;  Given a number of points and a spacing, return an
;  array of the wavelet fourier series and the
;  array of frequencies (2 pi/wavelength) for the
;  j, k wavelet as defined by Sato.

function refr_jk_wL, H, d, xh, j, k, wL

  jk2x0x1, H, xh, j, k, x0, x1
  psihatL = refr_wL(H, d, xh, x0, x1, wL)
  return, psihatL

end

pro refr_jk_wL_test

  H = 32.
  d = 1.
  j=1
  k=1
  psihatL = refr_jk_wL(H, d, 0., 0, 0, wL)
  psijkhatL = refr_jk_wL(H, d, 0., j, k, wL)
  window, 0, xs=1000,ys=500
  !p.multi=[0,2,0]
  plot, wL, abs(psihatL), xr=[-20,20]/(4.*H)
  oplot, wL, abs(psijkhatL), /li, ps=-4

end

pro refr_jk_wL_test2

  xh = 0.
  H = 32.
  d = 1.
  j=1
  psij0hatL = refr_jk_wL(H, d, 0., j, 0, wL)
  psij1hatL = refr_jk_wL(H, d, 0., j, 1, wL)
  window, 0, xs=1000,ys=500
  !p.multi=[0,2,0]
  jk2x0x1, H, xh, j, 0, x0, x1
  posn = 0.5*(x0+x1) - (xh-H)  ; shift
  plot, wL, arg(psij0hatL), xr=[-20,20]/(4.*H), ps=1
  oplot, wL, -wL/2. - wL * posn
  
  jk2x0x1, H, xh, j, 1, x0, x1
  posn = 0.5*(x0+x1) - (xh-H)  ; shift
  oplot, wL, arg(psij1hatL), ps=4
  oplot, wL, -wL/2. - wL * posn

end

pro refr_jk_wL_test3

  xh = 0.
  H = 32.
  d = 1.
  j=1
  psij0hatL = refr_jk_wL(H, d, 0., j, 0, wL)
  psij1hatL = refr_jk_wL(H, d, 0., j, 1, wL)
  k=1
  ishift = 2.^(-j) * (4.*H)*complex(0,1)*k
  psijkhatL = psij0hatL * exp(-ishift*wL)
  window, 0, xs=1000,ys=500
  !p.multi=[0,2,0]
  plot, wL, arg(psij0hatL), xr=[-20,20]/(4.*H), ps=1
  oplot, wL, arg(psij1hatL), ps=4
  oplot, wL, arg(psijkhatL), /li
  
  oplot, wL, abs(psij0hatL)

end