def compare_interpolated_spectrum():
fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111)
out = fft(ifftshift(f_full))
freqs = fftfreq(len(f_full), d=0.01) # spacing, Ang
sfreqs = fftshift(freqs)
taper = gauss_taper(freqs, sigma=0.0496) #Ang, corresponds to 2.89 km/s at 5150A.
tout = out * taper
ax.plot(sfreqs, fftshift(tout))
wl_h, fl_h = np.abs(np.load("PH6.8kms_0.01ang.npy"))
wl_l, fl_l = np.abs(np.load("PH2.5kms.npy"))
#end edges
wl_he = wl_h[200:-200]
fl_he = fl_h[200:-200]
interp = Sinc_w(wl_l, fl_l, a=5, window='kaiser')
fl_hi = interp(wl_he)
d = wl_he[1] - wl_he[0]
out = fft(ifftshift(fl_hi))
freqs = fftfreq(len(out), d=d)
ax.plot(fftshift(freqs), fftshift(out))
plt.show()
def plot_pixel_effect():
fig, axs = plt.subplots(nrows=2, ncols=2, figsize=(8, 8))
#fig = plt.figure()
#ax = fig.add_subplot(111)
out = fft(ifftshift(f_full))
freqs = fftfreq(len(f_full), d=0.01) # spacing, Ang
sfreqs = fftshift(freqs)
taper = gauss_taper(freqs, sigma=0.0496) #Ang, corresponds to 2.89 km/s at 5150A.
tout = out * taper
for ax in axs[:, 0]:
ax.plot(sfreqs, fftshift(tout) / tout[0])
ax.plot(sfreqs, fftshift(taper))
ax.plot(sfreqs, 0.0395 * np.sinc(0.0395 * sfreqs))
ax.plot(sfreqs, 0.0472 * np.sinc(0.0472 * sfreqs))
for ax in axs[:, 1]:
ax.plot(sfreqs, 10 * np.log10(np.abs(fftshift(tout) / tout[0])))
ax.plot(sfreqs, 10 * np.log10(np.abs(fftshift(taper))))
ax.plot(sfreqs, 10 * np.log10(np.abs(0.0395 * np.sinc(0.0395 * sfreqs))))
ax.plot(sfreqs, 10 * np.log10(np.abs(0.0472 * np.sinc(0.0472 * sfreqs))))
axs[0, 0].set_ylabel("Norm amp")
axs[1, 0].set_ylabel("Norm amp")
axs[0, 1].set_ylabel("dB")
axs[1, 1].set_ylabel("dB")
for ax in axs.flatten():
ax.set_xlabel(r"cycles/$\lambda$")
plt.show()
def plot_FFTs():
fig, ax = plt.subplots(nrows=4, figsize=(15, 8))
#n = 100000
##Take FFT of f_grid
#w_full = w_full[:-1]
#f_full = f_full[:-1]
out = np.fft.fft(np.fft.fftshift(f_full))
freqs = fftfreq(len(f_full), d=0.01) # spacing, Ang
sfreqs = fftshift(freqs)
taper = gauss_taper(freqs, sigma=0.0496) #Ang, corresponds to 2.89 km/s at 5150A.
tout = out * taper
ax[0].plot(sfreqs, np.fft.fftshift(out))
ax[1].plot(tout)
#ax[1].plot(sfreqs,np.fft.fftshift(taper)*tout[0])
ax[1].set_xlabel(r"cycles/$\lambda$")
n_wl = len(w_full)
print(n_wl)
#trucate at 3 Sigma = 3.21 cycles/Ang
#ind = np.abs(freqs) < 3.21
#Pad tout and window
f_restored = ifftshift(ifft(tout))
#ax[2].plot(w_full,f_full)
ax[2].plot(w_full, f_restored, "bo")
#where to pad zeros? In the middle near high frequencies, so it goes +, zeros, -
zeros = np.zeros((n_wl,))
nyq = np.ceil(n_wl / 2) #find where the nyquist frequency is stored in the array
t_pack = np.concatenate((tout[:nyq], zeros, tout[nyq:]))
wl0 = w_full[nyq]
scale_factor = len(t_pack) / n_wl
f_restored2 = scale_factor * ifftshift(ifft(t_pack))
wls = ifftshift(fftfreq(len(t_pack), d=0.01)) + wl0
#ax[2].plot(wls,f_restored2)
#print(np.sum(f_restored),np.sum(f_restored2))
#print(trapz(f_restored,w_full),trapz(f_restored2,wls))
#sample at an offset in phase
half_shift = tout * np.exp(-2j * np.pi * freqs * 0.0248)
f_restored_shift = ifftshift(ifft(half_shift))
ax[2].plot(w_full - 0.0248, f_restored_shift, "go")
plt.show()
def plot_truncation():
n_wl = len(w_full)
if n_wl % 2 == 0:
print("Full Even")
else:
print("Full Odd")
out = fft(ifftshift(f_full))
w0 = ifftshift(w_full)[0]
freqs = fftfreq(len(f_full), d=0.01) # spacing, Ang
#sfreqs = fftshift(freqs)
taper = gauss_taper(freqs, sigma=0.0496) #Ang, corresponds to 2.89 km/s at 5150A.
tout = out * taper
#ignore all samples higher than 5.0 km/s = 0.5/0.0429 cycles/Ang
sc = 0.5 / 0.0429
ind = np.abs(freqs) <= sc
ttrim = tout[ind]
if len(ttrim) % 2 == 0:
print("Trim Even")
else:
print("Trim Odd")
f_restored = fftshift(ifft(tout))
np.save("PH6.8kms_0.01ang.npy", np.array([w_full, np.abs(f_restored)]))
scale_factor = len(ttrim) / n_wl
f_restored2 = scale_factor * fftshift(ifft(ttrim))
d = freqs[1]
print(d)
# must keep track of which index!! AND which ifftshift vs fftshift
raw_wl = fftshift(fftfreq(len(ttrim), d=d))
wl_restored = raw_wl + w0
np.save("PH2.5kms.npy", np.array([wl_restored, np.abs(f_restored2)]))
plt.plot(w_full, f_restored)
plt.plot(wl_restored, f_restored2, "go")
plt.show()
return wl_restored
