I can across a really old Fortran program with a subroutine that interpolates a 1D array of N samples to 3N samples. It uses a 5-point operator, and the comments describe it as Bracewell method, spline approximation to sinc. I haven't seen this before. Bracewell's 1995 book on Two-Dimensional Imaging had a formula for 6 nearest points. Did he publish a formula for 1D interpolation with 5 points? BTW it sounds like it would be rather approximate, but I suppose in those days they had to make do (a "mainframe" with 8 MB of RAM)

# origin of "Bracewell interpolation"?

Started by ●January 17, 2019

Reply by ●January 17, 20192019-01-17

Hi conr..., Just for the heck of it, I checked Bracewell's 1965 Fourier Transform book. I didn't see any sort of 5-point interpolation information there.

Reply by ●January 17, 20192019-01-17

On 2019-01-17, conrrrod@gmail.com <conrrrod@gmail.com> wrote:> I can across a really old Fortran program with a subroutine that interpolates > a 1D array of N samples to 3N samples. It uses a 5-point operator, and > the comments describe it as > Bracewell method, spline approximation to sinc. > I haven't seen this before. Bracewell's 1995 book on Two-Dimensional Imaging > had a formula for 6 nearest points. > Did he publish a formula for 1D interpolation with 5 points? > > BTW it sounds like it would be rather approximate, but I suppose in those days > they had to make do (a "mainframe" with 8 MB of RAM)There's a 1D spline interpolation problem in the 3rd ed of his "The Fourier Transform and its Applications" (pp252-253) that shows a 4 point approximation. It may be in earlier editions, but I've lost my old one. There are several interpolations mentioned in Chapter 10 "Sampling and Series." There were NO digital computers available here in OZ when Bracewell started out as a budding radio-astronomer!