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import numpy as np
from numpy.fft import rfftn, irfftn
from scipy.fftpack import (fft, ifft, ifftshift, fft2, ifft2, fftn,
ifftn, fftfreq)
from scipy._lib._version import NumpyVersion
from scipy import signal
########################################
##### Test functions
########################################
def create_triangular_chirp(f = 0.2, periods = 100):
#f ... per sample
t_max = periods / float(f)
t = np.arange(t_max)
sig = signal.chirp(t, 0, t_max, f)
triangle = np.linspace(0, t_max, num = t_max) / t_max
sig = np.multiply(sig, triangle)
return sig
def add_delay_and_padding(sig, delay=0, padding=0):
n_sig = sig.shape[0]
n_total = n_sig + delay + padding
ret = np.zeros((n_total), dtype=sig.dtype)
ret[delay:delay + n_sig] = sig
return ret
def create_test_signal(f=0.05, periods=100, delay=0, padding=0):
return add_delay_and_padding(create_triangular_chirp(f=f, periods=periods),
delay=delay, padding=padding)
def visualize_test_signal(f=0.05, periods=100, delay=10, padding=100):
plt.plot(create_test_signal(f=f, periods=periods, delay=delay, padding=padding))
def down_sample(sig, n_every):
return sig[::n_every]
_rfft_mt_safe = (NumpyVersion(np.__version__) >= '1.9.0.dev-e24486e')
def _next_regular(target):
"""
Find the next regular number greater than or equal to target.
Regular numbers are composites of the prime factors 2, 3, and 5.
Also known as 5-smooth numbers or Hamming numbers, these are the optimal
size for inputs to FFTPACK.
Target must be a positive integer.
"""
if target <= 6:
return target
# Quickly check if it's already a power of 2
if not (target & (target-1)):
return target
match = float('inf') # Anything found will be smaller
p5 = 1
while p5 < target:
p35 = p5
while p35 < target:
# Ceiling integer division, avoiding conversion to float
# (quotient = ceil(target / p35))
quotient = -(-target // p35)
# Quickly find next power of 2 >= quotient
try:
p2 = 2**((quotient - 1).bit_length())
except AttributeError:
# Fallback for Python <2.7
p2 = 2**(len(bin(quotient - 1)) - 2)
N = p2 * p35
if N == target:
return N
elif N < match:
match = N
p35 *= 3
if p35 == target:
return p35
if p35 < match:
match = p35
p5 *= 5
if p5 == target:
return p5
if p5 < match:
match = p5
return match
def fft_lag(s1, s2, n_up = 1, debug=False):
if debug:
import matplotlib.pyplot as plt
s1 = np.flipud(s1) #mult becomes convolution -> filp to get correlation
sh1 = np.array(s1.shape)
sh2 = np.array(s2.shape)
complex_result = (np.issubdtype(s1.dtype, np.complex) or
np.issubdtype(s2.dtype, np.complex))
shape = (sh1 + sh2 - 1)
fshape = [_next_regular(int(d)) for d in shape]
fslice = tuple([slice(0, int(sz)) for sz in shape])
def upsample_fft(s_fft, n_up):
n = s_fft.shape[0]
dtype = s_fft.dtype
ret = None
if n % 2 == 0:
ret = np.zeros((n*n_up), dtype=dtype)
ret[:n/2] = s_fft[0:n/2]
ret[-n/2:] = s_fft[-n/2:]
else:
ret = np.zeros((n*n_up), dtype=dtype)
ret[:n/2] = s_fft[0:n/2]
ret[n/2+1] = s_fft[n/2+1] / 2.
ret[-(n/2+1)] = s_fft[n/2+1] / 2.
ret[-n/2:] = s_fft[-n/2:]
ret = ret * n_up
return ret
s1_fft = np.fft.fftn(s1, fshape)
s2_fft = np.fft.fftn(s2, fshape)
s1_s2_fft = upsample_fft(s1_fft * s2_fft, n_up)
s1_s2 = np.fft.ifftn(s1_s2_fft)
delay = np.argmax(s1_s2) / float(n_up) - sh1[0] + 1
#peak of correlation - size of original signal (robust against padding at the end)
if debug:
plt.subplot(411); plt.plot(s1_fft)
plt.subplot(412); plt.plot(s2_fft)
plt.subplot(413); plt.plot(s1_s2_fft)
plt.subplot(414); plt.plot(s1_s2)
plt.show()
print(s1_s2.shape, s1_fft.shape, s2_fft.shape, fshape, fslice)
#return np.argmax(s1_s2)/float(n_up)
#return np.argmax(s1_s2)/float(n_up) - s2.shape[0] + 1
return delay
def fft_lag_random_test(n_tests=1000):
def r():
return np.random.randint(0, 1000)
def rand(n):
return [np.random.randint(0, 1000) for i in range(n)]
for i in range(n_tests):
debug = (i == 0)
d1, d2, p1, p2 = rand(4)
n_down = 5
n_up = 32
sig1 = down_sample(create_test_signal(delay=d1, padding=p1), n_down)
sig2 = down_sample(create_test_signal(delay=d2, padding=p2), n_down)
d1, d2, p1, p2 = [x/float(n_down) for x in [d1, d2, p1, p2]]
delay = d2 - d1
delay_meas = fft_lag(sig1, sig2, n_up=n_up, debug = debug)
tol = 1./n_up
error = abs(delay - delay_meas)
assert(error < tol)
print("%d tests within tolerance" % n_tests)
if __name__ == "__main__":
fft_lag_random_test()
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