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atom.pyx
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atom.pyx
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cimport cython
import numpy as np
cimport numpy as np
#C external functions
cdef extern from "math.h":
double exp(double)
double sqrt(double)
double cos(double)
double sin(double)
double atan2(double, double)
double log(double)
cdef double pi = 3.1415926535897931
#Gaussian for C
############################################################
@cython.profile(False)
@cython.boundscheck(False)
cdef inline double gauss(int i, int N):
return exp(-( (i - N/2. )**2) / (2. * ( (0.125 * N)**2)))
#Hann for C#
############
@cython.profile(False)
@cython.boundscheck(False)
cdef inline double hann(int i, int N):
return 0.5 * (1 - cos( 2*pi*i / (N-1)))
#Blackman for C#
################
@cython.profile(False)
@cython.boundscheck(False)
cdef inline double blackman(int i, int N):
return 0.42 - 0.5 * cos(2*pi*i/(N-1)) + 0.08 * cos(4*pi*i/(N-1))
#Real Sinusoid for C
###########################################################################
@cython.profile(False)
@cython.boundscheck(False)
cdef inline double realSinusoid(int i, float omega, float chirp, float phi):
return cos(2 * pi * (omega + 0.5 * chirp * i) * i + phi)
#Real Vibrating Sinusoid for C
###########################################################################
@cython.profile(False)
@cython.boundscheck(False)
cdef inline double realSinusoidFM(int i, float omega, float chirp, float phi, float omega_m, float phi_m, depth):
return cos(2 * pi * (omega + 0.5 * chirp * i) * i + (depth/omega_m * sin(2 * pi * omega_m * i + phi_m)) + phi)
#Real Sinusoid for python
######################################################################################
@cython.profile(False)
@cython.boundscheck(False)
cpdef np.ndarray[np.float_t, ndim=1, mode="c"] _realSinusoid(int N, float omega, float chirp, float phi):
cdef np.ndarray[np.float_t, ndim=1, mode="c"] out = np.cos(2 * pi * (omega + chirp * 0.5 * np.arange(N)) * np.arange(N) + phi)
return out
#Gabor for python
#####################################################################################
@cython.profile(False)
@cython.boundscheck(False)
cpdef np.ndarray[np.float_t, ndim=1, mode="c"] _gabor(float phi, int N, float omega, float chirp):
'''A gabor atom where
phi := initial phase
N := scale, i.e. length
omega := normalized frequency'''
cdef np.ndarray[np.float_t, ndim=1, mode="c"] out = np.zeros(N, dtype=float)
cdef int i
for i in range(N):
out[i] = gauss(i, N) * realSinusoid(i, omega, chirp/N, phi)
return out
#GaborFM for python
#####################################################################################
@cython.profile(False)
@cython.boundscheck(False)
cpdef np.ndarray[np.float_t, ndim=1, mode="c"] _gaborFM(float phi, int N, float omega, float chirp, float omega_m=0., float phi_m=0., float depth=0.):
'''A gabor atom where
phi := initial phase
N := scale, i.e. length
omega := normalized frequency'''
cdef np.ndarray[np.float_t, ndim=1, mode="c"] out = np.zeros(N, dtype=float)
cdef int i
for i in range(N):
out[i] = gauss(i, N) * realSinusoidFM(i, omega, chirp, phi, omega_m, phi_m, depth)
return out
#Hann for python
#####################################################################################
@cython.profile(False)
@cython.boundscheck(False)
cpdef np.ndarray[np.float_t, ndim=1, mode="c"] _hann(float phi, int N, float omega, float chirp):
'''A hann atom where
phi := initial phase
N := scale, i.e. length
omega := normalized frequency'''
cdef np.ndarray[np.float_t, ndim=1, mode="c"] out = np.zeros(N, dtype=float)
cdef int i
for i in range(N):
out[i] = hann(i, N) * realSinusoid(i, omega, chirp/N, phi)
return out
#HannFM for python
#####################################################################################
@cython.profile(False)
@cython.boundscheck(False)
cpdef np.ndarray[np.float_t, ndim=1, mode="c"] _hannFM(float phi, int N, float omega, float chirp, float omega_m=0., float phi_m=0., float depth=0.):
'''A hann atom where
phi := initial phase
N := scale, i.e. length
omega := normalized frequency'''
cdef np.ndarray[np.float_t, ndim=1, mode="c"] out = np.zeros(N, dtype=float)
cdef int i
for i in range(N):
out[i] = hann(i, N) * realSinusoidFM(i, omega, chirp, phi, omega_m, phi_m, depth)
return out
#Blackman for python
#####################################################################################
@cython.profile(False)
@cython.boundscheck(False)
cpdef np.ndarray[np.float_t, ndim=1, mode="c"] _blackman(float phi, int N, float omega, float chirp):
'''A blackman atom where
phi := initial phase
N := scale, i.e. length
omega := normalized frequency'''
cdef np.ndarray[np.float_t, ndim=1, mode="c"] out = np.zeros(N, dtype=float)
cdef int i
for i in range(N):
out[i] = blackman(i, N) * realSinusoid(i, omega, chirp/N, phi)
return out
#BlackmanFM for python
#####################################################################################
@cython.profile(False)
@cython.boundscheck(False)
cpdef np.ndarray[np.float_t, ndim=1, mode="c"] _blackmanFM(float phi, int N, float omega, float chirp, float omega_m=0., float phi_m=0., float depth=0.):
'''A blackman FM atom where
phi := initial phase
N := scale, i.e. length
omega := normalized frequency'''
cdef np.ndarray[np.float_t, ndim=1, mode="c"] out = np.zeros(N, dtype=float)
cdef int i
for i in range(N):
out[i] = blackman(i, N) * realSinusoidFM(i, omega, chirp, phi, omega_m, phi_m, depth)
return out
#Gamma for python
##################################################################################################################
@cython.profile(False)
@cython.boundscheck(False)
cpdef np.ndarray[np.float_t, ndim=1, mode="c"] _gamma(float phi, int N, float omega, float chirp, float order, float bandwidth):
cdef np.ndarray[np.float_t, ndim=1, mode="c"] out = np.zeros(N, dtype=float)
cdef int i
for i in range(N):
out[i] = (i**order-1) * exp(-2 * pi * bandwidth * i) * realSinusoid(i, omega, chirp/N, phi)
return out
#GammaFM for python
##################################################################################################################
@cython.profile(False)
@cython.boundscheck(False)
cpdef np.ndarray[np.float_t, ndim=1, mode="c"] _gammaFM(float phi, int N, float omega, float chirp, float order, float bandwidth, float omega_m=0., float phi_m=0., float depth=0.):
cdef np.ndarray[np.float_t, ndim=1, mode="c"] out = np.zeros(N, dtype=float)
cdef int i
for i in range(N):
out[i] = (i**order-1) * exp(-2 * pi * bandwidth * i) * realSinusoidFM(i, omega, chirp, phi, omega_m, phi_m, depth)
return out
#Damped for python
##################################################################################################################
@cython.profile(False)
@cython.boundscheck(False)
cpdef np.ndarray[np.float_t, ndim=1, mode="c"] _damped(float phi, int N, float omega, float chirp, float damp):
cdef np.ndarray[np.float_t, ndim=1, mode="c"] out = np.zeros(N, dtype=float)
cdef int i
for i in range(N):
out[i] = exp(-damp * i) * realSinusoid(i, omega, chirp/N, phi)
return out
#DampedFM for python
##################################################################################################################
@cython.profile(False)
@cython.boundscheck(False)
cpdef np.ndarray[np.float_t, ndim=1, mode="c"] _dampedFM(float phi, int N, float omega, float chirp, float damp, float omega_m=0., float phi_m=0., float depth=0.):
cdef np.ndarray[np.float_t, ndim=1, mode="c"] out = np.zeros(N, dtype=float)
cdef int i
for i in range(N):
out[i] = exp(-damp * i) * realSinusoidFM(i, omega, chirp, phi, omega_m, phi_m, depth)
return out
#FOF
#################################################################################################################
@cython.profile(False)
@cython.boundscheck(False)
cpdef np.ndarray[np.float_t, ndim=1, mode="c"] _fof(float phi, int N, float omega, float chirp, int rise_n, int decay_n):
cdef np.ndarray[np.float_t, ndim=1, mode='c'] out = np.zeros(N, dtype=float)
cdef int t
cdef float op = log(decay_n) / decay_n
cdef float factor = pi/rise_n
cdef float p, a
for t in range(rise_n):
out[t] = 0.5 * (1. - np.cos(factor * t) * exp(-op * t))
p = out[rise_n-1]
for t in range(rise_n, N):
out[t-1] = exp(-op*t)
a = max(abs(out[rise_n-1:N-1]))
for t in range(rise_n-1, N-1):
out[t] = out[t]/a * p
for i in range(N):
out[i] = out[i] * realSinusoid(i, omega, chirp/N, phi)
return out
#FOFFM
#################################################################################################################
@cython.profile(False)
@cython.boundscheck(False)
cpdef np.ndarray[np.float_t, ndim=1, mode="c"] _fofFM(float phi, int N, float omega, float chirp, int rise_n, int decay_n, float omega_m=0., float phi_m=0., float depth=0.):
cdef np.ndarray[np.float_t, ndim=1, mode='c'] out = np.zeros(N, dtype=float)
cdef int t
cdef float op = log(decay_n) / decay_n
cdef float factor = pi/rise_n
cdef float p, a
for t in range(rise_n):
out[t] = 0.5 * (1. - np.cos(factor * t) * exp(-op * t))
p = out[rise_n-1]
for t in range(rise_n, N):
out[t-1] = exp(-op*t)
a = max(abs(out[rise_n-1:N-1]))
for t in range(rise_n-1, N-1):
out[t] = out[t]/a * p
for i in range(N):
out[i] = out[i] * realSinusoidFM(i, omega, chirp, phi, omega_m, phi_m, depth)
return out