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D Fournier
86 lines
2.2 KiB
Python
86 lines
2.2 KiB
Python
def interpFFT(x,y,m):
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"""
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Load in a 2D grid and resample
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OUTPUT:
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m_out
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"""
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from SimPEG import np, sp
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import scipy.signal as sn
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# Add padding values by reflection (2**n)
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lenx = np.round( np.log2( 2*len(x) ) )
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npadx = int(np.floor( ( 2**lenx - len(x) ) /2. ))
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#Create hemming taper
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if np.mod(npadx*2+len(x),2) != 0:
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oddx = 1
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else:
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oddx = 0
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tap0 = sn.hamming(npadx*2)
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tapl = sp.spdiags(tap0[0:npadx],0,npadx,npadx)
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tapr = sp.spdiags(tap0[npadx:],0,npadx,npadx+oddx)
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# Mirror the 2d data over the half lenght and apply 0-taper
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mpad = np.hstack([np.fliplr(m[:,0:npadx]) * tapl, m, np.fliplr(m[:,-npadx:]) * tapr])
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# Repeat along the second dimension
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leny = np.round( np.log2( 2*len(y) ) )
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npady = int(np.floor( ( 2**leny - len(y) ) /2. ))
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#Create hemming taper
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if np.mod(npady*2+len(y),2) != 0:
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oddy = 1
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else:
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oddy = 0
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tap0 = sn.hamming(npady*2)
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tapu = sp.spdiags(tap0[0:npady],0,npady,npady)
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tapd = sp.spdiags(tap0[npady:],0,npady+oddy,npady)
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mpad = np.vstack([tapu*np.flipud(mpad[0:npady,:]), mpad, tapd*np.flipud(mpad[-npady:,:])])
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# Compute FFT
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FFTm = np.fft.fft2(mpad)
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# Do an FFT shift
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FFTshift = np.fft.fftshift(FFTm)
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# Pad high frequencies with zeros to increase the sampling rate
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py = int(FFTm.shape[0]/2)
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px = int(FFTm.shape[1]/2)
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FFTshift = np.hstack([np.zeros((FFTshift.shape[0],px)),FFTshift,np.zeros((FFTshift.shape[0],px))])
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FFTshift = np.vstack([np.zeros((py,FFTshift.shape[1])),FFTshift,np.zeros((py,FFTshift.shape[1]))])
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# Inverse shift
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FFTm = np.fft.ifftshift(FFTshift)
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# Compute inverse FFT
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IFFTm = np.fft.ifft2(FFTm)*FFTm.size/mpad.size
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m_out = np.real(IFFTm)
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# Extract core
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#m_out = np.real(IFFTm[npady*2:-(npady*2+oddy+1),npadx*2:-(npadx*2+oddx+1)])
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m_out = m_out[npady*2:-(npady+oddy)*2,npadx*2:-(npadx+oddx)*2]
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if np.mod(m.shape[0],2) != 0:
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m_out = m_out[:-1,:]
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if np.mod(m.shape[1],2) != 0:
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m_out = m_out[:,:-1]
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return m_out
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