-- Fast Fourier Transform Demos / fft.lua
 -- 
 -- Copyright (C) 2009, 2010 Francesco Abbate
 -- 
 -- This program is free software; you can redistribute it and/or modify
 -- it under the terms of the GNU General Public License as published by
 -- the Free Software Foundation; either version 3 of the License, or (at
 -- your option) any later version.
 -- 
 -- This program is distributed in the hope that it will be useful, but
 -- WITHOUT ANY WARRANTY; without even the implied warranty of
 -- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
 -- General Public License for more details.
 -- 
 -- You should have received a copy of the GNU General Public License
 -- along with this program; if not, write to the Free Software
 -- Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
use 'math'
use 'graph'
use 'num'
local function demo1()
 local n, ncut = 8*3*5, 16
 local sq = matrix.new(n, 1, &#124;i&#124; i < n/3 and 0 or (i < 2*n/3 and 1 or 0))
 local pt = plot('Original signal / reconstructed')
 pt:addline(filine(&#124;i&#124; sq[i], n), 'black')
 local ft = fft(sq)
 local pf = fibars(&#124;k&#124; complex.abs(ft[k]), 0, n/2, 'black')
 pf.title = 'FFT Power Spectrum'
 for k=ncut, n - ncut do ft[k] = 0 end
 sqt = fftinv(ft)
 pt:addline(filine(&#124;i&#124; sqt[i], n), 'red')
 pt:show()
 return pt, pf
end
local function demo2()
 local n, ncut = 256, 16
 local sq = matrix.new(n, 1, &#124;i&#124; i < n/3 and 0 or (i < 2*n/3 and 1 or 0))
 local pt = plot('Original signal / reconstructed')
 local pf = plot('FFT Power Spectrum')
 pt:addline(filine(&#124;i&#124; sq[i], n), 'black')
 ft = fft(sq, true)
 pf:add(ibars(iter.isample(&#124;k&#124; complex.abs(ft[k]), 0, n/2)), 'black')
 for k=ncut, n - ncut do ft[k] = 0 end
 fftinv(ft, true)
 pt:addline(filine(&#124;i&#124; sq[i], n), 'red')
 pf:show()
 pt:show()
 return pt, pf
end
local function demo3()
 local n, ncut, order = 512, 11, 8
 local x1 = sf.besselJ_zero(order, 14)
 local xsmp = &#124;k&#124; x1*(k-1)/(n-1)
 local bess = matrix.new(n, 1, &#124;i&#124; sf.besselJ(order, xsmp(i)))
 local p = plot('Original signal / reconstructed')
 p:addline(filine(&#124;i&#124; bess[i], n), 'black')
 local ft = fft(bess)
 fftplot = plot('FFT power spectrum')
 bars = ibars(iter.isample(&#124;k&#124; complex.abs(ft[k]), 0, 60))
 fftplot:add(bars, 'black')
 fftplot:show()
 for k=ncut, n/2 do ft[k] = 0 end
 local bessr = fftinv(ft)
 p:addline(filine(&#124;i&#124; bessr[i], n), 'red', {{'dash', 7, 3}})
 p:show()
 return p, fftplot
end
return {'FFT', {
 {
 name = 'fft1',
 f = demo1, 
 description = 'GSL example with square function and frequency cutoff'
 },
 {
 name = 'fft2',
 f = demo2,
 description = 'The same as before but the FFT transform is done in place'
 },
 {
 name = 'fft3',
 f = demo3,
 description = 'frequency cutoff example on bessel function'
 },
}}
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