# -*- coding: utf-8 -*-
"""
Created on Fri Nov 19 15:13:47 2010

@author: daryl

Presents an "efficient" implementation of a simple 
QMF filter bank for simulation purposes.

If you find my code useful, I'd appreciate it if
you'd email me my email address is wasden <at>
eng <dot> utah <dot> edu.
"""

import numpy as np
from numpy.fft import fft,ifft

def qmfSynthesis(xp):
    '''
    Performs the synthesis portion of a simple
    Quadrature Mirror Filterbank. The filter
    coefficients are [1.0,1.0] for the low-pass
    and [1.0,-1.0] for the highpass. The input
    should be a 2-D array with the first column
    representing the low pass component and the
    second column representing the high pass 
    component. Returns the signal in a 1-D array.
    '''

    # Calculate polyphase outputs
    sp = np.vstack((xp[:,0]+xp[:,1], xp[:,0]-xp[:,1])).T
    s = sp.flatten()

    # Calculate outut
    return s

def qmfAnalysis(s):
    '''
    Performs the analysis portion of a simple
    Quadrature Mirror Filterbank. The filter
    coefficients are [0.5,0.5] for the low-pass
    and [0.5,-0.5] for the highpass. Returns the
    two components in a 2-D array with each column
    representing one of the signals (first column
    is the lowpass signal, second is the high pass).
    '''
    # Force a 1-D array
    s = s.flatten()

    # Make sure the array length is even
    if(float(s.size)/2.0 != s.size/2):
        s = np.hstack((s.flatten,np.array([0.0])))

    # Separate polyphase components
    sp = s/2.0
    sp.shape = (-1,2)

    # Calculate outputs
    xp = np.vstack((sp[:,0]+sp[:,1], sp[:,0]-sp[:,1]))

    return xp.T
    
# Begin Script
if __name__ == '__main__':
    import matplotlib.pyplot as pyplot
    import numpy.random as npr
    
    s = npr.standard_normal(1000)
    xp = qmfAnalysis(s)
    s2 = qmfSynthesis(xp)
    pyplot.figure()
    pyplot.plot(s,'b',linewidth=2.0)
    pyplot.plot(s2,'r-.',linewidth=2.0)