Akvo/akvo/tressel/harmonic.py

import numpy as np 
from scipy.optimize import least_squares 
from scipy.optimize import minimize
from scipy.linalg import lstsq as sclstsq
import scipy.linalg as lin

def harmonicEuler ( sN, fs, t, f0, k1, kN, ks ): 
    """
    Performs inverse calculation of harmonics contaminating a signal. 
    Args:
        sN = signal containing noise 
        fs = sampling frequency
        t = time samples 
        f0 = base frequency of the sinusoidal noise 
        nK = number of harmonics to calculate 

    """
    KK = np.arange(k1, kN+1, 1/ks )
    nK = len(KK)
    A = np.exp(1j* np.tile(KK,(len(t), 1)) * 2*np.pi* (f0/fs) * np.tile(np.arange(1, len(t)+1, 1),(nK,1)).T)

    v = np.linalg.lstsq(A, sN, rcond=None) 
    alpha = np.real(v[0]) 
    beta  = np.imag(v[0]) 

    amp = np.abs(v[0])     
    phase = np.angle(v[0]) 

    h = np.zeros(len(t))
    for ik, k in enumerate(KK):
        h +=  2*amp[ik] * np.cos( 2.*np.pi*(k) * (f0/fs) * np.arange(1, len(t)+1, 1 )  + phase[ik] )
    
    return sN-h

def harmonicNorm (f0, sN, fs, t, k1, kN, ks): 
    #return np.linalg.norm( harmonicEuler(sN, fs, t, f0, k1, kN, ks)) 
    ii =  sN < (3.* np.std(sN))
    return np.linalg.norm( harmonicEuler(sN, fs, t, f0, k1, kN, ks)[ii] ) 

def minHarmonic(sN, fs, t, f0, k1, kN, ks):
    # CG, BFGS, Newton-CG, L-BFGS-B, TNC, SLSQP, dogleg, trust-ncg, trust-krylov, trust-exact and trust-constr
    res = minimize(harmonicNorm, np.array((f0)), args=(sN, fs, t, k1, kN, ks), jac='2-point', method='BFGS') # hess=None, bounds=None )
    #print(res)
    #print ( "guess", guessf0(  harmonicEuler(sN, fs, t, res.x[0], k1, kN, ks), fs  ) )
    return harmonicEuler(sN, fs, t, res.x[0], k1, kN, ks)#[0]

def harmonicEuler2 ( sN, fs, t, f0, f0k1, f0kN, f0ks, f1, f1k1, f1kN, f1ks ): 
    """
    Performs inverse calculation of harmonics contaminating a signal. 
    Args:
        sN = signal containing noise 
        fs = sampling frequency
        t = time samples 
        f0 = first base frequency of the sinusoidal noise 
        f0k1 = First harmonic to calulate for f0 
        f0kN = Last base harmonic to calulate for f0
        f0ks = subharmonics to calculate 
        f1 = second base frequency of the sinusoidal noise 
        f1k1 = First harmonic to calulate for f1
        f1kN = Last base harmonic to calulate for f1
        f1ks = subharmonics to calculate at f1 base frequency
    """
    KK0 = np.arange(f0k1, f0kN+1, 1/f0ks)
    nK0 = len(KK0)
    A0 = np.exp(1j* np.tile(KK0,(len(t), 1)) * 2*np.pi* (f0/fs) * np.tile( np.arange(1, len(t)+1, 1), (nK0,1)).T)

    KK1 = np.arange(f1k1, f1kN+1, 1/f1ks)
    nK1 = len(KK1)
    A1 = np.exp(1j* np.tile(KK1,(len(t), 1)) * 2*np.pi* (f1/fs) * np.tile( np.arange(1, len(t)+1, 1),(nK1,1)).T)

    A = np.concatenate((A0, A1), axis=1)

    v = np.linalg.lstsq(A, sN, rcond=None) # rcond=None) #, rcond=1e-8)
    
    amp0 = np.abs(v[0][0:nK0])     
    phase0 = np.angle(v[0][0:nK0]) 
    amp1 = np.abs(v[0][nK0::])     
    phase1 = np.angle(v[0][nK0::]) 

    h = np.zeros(len(t))
    for ik, k in enumerate(KK0):
        h +=  2*amp0[ik] * np.cos( 2.*np.pi*(k) * (f0/fs) * np.arange(1, len(t)+1, 1 ) + phase0[ik] )
    for ik, k in enumerate(KK1):
        h +=  2*amp1[ik] * np.cos( 2.*np.pi*(k) * (f0/fs) * np.arange(1, len(t)+1, 1 ) + phase1[ik] )

    return sN-h

def harmonic2Norm (f0, sN, fs, t, f0k1, f0kN, f0ks, f1k1, f1kN, f1ks): 
    #return np.linalg.norm(harmonicEuler2(f0[0], f0[1], sN, fs, nK, t))
    ii =  sN < (3.* np.std(sN))
    return np.linalg.norm( harmonicEuler2(sN, fs, t, f0[0], f0k1, f0kN, f0ks, f0[1], f1k1, f1kN, f1ks)[ii] ) 

def minHarmonic2(sN, fs, t, f0, f0k1, f0kN, f0ks, f1, f1k1, f1kN, f1ks):
    # CG, BFGS, Newton-CG, L-BFGS-B, TNC, SLSQP, dogleg, trust-ncg, trust-krylov, trust-exact and trust-constr
    res = minimize(harmonic2Norm, np.array((f0, f1)), args=(sN, fs, t, f0k1, f0kN, f0ks, f1k1,f1kN, f1ks), jac='2-point', method='BFGS') # hess=None, bounds=None )
    #print(res)
    #print ( "guess", guessf0(harmonicEuler2(sN, fs, t, res.x[0], f0k1, f0kN, f0ks, res.x[1], f1k1, f1kN, f1ks), fs)  )
    return harmonicEuler2(sN, fs, t, res.x[0], f0k1, f0kN, f0ks, res.x[1], f1k1, f1kN, f1ks)#[0]

def guessf0( sN, fs ):
    S = np.fft.fft(sN)
    w = np.fft.fftfreq( len(sN), 1/fs )
    imax = np.argmax( np.abs(S) )
    #plt.plot( w, np.abs(S) )
    #plt.show()
    #print(w)
    #print ( w[imax], w[imax+1] )
    return abs(w[imax])

if __name__ == "__main__":
    
    import matplotlib.pyplot as plt 

    f0 = 60      # Hz
    f1 = 60      # Hz
    delta  = np.random.rand() - .5 
    delta2 = np.random.rand() - .5 
    print("delta", delta)
    print("delta2", delta2)
    fs = 10000   # GMR 
    t = np.arange(0, 1, 1/fs)
    phi =  2.*np.pi*np.random.rand() - np.pi 
    phi2 = 2.*np.pi*np.random.rand() - np.pi
    print("phi", phi, phi2)
    A =  1.0
    A2 = 0.0 
    A3 = 1.0 
    nK = 10
    T2 = .200
    sN  = A *np.sin( ( 1*(delta  +f0))*2*np.pi*t + phi ) + \
          A2*np.sin( ( 1*(delta2 +f1))*2*np.pi*t + phi2 ) + \
              np.random.normal(0,.1,len(t)) + \
              + A3*np.exp( -t/T2  ) 

    sNc = A *np.sin(  (1*(delta +f0))*2*np.pi*t + phi ) + \
          A2*np.sin(  (1*(delta2+f1))*2*np.pi*t + phi2 ) + \
              + A3*np.exp( -t/T2  ) 


    guessf0(sN, fs)

    # single freq
    #h = harmonicEuler( f0, sN, fs, nK, t) 
    h = minHarmonic( f0, sN, fs, nK, t) 
    
    # two freqs 
    #h = minHarmonic2( f0+1e-2, f1-1e-2, sN, fs, nK, t) 
    #h = harmonicEuler2( f0, f1, sN, fs, nK, t) 

    plt.figure()
    plt.plot(t, sN, label="sN")
    #plt.plot(t, sN-h, label="sN-h")
    plt.plot(t, h, label='h')
    plt.title("harmonic")
    plt.legend()

    plt.figure()
    plt.plot(t, sN-sNc, label='true noise')
    plt.plot(t, h, label='harmonic removal')
    plt.plot(t, np.exp(-t/T2), label="nmr")
    plt.legend()
    plt.title("true noise")
    
    plt.show()