Mercurial > repos > public > sbplib

annotate four.m @ 1198:2924b3a9b921 feature/d2_compatible

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
author Martin Almquist <malmquist@stanford.edu>
date Fri, 16 Aug 2019 14:30:28 -0700
parents f6ada1719420
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
598
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
1 % four returns the fourier transform u_hat of the function u and the frequencies w
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
2 function [w, u_hat] = four(x, u)
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
3 u_hat = fft(u);
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
4
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
5 N = length(x);
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
6 L = x(end) - x(1);
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
7
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
8 k = shift_k(0:N-1);
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
9
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
10 u_hat = fftshift(u_hat);
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
11
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
12 dw = 2*pi/L;
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
13 w = dw*k;
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
14 end
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
15
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
16 function k_shifted = shift_k(k)
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
17 N = length(k);
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
18 k_shifted = [-floor(N/2):-1, 0, 1:ceil(N/2)-1];
f6ada1719420 Add functions for calculating fourier transforms
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
19 end