def test_inversion_understanding_digitization(self):
# From simulations, thresh = 0.1 is about right for rounding with
# levels at S/3 -> S/N ~ 10.
n_sample = 128
self.nh.seek(3 * 2048)
d_in = self.nh.read(n_sample * 2048).reshape(-1, 2048)
# Check effect of digitization.
ft_check = np.fft.rfft(d_in, axis=1)
ft_check_dig = digitize(ft_check, ft_check.real.std() / 3.)
d_check = np.fft.irfft(ft_check_dig, axis=1, n=2048)
assert np.isclose((d_check - d_in).std(), 0.1, atol=0.005)
pfb = PolyphaseFilterBank(self.nh,
self.chime_pfb,
samples_per_frame=n_sample)
ft_pfb = pfb.read(n_sample + 3)
ft_pfb_level = ft_pfb.real.std() / 3.
ft_pfb_dig = (
np.round(ft_pfb.view(float) / ft_pfb_level).view(complex) *
ft_pfb_level)
d_pfb = np.fft.irfft(ft_pfb_dig, axis=1)
# Deconvolve.
ft_fine = np.fft.rfft(d_pfb, axis=0)
ft_resp = pfb._ft_response_conj
threshold = 0.1
inverse = (ft_resp.conj() / (threshold**2 + np.abs(ft_resp)**2) *
(1 + threshold**2))
ft_dec = ft_fine * inverse
d_out = np.fft.irfft(ft_dec, axis=0, n=d_pfb.shape[0])
d_out = d_out[3:]
assert np.isclose((d_out - d_in)[32:-32].std(), 0.125, atol=0.01)
# Still get noisier data near middle, of course, but recover
# to within 1 sigma of input noise signal.
assert_allclose(d_in[32:-32], d_out[32:-32], atol=1)
def test_understanding(self, offset):
"""Stepping or frequency selection should give same answer.
Often think of PFB as multiplying with an array that is, e.g.,
4 times larger, then FFTing and taking every 4th frequency.
But this is equivalent to, after multiplication, summing 4
subsequent arrays and taking the FT of that.
"""
self.nh.seek(offset * 2048)
# First check for real data.
d = self.nh.read(5 * 2048).reshape(-1, 2048)
hd = self.chime_pfb * d[:4]
ft1_hd = np.fft.rfft(hd.ravel())[::4]
ft2_hd = np.fft.rfft(hd.sum(0))
assert_allclose(ft1_hd, ft2_hd)
# Check actual implementations.
pfb = PolyphaseFilterBankSamples(self.nh, self.chime_pfb)
pfb.seek(offset)
ft_pfb = pfb.read(2)
assert_allclose(ft_pfb[0], ft2_hd)
assert_allclose(ft_pfb[1], np.fft.rfft(
(self.chime_pfb * d[1:]).sum(0)))
pfb2 = PolyphaseFilterBank(self.nh, self.chime_pfb)
pfb2.seek(offset)
ft_pfb2 = pfb2.read(2)
assert_allclose(ft_pfb2, ft_pfb)
def test_inversion_understanding(self):
# From simulations, thresh = 0.05 is about right for no rounding
# with n_sample=128 (it is 0.03 for n_sample=1024).
n_sample = 128
self.nh.seek(3 * 2048)
d_in = self.nh.read(n_sample * 2048).reshape(-1, 2048)
pfb = PolyphaseFilterBank(self.nh,
self.chime_pfb,
samples_per_frame=n_sample)
ft_pfb = pfb.read(n_sample + 3)
# Dechannelize.
d_pfb = np.fft.irfft(ft_pfb, axis=1)
# Deconvolve.
ft_fine = np.fft.rfft(d_pfb, axis=0)
ft_resp = pfb._ft_response_conj
ft_dec = ft_fine / ft_resp
d_out = np.fft.irfft(ft_dec, axis=0, n=d_pfb.shape[0])
d_out = d_out[3:]
# We cannot hope to deconvolve near the edges and the PFB is such
# that we loose the middle samples.
assert_allclose(d_in[32:-32, :900], d_out[32:-32, :900], atol=0.001)
assert_allclose(d_in[32:-32, 1150:], d_out[32:-32, 1150:], atol=0.001)
# We can do better by Wiener filtering. For no digitization noise,
# threshold=(d_in-d_out)[32:-32].var()~0.01 seems roughly right.
threshold = 0.05
inverse = (ft_resp.conj() / (threshold**2 + np.abs(ft_resp)**2) *
(1 + threshold**2))
ft_dec2 = ft_fine * inverse
d_out2 = np.fft.irfft(ft_dec2, axis=0, n=d_pfb.shape[0])
d_out2 = d_out2[3:]
# Cannot help near the edges, but middle elements are now better.
assert_allclose(d_in[32:-32], d_out2[32:-32], atol=0.3)
def test_inversion_guppi_pfb(self):
n_sample = 512
pad = 128
self.nh.seek(pad * 64 + 11 * 64 // 2)
d_in = self.nh.read(n_sample * 64).reshape(-1, 64)
pfb = PolyphaseFilterBank(self.nh, self.guppi_pfb)
ipfb = InversePolyphaseFilterBank(pfb,
self.guppi_pfb,
sn=30,
pad_start=pad,
pad_end=pad,
samples_per_frame=n_sample * 64,
dtype=self.nh.dtype)
d_out = ipfb.read(n_sample * 64).reshape(-1, 64)
# Note that the PFB cuts off the channel edges so badly that
# it is not possible to reproduce the original well.
assert_allclose(d_in, d_out, atol=0.15)
# It is almost exclusively the edge samples that are bad.
ipfb2 = InversePolyphaseFilterBank(pfb,
self.guppi_pfb,
sn=1e9,
pad_start=pad,
pad_end=pad,
samples_per_frame=n_sample * 64,
dtype=self.nh.dtype)
d_out2 = ipfb2.read(n_sample * 64).reshape(-1, 64)
assert_allclose(d_in[:, 2:-2], d_out2[:, 2:-2], atol=0.005)
def test_understanding_complex(self, offset):
# Check above holds for complex too.
self.nc.seek(offset * 2048)
c = self.nc.read(4 * 2048).reshape(-1, 2048)
hc = self.chime_pfb * c
ft1_hc = np.fft.fft(hc.ravel())[::4]
ft2_hc = np.fft.fft(hc.sum(0))
assert_allclose(ft1_hc, ft2_hc)
# And check actual implementation.
pfb = PolyphaseFilterBankSamples(self.nc, self.chime_pfb)
pfb.seek(offset)
ft_pfb = pfb.read(1)[0]
assert_allclose(ft_pfb, ft2_hc)
pfb2 = PolyphaseFilterBank(self.nc, self.chime_pfb)
pfb2.seek(offset)
ft_pfb2 = pfb2.read(1)[0]
assert_allclose(ft_pfb2, ft2_hc)
def test_inversion_guppi_pfb_digitized(self):
n_sample = 512
pad = 128
self.nh.seek(pad * 64 + 11 * 64 // 2)
d_in = self.nh.read(n_sample * 64).reshape(-1, 64)
pfb = PolyphaseFilterBank(self.nh, self.guppi_pfb)
dig_level = pfb.read(n_sample).real.std() / 30.
pfb_dig = Task(pfb,
task=lambda ft: digitize(ft, dig_level),
samples_per_frame=n_sample)
ipfb = InversePolyphaseFilterBank(pfb_dig,
self.guppi_pfb,
sn=30,
pad_start=pad,
pad_end=pad,
samples_per_frame=n_sample * 64,
dtype=self.nh.dtype)
d_out = ipfb.read(n_sample * 64).reshape(-1, 64)
# Not much effect of digitization since it introduces little noise.
assert_allclose(d_in, d_out, atol=0.15)
def test_inversion_chime_pfb_digitized(self):
# Now test the same, but with the actual inversion class.
# Here, we do not give samples_per_frame for the PFB, since we do
# not need its FT (and it is exact for any value).
n_sample = 128
pad = 32
self.nh.seek(pad * 2048 + 3 * 2048 // 2)
d_in = self.nh.read(n_sample * 2048).reshape(-1, 2048)
pfb = PolyphaseFilterBank(self.nh, self.chime_pfb)
dig_level = pfb.read(n_sample).real.std() / 3.
pfb_dig = Task(pfb,
task=lambda ft: digitize(ft, dig_level),
samples_per_frame=n_sample)
ipfb = InversePolyphaseFilterBank(pfb_dig,
self.chime_pfb,
sn=10,
pad_start=pad,
pad_end=pad,
samples_per_frame=n_sample * 2048,
dtype=self.nh.dtype)
d_out = ipfb.read(n_sample * 2048).reshape(-1, 2048)
assert np.isclose((d_out - d_in).std(), 0.125, atol=0.01)
assert_allclose(d_in, d_out, atol=1.1)
def test_inversion_chime_pfb(self):
# Now test the same, but with the actual inversion class.
# Here, we do not give samples_per_frame for the PFB, since we do
# not need its FT (and it is exact for any value).
n_sample = 128
pad = 48
self.nh.seek(pad * 2048 + 3 * 2048 // 2)
d_in = self.nh.read(n_sample * 2048).reshape(-1, 2048)
pfb = PolyphaseFilterBank(self.nh, self.chime_pfb)
ipfb = InversePolyphaseFilterBank(pfb,
self.chime_pfb,
sn=100,
pad_start=pad,
pad_end=pad,
samples_per_frame=n_sample * 2048,
dtype=self.nh.dtype)
d_out = ipfb.read(n_sample * 2048).reshape(-1, 2048)
assert_allclose(d_in[:, 50:-50], d_out[:, 50:-50], atol=0.01)