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harmonic removal

tags/1.6.1
Trevor Irons 5 年之前
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共有 1 個文件被更改,包括 79 次插入0 次删除
  1. 79
    0
      akvo/tressel/harmonic.py

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akvo/tressel/harmonic.py 查看文件

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+import numpy as np 
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+from scipy.optimize import least_squares 
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+
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+def harmonic ( sN, f0, fs, nK, t  ): 
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+    """
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+    Performs inverse calculation of harmonics contaminating a signal. 
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+    Args:
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+        sN = signal containing noise 
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+        f0 = base frequency of the sinusoidal noise 
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+        fs = sampling frequency
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+        nK = number of harmonics to calculate 
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+        t = time samples 
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+    """
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+    print("building matrix ")
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+    A = np.zeros( (len(t),  2*nK) )
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+    for irow, tt in enumerate(t): 
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+        A[irow, 0::2] = np.cos( np.arange(nK)*2*np.pi*(f0/fs)*irow )
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+        A[irow, 1::2] = np.sin( np.arange(nK)*2*np.pi*(f0/fs)*irow )
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+        # brutal 
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+        #for k, ik in enumerate( np.arange(0, 2*nK, 2) ):
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+        #    A[irow, ik  ] = np.cos( k*2*np.pi*(f0/fs)*irow )
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+        #    A[irow, ik+1] = np.sin( k*2*np.pi*(f0/fs)*irow )
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+
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+    v = np.linalg.lstsq(A, sN, rcond=None) #, rcond=1e-8)
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+
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+    alpha = v[0][0::2]
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+    beta  = v[0][1::2]
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+
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+    amp = np.sqrt( alpha**2 + beta**2 )
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+    phase = np.arctan(- beta/alpha)
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+
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+    h = np.zeros(len(t))
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+    for ik in range(nK):
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+        h +=  np.sqrt(alpha[ik]**2 + beta[ik]**2) * np.cos( 2.*np.pi*ik * (f0/fs) * np.arange(0, len(t), 1 )  + phase[ik] )
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+
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+    #plt.matshow(A, aspect='auto')
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+    #plt.colorbar()
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+
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+    #plt.figure()
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+    #plt.plot(alpha)
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+    #plt.plot(beta)
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+    #plt.plot(amp)
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+
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+    #plt.figure()
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+    #plt.plot(h)
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+    #plt.title("modelled noise")
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+
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+    return h
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+
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+if __name__ == "__main__":
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+    import matplotlib.pyplot as plt 
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+
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+    f0 = 60      # Hz
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+    delta = np.random.rand()
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+    fs = 50000  #1e4    
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+    t = np.arange(0, 1, 1/fs)
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+    phi = .234
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+    A = 1.0
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+    nK = 20
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+    sN = A * np.sin( (delta+f0)*2*np.pi*t + phi ) + np.random.normal(0,.1,len(t)) 
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+    sNc = A * np.sin( (delta+f0)*2*np.pi*t + phi ) 
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+    h = harmonic(sN, f0, fs, nK, t)
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+
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+    plt.figure()
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+    plt.plot(t, sN, label="sN")
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+    plt.plot(t, sN-h, label="sN-h")
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+    plt.plot(t, h, label='h')
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+    plt.title("true noise")
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+    plt.legend()
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+
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+    plt.figure()
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+    plt.plot(t, sN-sNc, label='true noise')
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+    plt.plot(t, sN-h, label='harmonic removal')
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+    plt.legend()
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+    plt.title("true noise")
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+    
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+    plt.show()
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+
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+    print("hello")

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