests that a continuous signal can be sampled, then recreated perfectly as long as the sampling rate is larger than two times the signal bandwidth. The means to maximize captured and recreated bandwidth is a perfect brickwall lowpass filter, which turns out to be a sinc(x) function in the time domain. Failure to do that filtering will either manifest itself as a drop in the passband («unsharp»), or nonlinear aliasing and imaging, where spectral components pop up where they do not belong.
Practical engineering needs to do some compromises, so we design various lowpass filters that are more or less similar to that sinc function. Bilinear filtering turns out to be equivalent to two samples of a triangular function. That is a poor lowpass filter, but implementation cost and latency is low.
«Trilinear» is not a term I recognize in this context. I know that OpenGL use that term for scaling images when a pre-scaled pyramid of ever lower resolution images are available, and each output pixel is linearly interpolated in height, width and the «pyramid» dimension.
-k
