def MDCTsynfb(y, fb):
#MDCT synthesis filter bank.
#Arguments: y: 2-d array of blocks of subbands, of shape (N, # of blokcs)
#returns xr, the reconstructed signal, a 1-d array.
N = y.shape[0]
Fa = symFmatrix(fb)
#invert Fa matrix for synthesis after removing last dim:
Fs = np.linalg.inv(Fa[:, :, 0])
#add again last dimension for function polmatmult:
Fs = np.expand_dims(Fs, axis=-1)
Dinv = Dinvmatrix(N)
#add first dimension to y for polmatmult:
y = np.expand_dims(y, axis=0)
xp = DCT4(y)
xp = polmatmult(xp, Dinv)
xp = polmatmult(xp, Fs)
xr = polyphase2x(xp)
return xr
def LDFBsyn(y, fb):
#Low Delay synthesis filter bank.
#Arguments: y: 2-d array of blocks of subbands, of shape (N, # of blokcs)
#returns xr, the reconstructed signal, a 1-d array.
Fa = symFmatrix(fb[0:int(1.5 * N)])
#invert Fa matrix for synthesis after removing last dim:
Fs = np.linalg.inv(Fa[:, :, 0])
#add again last dimension for function polmatmult:
Fs = np.expand_dims(Fs, axis=-1)
Ginv = Ginvmatrix(fb[int(1.5 * N):(2 * N)])
Dinv = Dinvmatrix(N)
#Display the synthesis folding matrix Fs(z):
Fsz = polmatmult(polmatmult(Ginv, Dinv), Fs)
#add first dimension to y for polmatmult:
y = np.expand_dims(y, axis=0)
xp = DCT4(y)
xp = polmatmult(xp, Ginv)
xp = polmatmult(xp, Dinv)
xp = polmatmult(xp, Fs)
xr = polyphase2x(xp)
return xr
xp = DCT4(y)
xp = polmatmult(xp, Dinv)
xp = polmatmult(xp, Fs)
xr = polyphase2x(xp)
return xr
#Testing:
if __name__ == '__main__':
import numpy as np
import matplotlib.pyplot as plt
#Number of subbands:
N = 4
D = Dmatrix(N)
Dinv = Dinvmatrix(N)
#Filter bank coefficients for sine window:
#fb=np.sin(np.pi/(2*N)*(np.arange(int(1.5*N))+0.5))
fb = np.loadtxt("MDCTcoeff.txt") #Coeff. from optimization
print("fb=", fb)
#input test signal, ramp:
x = np.arange(64)
plt.plot(x)
plt.title('Input Signal')
plt.xlabel('Sample')
plt.show()
y = MDCTanafb(x, N, fb)
print("y=\n", y)
plt.imshow(np.abs(y))
plt.title('MDCT Subbands')
plt.xlabel('Block No.')