/
MRPy.py
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MRPy.py
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# -*- coding: utf-8 -*-
import sys
import gzip as gz
import pickle as pk
import numpy as np
import pandas as pd
from warnings import warn
from scipy.interpolate import interp1d
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
#=============================================================================
#=============================================================================
class MRPy(np.ndarray):
#=============================================================================
#=============================================================================
# 1. Class initialization
#=============================================================================
def __new__(cls, np_array, fs=None, Td=None):
X = np.asarray(np_array).view(cls)
if (X.size == 0):
sys.exit('Empty array not allowed for new objects!')
sh = X.shape
if (len(sh) == 1):
X = np.reshape(X,(1,sh[0]))
elif (sh[0] > sh[1]):
X = X.T
sh = X.shape
X.NX = sh[0]
X.N = sh[1]
if (X.N < 2):
sys.exit('Come on!!! Start with at least 2 elements!')
err = 1.0
if (np.mod(X.N, 2) != 0): # enforce N to be even...
X = X[:,:-1] # ... odd element is discarded!!!
err = (X.N - 1)/X.N # correction over Td
X.N = X.N - 1
if (fs != None): # if fs is prescribed...
X.fs = float(fs)
X.Td = X.N/X.fs # ... Td is calculated
elif (Td != None): # but if Td is prescribed...
X.Td = err*float(Td)
X.fs = X.N/X.Td # ... fs is calculated
else: sys.exit('Either fs or Td must be provided!')
X.M = X.N//2 + 1
return X
#-----------------------------------------------------------------------------
def __array_finalize__(self, X):
if X is None: return
self.fs = getattr(X, 'fs', None)
self.Td = getattr(X, 'Td', None)
self.NX = getattr(X, 'NX', None)
self.N = getattr(X, 'N', None)
self.M = getattr(X, 'M', None)
#=============================================================================
# 2. Class constructors from other sources
#=============================================================================
def from_file(filename, form='mrpy'):
"""
Load time series from file. Please contact the author for
including other types of datafile.
Parameters: filename: file to be loaded, including path,
whithout file extension
form: data formatting. Options are
'mrpy' - default gzip pickle loading
'excel' - excel generated with pandas
'columns' - t, X1, [X2, X3 ...]
'invh ' - csv file by iNVH app
'mpu6050' - gzip excel 6 axis data
"""
try:
#-------------
if (form.lower() == 'mrpy'):
with gz.GzipFile(filename+'.csv.gz', 'rb') as target:
return MRPy(*pk.load(target))
#---------------
elif (form.lower() == 'excel'):
with open(filename+'.xlsx', 'rb') as target:
data = pd.read_excel(target,
index_col=0,
sheet_name='MRPy')
ti = np.array(data.index, dtype=float)
return MRPy.resampling(ti, data.values)
#---------------
elif (form.lower() == 'columns'):
with open(filename+'.txt', 'rb') as target:
data = np.genfromtxt(target,
delimiter='\t')
ti = data[:,0]
return MRPy.resampling(ti, data[:,1:])
#---------------
elif (form.lower() == 'invh'):
with open(filename+'.csv', 'rb') as target:
data = np.genfromtxt(target,
delimiter=',',
skip_header=1)
ti = data[:,0]
return MRPy.resampling(ti, data[:,1:-1])
#---------------
elif (form.lower() == 'mpu6050'):
with gz.open(filename+'.csv.gz', 'rb') as target:
data = np.genfromtxt(target,
delimiter=',')
ti = data[:,0] - data[0,0]
return MRPy.resampling(ti, data[:,1:]/16384)
#---------------
else:
sys.exit('Data formatting not available!')
return None
except:
sys.exit('Could not read file "{0}"!'.format(filename))
return None
#-----------------------------------------------------------------------------
def from_periodogram(Sx, fs):
"""
Simulate RPs from given spectral densities.
Parameters: Sx: spectral densities as ndarray (must have odd
length, otherwise it will be truncated by 1 and
the length of simulation will not be as expected!)
The largest dimension of Sx is assumed to be the
frequency axis.
fs: sampling frequency in Hz
"""
sh = Sx.shape
if (len(sh) == 1):
Sx = np.reshape(Sx,(1,sh[0]))
elif (sh[0] > sh[1]):
Sx = Sx.T
sh = Sx.shape
NX = sh[0]
M0 = sh[1]
M = M0 - (np.mod(M0,2) == 0) # ensure M is odd
N = 2*(M - 1)
Sx = N*fs*np.abs(Sx[:,0:M])/2
X = np.empty((NX, N))
for k in range(NX):
phi = 2*np.pi*np.random.rand(M);
phi[0] = 0.
Pw = np.sqrt(Sx[k,:]) * (np.cos(phi) + 1j*np.sin(phi))
Pw = np.hstack((Pw, np.conj(Pw[-2:0:-1])))
X[k,:] = np.real(np.fft.ifft(Pw))
return MRPy(X, fs)
#-----------------------------------------------------------------------------
def from_autocov(Cx, Tmax):
"""
Simulate RPs from given autocovariance functions.
Parameters: Cx: autocovariances as ndarray (must have odd
length, otherwise it will be truncated by 1 and
the length of simulation will not be as expected!)
The largest dimension of Cx is assumed to be the
time gap axis.
Tmax: largest time gap, associated to the last element
in array Cx. Defines process duration, which
will be approximately 2Tmax.
"""
Sx, fs = MRPy.Cx2Sx(Cx, Tmax)
return MRPy.from_periodogram(Sx, fs)
#-----------------------------------------------------------------------------
def from_pseudo(Sa, Tmax, T, zeta=0.05): # NOT READY!!!
"""
Simulate ground acceleration records from a given pseudo acceleration
spectra.
Parameters: Sa: acceleration pseudo spectra as ndarray (must have
odd length, otherwise it will be truncated by 1 and
the length of simulation will not be as expected!)
The largest dimension of Sa is assumed to be the
period axis.
Tmax: largest period, associated to the last element
in array Sa. Defines process duration, which
will be approximately 2Tmax.
T: tuple (T1, T2, T0) defining envelope timing, where
T1 is the end of attack time, T2 is the end of
sustain time, and T0 is the time constant of the
exponential amplitude decay.
zeta: system damping (ratio of critical) can be
provided or default value of 5% is assumed.
"""
sh = Sa.shape
if (len(sh) == 1):
Sa = np.reshape(Sa,(1,sh[0]))
else:
if (sh[0] > sh[1]):
Sa = Sa.T
sh = Sa.shape
NX = sh[0]
M0 = sh[1]
M = M0 - (np.mod(M0,2) == 0) # ensure M is odd
N = 2*(M - 1)
err = M/M0
fs = (M - 1)/(err*Tmax) # eventually corrects for Tmax
f = np.linspace(0, fs/2, M)
tau = np.linspace(0, Tmax, M)
fi = np.zeros(M)
fi[1:] = 1/tau[:0:-1]
X = np.empty((NX,N))
for k in range(NX):
Sxi = np.zeros(M)
Sxi[1:] = Sa[k,1:]
fSx = interp1d(fi, Sxi, kind='quadratic')
X[k] = MRPy.from_periodogram(fSx(f), fs)
X[k] *= Sa.max()/X[k].max()
return MRPy(X, fs).Kanai().envelope(T)
#=============================================================================
# 3. Class constructors by modification
#=============================================================================
def zero_mean(self):
"""
Clean mean values.
"""
X = MRPy.copy(self)
Xm = X.mean(axis=1)
for k in range(self.NX):
X[k,:] -= Xm[k]
return X
#-----------------------------------------------------------------------------
def superpose(self, weight=1.):
"""
Add up all series in MRPy weighted by 'weight', which is a
scalar or list with weights for summation. This method can be
used, for instance, for combining modal responses according to
modal shape coordinate at a given structural node.
"""
if ~hasattr(weight, "__len__"):
weight = weight*np.ones(self.NX)
elif (len(weight) != self.NX):
sys.exit('Weight length must equal number of processes!')
X = np.zeros((1, self.N))
for kX, row in enumerate(self):
X[0,:] += weight[kX]*row
return MRPy(X, self.fs)
#-----------------------------------------------------------------------------
def double(self):
"""
Double MRPy duration by filling with mean values.
"""
Xm = self.mean(axis=1)
X = np.hstack((self, np.tile(Xm,(self.N, 1)).T))
return MRPy(X, self.fs)
#-----------------------------------------------------------------------------
def extract(self, segm=(1/4, 3/4), by='fraction'):
"""
Extract a central segment of time range. The lower and upper
cutting point as defined as a tuple or list, which meaning is
defined by a code 'by':
Parameters: segm: tuple or list with the lower and upper
cutting points.
by: code indicating the meaning of cutting points:
'fraction': default meaning
'time' : time axis related
'index' : directly through indexing
"""
if (segm[0] >= segm[1]):
sys.exit('Upper limit must be larger than lower limit!')
if (by.lower() == 'fraction'):
i0 = int(segm[0]*self.N)
i1 = int(segm[1]*self.N)
elif (by.lower() == 'time'):
i0 = int(segm[0]*self.fs)
i1 = int(segm[1]*self.fs)
elif (by.lower() == 'index'):
i0 = int(segm[0])
i1 = int(segm[1])
else:
sys.exit('Segment definition code is unknown!')
return None
i1 = i1 - np.mod(i1-i0, 2) # ensure even length
if (i0 < 0 ): i0 = 0 # do not go over boundaries
if (i1 > self.N): i1 = self.N
return MRPy(self[:,i0:i1], self.fs)
#-----------------------------------------------------------------------------
def envelope(self, T):
"""
Apply an amplitude envelope with exponential attack e decay.
This type of envelope is used for simulation of seismic acceleration.
Parameters: T: tuple (T1, T2, T0) defining envelope timing, where
T1 is the end of attack time, T2 is the end of
sustain time, and T0 is the time constant of the
exponential amplitude attack and decay.
"""
t = self.t_axis()
X = MRPy.copy(self)
env = np.ones(self.N)
env[t < T[0]] = (1 - np.exp(-t[t < T[0]]/T[0]))/(1 - np.exp(-1))
env[t > T[1]] = np.exp((T[1] - t[t > T[1]])/T[2])
for k in range(self.NX):
X[k,:] *= env
return X
#-----------------------------------------------------------------------------
def mov_average(self, n=3, win='tri'):
"""
Apply moving average with specified window.
Parameters: n: window width (truncated to be odd integer)
win: window type. Available windows are:
'rec': rectangular
'tri': triangular (default)
"""
n = int(n) # truncate to integer
n = n - (1 - np.mod(n,2)) # n is odd or will be decreased by 1
m = (n - 1)//2 + 1 # window center
W = np.ones(n) # default rectangular window
if (win.lower() == 'rec'):
pass
elif (win.lower() == 'tri'):
W[ :m] = np.linspace(1/m, 1., m)
W[m-1: ] = np.linspace(1., 1/m, m)
else:
sys.error('Averaging window type not available!')
m = m - 1
W = W/W.sum()
X = MRPy.copy(self)
for kX in range(self.NX):
for k in range(0, m):
k0 = m - k
W0 = W[k0:]/np.sum(W[k0:])
X[kX,k] = np.sum(W0*self[kX,:k+m+1])
for k in range(m, self.N-m-1):
X[kX,k] = np.sum(W*self[kX,k-m:k+m+1])
for k in range(self.N-m-1, self.N):
k0 = m - k + self.N
W0 = W[:k0]/np.sum(W[:k0])
X[kX,k] = np.sum(W0*self[kX,k-m:])
return X
#-----------------------------------------------------------------------------
def filtered(self, band, mode='pass'):
"""
Apply filtering in frequency domain. Series size is doubled by
trailing zeros before filtering, in order to minimize aliasing.
Parameters: band: frequency band as tuple or list: [f_low, f_high]
mode: filter type. Available:
'pass': band pass (default)
'stop': band stop
"""
X = self.double()
f = X.f_axis()
b0, b1 = MRPy.check_band(self.fs, band)
for kX in range(X.NX):
Xw = np.fft.fft(X[kX,:])[0:X.M]
if mode.lower() == 'pass':
Xw[(f < b0) | (f >= b1)] = 0.
elif mode.lower() == 'stop':
Xw[(f >= b0) & (f < b1)] = 0.
else:
warn('Filter type not available!')
X[kX,:] = np.real(np.fft.ifft(
np.hstack((Xw, np.conj(Xw[-2:0:-1])))))
return MRPy(X[:,0:self.N], self.fs)
#-----------------------------------------------------------------------------
def Kanai(self, H1=(4.84, 0.60), H2=(0.97, 0.60)):
"""
Apply Kanai/Tajimi filtering, with low frequency range attenuation
to avoid integration drifting. This filter is used for simulation
of seismic acceleration.
Parameters: H1: tuple (f1, zeta1) for first filter part,
where default values represent firm soil condition.
H2: tuple (f2, zeta2) for second filter part, which
must properly attenuate low frequency range.
"""
X = np.empty((self.NX, self.N))
for kX, row in enumerate(self):
Xw = np.fft.fft(row)[0:self.M]
w1 = self.f_axis()/H1[0]
w2 = self.f_axis()/H2[0]
Hw1 = (1 + 2j*H1[1]*w1)/(1 - w1*w1 + 2j*H1[1]*w1)
Hw2 = (w2*w2)/(1 - w2*w2 + 2j*H2[1]*w2)
Xw = Xw*Hw1*Hw2
Xk = np.real(np.fft.ifft(np.hstack((Xw, np.conj(Xw[-2:0:-1])))))
X[kX,:] = Xk[0:self.N]
return MRPy(X, self.fs)
#-----------------------------------------------------------------------------
def integrate(self, band=None):
"""
Frequency domain integration with passing band.
Parameters: band: frequency band to keep, tuple: (f_low, f_high)
"""
b0, b1 = MRPy.check_band(self.fs, band)
X = np.empty((self.NX, self.N))
f = self.f_axis(); f[0] = f[1] # avoid division by zero
for kX, row in enumerate(self):
Xw = np.fft.fft(row)[0:self.M]
Xw = Xw / (2j*np.pi*f) # division means integration
Xw[0] = 0. # disregard integration constant
Xw[(f <= b0) | (f > b1)] = 0.
X[kX,:] = np.real(np.fft.ifft(
np.hstack((Xw, np.conj(Xw[-2:0:-1])))))
return MRPy(X, self.fs)
#-----------------------------------------------------------------------------
def differentiate(self, band=None):
"""
Frequency domain differentiation with passing band.
Parameters: band: frequency band to keep, tuple: (f_low, f_high)
"""
b0, b1 = MRPy.check_band(self.fs, band)
X = np.empty((self.NX, self.N))
f = self.f_axis(); f[0] = f[1] # avoid division by zero
for kX, row in enumerate(self):
Xw = np.fft.fft(row)[0:self.M]
Xw = Xw * (2j*np.pi*f) # multiplication means derivation
Xw[(f <= b0) | (f > b1)] = 0.
X[kX,:] = np.real(np.fft.ifft(
np.hstack((Xw, np.conj(Xw[-2:0:-1])))))
return MRPy(X, self.fs)
#-----------------------------------------------------------------------------
def sdof_fdiff(self, fn, zeta, U0=0., V0=0.):
"""
Integrates the dynamic equilibrium differential equation by
the central finite differences method.
The input is assumed to be an acceleration (force over mass),
otherwise the result must be divided by system mass to have
displacement unit.
System properties (frequency and damping) may be provided as
scalars or lists. If they are scalars, same properties are used
for all series in the MRP. The same applies for initial conditions
U0 (displacement) and V0 (velocity)
Parameters: fn: sdof natural frequency (Hz)
zeta: sdof damping as ratio of critial (nondim)
U0: initial position (default is all zero)
V0: initial velocity (default is all zero)
"""
if ~hasattr(fn, "__len__"):
fn = fn*np.ones(self.NX)
if ~hasattr(zeta, "__len__"):
zeta = zeta*np.ones(self.NX)
if ~hasattr(U0, "__len__"):
U0 = U0*np.ones(self.NX)
if ~hasattr(V0, "__len__"):
V0 = V0*np.ones(self.NX)
dt = 1/self.fs
X = MRPy(np.empty((self.NX, self.N)), self.fs)
for kX, row in enumerate(self):
zt = zeta[kX]
wn = 2*np.pi*fn[kX]
b1 = ( zt*wn + 1/dt)/dt
b2 = ( zt*wn - 1/dt)/dt
b3 = (dt*wn*wn - 2/dt)/dt
X[kX,0] = U0
X[kX,1] = U0 + V0*dt + row[0]*dt*dt/2
for k in range(2,self.N):
X[kX,k] = (row[k-1] + b2*X[kX,k-2] - b3*X[kX,k-1])/b1
return X
#-----------------------------------------------------------------------------
def sdof_Duhamel(self, fn, zeta, U0=0., V0=0.):
"""
Integrates the dynamic equilibrium differential equation by Duhamel.
The input is assumed to be an acceleration (force over mass),
otherwise the result must be divided by system mass to have
displacement unit.
System properties (frequency and damping) may be provided as
scalars or lists. If they are scalars, same properties are used
for all series in the MRP. The same applies for initial conditions
U0 (displacement) and V0 (velocity)
Parameters: fn: sdof natural frequency (Hz)
zeta: sdof damping as ratio of critial (nondim)
U0: initial position (default is all zero)
V0: initial velocity (default is all zero)
"""
if ~hasattr(fn, "__len__"):
fn = fn*np.ones(self.NX)
if ~hasattr(zeta, "__len__"):
zeta = zeta*np.ones(self.NX)
if ~hasattr(U0, "__len__"):
U0 = U0*np.ones(self.NX)
if ~hasattr(V0, "__len__"):
V0 = V0*np.ones(self.NX)
t = self.t_axis()
dt = 1/self.fs
X = MRPy(np.empty((self.NX, self.N)), self.fs)
for kX, row in enumerate(self):
zt = zeta[kX]
wn = 2*np.pi*fn[kX]
wd = wn*np.sqrt(1 - zt**2)
et = np.exp(zt*wn*t)
st = np.sin(wd*t)
ct = np.cos(wd*t)
X[kX,:] = (U0[kX]*ct + (V0[kX] + U0[kX]*zt*wn)*st/wd)/et
A = dt*np.cumsum(row*et*ct)
B = dt*np.cumsum(row*et*st)
X[kX,:] += (A*st - B*ct)/et/wd
return X
#-----------------------------------------------------------------------------
def sdof_Fourier(self, fn, zeta):
"""
Integrates the dynamic equilibrium differential equation by Fourier.
The input MRPy is assumed to be an acceleration (force over mass),
otherwise the result must be divided by system mass to have
displacement unit.
System properties (frequency and damping) may be provided as
scalars or lists. If they are scalars, same properties are used
for all series in the MRP.
Parameters: fn: sdof natural frequency (Hz)
zeta: sdof damping (nondim)
"""
if ~hasattr(fn, "__len__"):
fn = fn*np.ones(self.NX)
if ~hasattr(zeta, "__len__"):
zeta = zeta*np.ones(self.NX)
X = MRPy(np.empty((self.NX, self.N)), self.fs)
for kX, row in enumerate(self):
zt = zeta[kX]
wn = 2*np.pi*fn[kX]
K = wn*wn
b = 2*np.pi*self.f_axis()/wn
Hw = (K*((1.0 - b**2) + 1j*(2*zt*b)))**(-1)
Hw = np.hstack((Hw,np.conj(Hw[-2:0:-1])))
X[kX,:] = np.real(np.fft.ifft(Hw*np.fft.fft(row)))
return X
#-----------------------------------------------------------------------------
def random_decrement(self, div=4, thr=1.0, ref=0):
"""
MATHEUS CARINI HAS FOUND A PROBLEM HERE! MUST BE REVISED!!!
Estimate the free decay response of a dynamic system from the
response to a wide band excitation by the random decrement (RD)
method.
Parameters: div: number of divisions of total length, N//n,
to define the length of decrement series.
The divided length will be eventually truncated
to be even.
thr: threshold level that defines the reference
upcrossing level, given as a multiple of the
standard deviation of the reference MRP.
ref: row of MRPy to be used as reference series.
The other series will be splitted at the same
crossing points, what implies phase consistency.
"""
n = self.N//div # convert to length
n = n - (np.mod(n,2) == 1) # force length to be even
Xm = self.mean(axis=1) # mean values are zero
Xref = self[ref,:] # reference series
X0 = thr*(Xref.std()) # crossing reference level
kref = ( ((Xref[0:(self.N-1)] < X0) & (Xref[1:self.N] >= X0)) |
((Xref[0:(self.N-1)] > X0) & (Xref[1:self.N] <= X0)) )
nk = sum(kref)
Y = MRPy(np.zeros((self.NX, n)), self.fs)
for kX, row in enumerate(self):
row -= Xm[kX] # remove mean value
for k in range(self.N - n):
if kref[k]:
Y[kX,:] += row[k:(k+n)]
return Y/nk
#-----------------------------------------------------------------------------
def fit_decay(self):
"""
Fit the theoretical free decay function of a sdof dynamic system
to the provided MRP. The MRPy mean value is discarded. The fitted
parameters are output as a tuple P = (Xp, fn, zt, ph), where
Xp is the amplitude, fn is the fundamental (undamped) frequency,
zt is the damping as the ratio of critical, and ph is the phase
angle with respect with the cosinus function. This method is
typically used to fit the output of the random decrement method.
"""
#-------------------------------------------------------
def decay(t, Xp, fn, zt, ph):
wn = 2*np.pi*fn
wd = wn*np.sqrt(1. - zt*zt)
return Xp*np.exp(-zt*wn*t)*np.cos(wd*t - ph)
#-------------------------------------------------------
t = self.t_axis()
f = self.f_axis()
P = np.zeros((self.NX, 4))
X = self.zero_mean()
Sx, fs = X.periodogram()
for kX, row in enumerate(X):
Xp = np.max(row) # initial amplitude value
fn = f[np.argmax(Sx[kX,:])] # initial natural frequency
zt = 0.03 # initial damping
ph = 0.00 # initial phase
Pmin = (0.5*Xp, 1/t[-1], 0.0, -np.pi) # lower bounds
P0 = ( Xp, fn, zt, ph ) # initial guesses
Pmax = (1.5*Xp, 1*f[-1], 0.5, np.pi) # upper bounds
try:
P[kX,:], cv = curve_fit(decay, t, row,
p0=P0, bounds=(Pmin, Pmax))
except:
P[kX,:] = np.zeros(5)
print('Not able to fit decay function!!!')
pass
X[kX,:] = decay(t, *P[kX,:])
return MRPy(X, fs), P
#=============================================================================
# 4. Class constructors from conceptual properties
#=============================================================================
def zeros(NX=1, N=1024, fs=None, Td=None):
"""
Add up all series in MRPy weighted by 'weight'.
Parameters: NX: number of processes in the MRPy object.
N: length of each process.
fs: sampling frequency (in Hz), or alternatively
Td: processes duration (second)
"""
fs, Td = MRPy.check_fs(N, fs, Td)
return MRPy(np.zeros((NX,N)), fs)
#-----------------------------------------------------------------------------
def Dirac(NX=1, N=1024, t0=0.0, fs=None, Td=None):
"""
Add up all series in MRPy weighted by 'weight'.
Parameters: NX: number of processes in the MRPy object.
N: length of each process.
t0: time at which impulse must be given
fs: sampling frequency (in Hz), or alternatively
Td: processes duration (second)
"""
fs, Td = MRPy.check_fs(N, fs, Td)
i0 = int(t0//fs)
X = np.zeros((NX,N))
X[:,i0] = 1.0
return MRPy(X, fs)
#-----------------------------------------------------------------------------
def Heaviside(NX=1, N=1024, t0=0.0, fs=None, Td=None):
"""
Add up all series in MRPy weighted by 'weight'.
Parameters: NX: number of processes in the MRPy object.
N: length of each process.
t0: time at which step must be given
fs: sampling frequency (in Hz), or alternatively
Td: processes duration (second)
"""
fs, Td = MRPy.check_fs(N, fs, Td)
i0 = int(t0*fs)
X = np.zeros((NX,N))
X[:,i0:] = 1.0
return MRPy(X, fs)
#-----------------------------------------------------------------------------
def harmonic(NX=1, N=1024, fs=None, Td=None, X0=1.0, f0=1.0, phi=0.0):
"""
Creates an instance with harmonic functions with unity amplitude.
Parameters: NX: number of processes in the MRPy object.
N: length of each process.
fs: sampling frequency (in Hz), or alternatively
Td: processes duration (second)
X0: process amplitude
f0: signal frequency (in Hz)
phi: signal phase (rad).
"""
fs, Td = MRPy.check_fs(N, fs, Td)
X = np.zeros((NX,N))
if ~hasattr(X0, "__len__"):
X0 = X0*np.ones(NX)
if ~hasattr(f0, "__len__"):
f0 = f0*np.ones(NX)
if ~hasattr(phi, "__len__"):
phi = phi*np.ones(NX)
t = np.linspace(0, Td, N)
for kX in range(NX):
X[kX,:] = X0[kX]*np.sin(2*np.pi*f0[kX]*t + phi[kX])
return MRPy(X, fs)
#-----------------------------------------------------------------------------
def white_noise(NX=1, N=1024, fs=None, Td=None, band=None):
"""
Simulates a band-limited Gaussian white noise'.
Parameters: NX: number of processes in the MRPy object.
N: length of each process.
fs: sampling frequency (in Hz), or alternatively
Td: processes duration (second)
band: band with nonzero power (in Hz)
"""
fs, Td = MRPy.check_fs(N, fs, Td)
b0, b1 = MRPy.check_band(fs, band)
M = N//2 + 1
Sx = np.ones((NX, M))
k0 = int(2*M*b0/fs)
k1 = int(2*M*b1/fs)
Sx[:,:k0] = 0.
Sx[:,k1:] = 0.
for kX in range(NX):
Sx[kX,:] /= np.trapz(Sx[kX,:], dx=1./Td)
return MRPy.from_periodogram(Sx, fs)
#-----------------------------------------------------------------------------
def pink_noise(NX=1, N=1024, fs=None, band=None):
"""
Add up all series in MRPy weighted by 'weight'.
Parameters: NX: number of processes in the MRPy object.
N: length of each process.
fs: sampling frequency (in Hz), or alternatively
Td: processes duration (second)
band: band with nonzero power (in Hz)
"""
fs, Td = MRPy.check_fs(N, fs, Td)
b0, b1 = MRPy.check_band(fs, band)
M = N//2 + 1
Sx = np.ones((NX, M))
k0 = int(2*M*b0/fs)
k1 = int(2*M*b1/fs)
Sx[:,:k0] = 0.
Sx[:,k1:] = 0.
for kX in range(NX):
Sx[kX,:] /= np.trapz(Sx[kX,:], dx=1./Td)
return MRPy.from_periodogram(Sx, fs)
#=============================================================================
# 5. MRPy properties (as non-MRPy outputs)
#=============================================================================
def periodogram(self):
"""
Estimates the one-side power spectrum of a MRP.
"""
Sx = np.empty((self.NX, self.M))
for kX in range(self.NX):
Fx = np.fft.fft(self[kX,:] - self[kX,:].mean())
Sxk = np.real(Fx*Fx.conj())*2/self.N/self.fs
Sx[kX,:] = Sxk[:self.M]
return Sx, self.fs
#-----------------------------------------------------------------------------
def autocov(self):
"""
Estimates the autocovariance functions of a MRP.
"""
Tmax = (self.M - 1)/self.fs
Cx = np.empty((self.NX, self.M))
Sx, fs = self.periodogram()
for kX in range(self.NX):
Sxk = np.hstack((Sx[kX,:], Sx[kX,-2:0:-1]))
Cxk = np.fft.ifft(Sxk)*fs/2
Cx[kX,:] = np.real(Cxk[:self.M])
return Cx, Tmax
#-----------------------------------------------------------------------------
def autocorr(self):
"""
Estimates the autocorrelation function of a MRP.
"""
Xs = self.std(axis=1)
Rx = np.empty((self.NX,self.M))