def OS_filter(x,h,N,mode=0):
    """
    Overlap and save transform domain FIR filtering.
    
    This function implements the classical overlap and save method of
    transform domain filtering using a length P FIR filter.
    
    Parameters
    ----------
    x : input signal to be filtered as an ndarray
    h : FIR filter coefficients as an ndarray of length P
    N : FFT size > P, typically a power of two
    mode : 0 or 1, when 1 returns a diagnostic matrix
    
    Returns
    -------
    y : the filtered output as an ndarray
    y_mat : an ndarray whose rows are the individual overlap outputs.
    
    Notes
    -----
    y_mat is used for diagnostics and to gain understanding of the algorithm.
    
    Examples
    --------
    >>> n = arange(0,100)
    >>> x = cos(2*pi*0.05*n)
    >>> b = ones(10)
    >>> y = OS_filter(x,h,N)
    >>> # set mode = 1
    >>> y, y_mat = OS_filter(x,h,N,1)
    """
    
    P = len(h)
    # zero pad start of x so first frame can recover first true samples of x
    x = np.hstack((np.zeros(P-1),x))
    L = N - P + 1
    Nx = len(x)
    Nframe = int(np.ceil(Nx/float(L)))
    # zero pad end of x to full number of frames needed
    x = np.hstack((x,np.zeros(Nframe*L-Nx)))
    y = np.zeros(int(Nframe*N))
    # create an instrumentation matrix to observe the overlap and save behavior
    y_mat = np.zeros((Nframe,int(Nframe*N)))

    H = fft.fft(h,N)
    # begin the filtering operation
    for k in range(Nframe):
        xk = x[k*L:k*L+N]
        Xk = fft.fft(xk,N)
        Yk = H*Xk
        yk = np.real(fft.ifft(Yk)) # imag part should be zero
        y[k*L+P-1:k*L+N] = yk[P-1:]
        y_mat[k,k*L:k*L+N] = yk
    if mode == 1:
        return y[P-1:Nx], y_mat[:,P-1:Nx]
    else:
        return y[P-1:Nx]
def OS_filter(x,h,N,mode=0):
    """
    Overlap and save transform domain FIR filtering.
    
    This function implements the classical overlap and save method of
    transform domain filtering using a length P FIR filter.
    
    Parameters
    ----------
    x : input signal to be filtered as an ndarray
    h : FIR filter coefficients as an ndarray of length P
    N : FFT size > P, typically a power of two
    mode : 0 or 1, when 1 returns a diagnostic matrix
    
    Returns
    -------
    y : the filtered output as an ndarray
    y_mat : an ndarray whose rows are the individual overlap outputs.
    
    Notes
    -----
    y_mat is used for diagnostics and to gain understanding of the algorithm.
    
    Examples
    --------
    >>> n = arange(0,100)
    >>> x = cos(2*pi*0.05*n)
    >>> b = ones(10)
    >>> y = OS_filter(x,h,N)
    >>> # set mode = 1
    >>> y, y_mat = OS_filter(x,h,N,1)
    """
    
    P = len(h)
    # zero pad start of x so first frame can recover first true samples of x
    x = np.hstack((np.zeros(P-1),x))
    L = N - P + 1
    Nx = len(x)
    Nframe = int(np.ceil(Nx/float(L)))
    # zero pad end of x to full number of frames needed
    x = np.hstack((x,np.zeros(Nframe*L-Nx)))
    y = np.zeros(int(Nframe*N))
    # create an instrumentation matrix to observe the overlap and save behavior
    y_mat = np.zeros((Nframe,int(Nframe*N)))

    H = fft.fft(h,N)
    # begin the filtering operation
    for k in range(Nframe):
        xk = x[k*L:k*L+N]
        Xk = fft.fft(xk,N)
        Yk = H*Xk
        yk = np.real(fft.ifft(Yk)) # imag part should be zero
        y[k*L+P-1:k*L+N] = yk[P-1:]
        y_mat[k,k*L:k*L+N] = yk
    if mode == 1:
        return y[P-1:Nx], y_mat[:,P-1:Nx]
    else:
        return y[P-1:Nx]
def OS_filter ( x , h , N , mode = 0 ) : P = len ( h ) # zero pad start of x so first frame can recover first true samples of x x = np . hstack ( ( np . zeros ( P - 1 ) , x ) ) L = N - P + 1 Nx = len ( x ) Nframe = int ( np . ceil ( Nx / float ( L ) ) ) # zero pad end of x to full number of frames needed x = np . hstack ( ( x , np . zeros ( Nframe * L - Nx ) ) ) y = np . zeros ( int ( Nframe * N ) ) # create an instrumentation matrix to observe the overlap and save behavior y_mat = np . zeros ( ( Nframe , int ( Nframe * N ) ) ) H = fft . fft ( h , N ) # begin the filtering operation for k in range ( Nframe ) : xk = x [ k * L : k * L + N ] Xk = fft . fft ( xk , N ) Yk = H * Xk yk = np . real ( fft . ifft ( Yk ) ) # imag part should be zero y [ k * L + P - 1 : k * L + N ] = yk [ P - 1 : ] y_mat [ k , k * L : k * L + N ] = yk if mode == 1 : return y [ P - 1 : Nx ] , y_mat [ : , P - 1 : Nx ] else : return y [ P - 1 : Nx ]
Overlap and save transform domain FIR filtering.
    
    This function implements the classical overlap and save method of
    transform domain filtering using a length P FIR filter.
    
    Parameters
    ----------
    x : input signal to be filtered as an ndarray
    h : FIR filter coefficients as an ndarray of length P
    N : FFT size > P, typically a power of two
    mode : 0 or 1, when 1 returns a diagnostic matrix
    
    Returns
    -------
    y : the filtered output as an ndarray
    y_mat : an ndarray whose rows are the individual overlap outputs.
    
    Notes
    -----
    y_mat is used for diagnostics and to gain understanding of the algorithm.
    
    Examples
    --------
    >>> n = arange(0,100)
    >>> x = cos(2*pi*0.05*n)
    >>> b = ones(10)
    >>> y = OS_filter(x,h,N)
    >>> # set mode = 1
    >>> y, y_mat = OS_filter(x,h,N,1)
Overlap and save transform domain FIR filtering . This function implements the classical overlap and save method of transform domain filtering using a length P FIR filter . Parameters ---------- x : input signal to be filtered as an ndarray h : FIR filter coefficients as an ndarray of length P N : FFT size > P typically a power of two mode : 0 or 1 when 1 returns a diagnostic matrix Returns ------- y : the filtered output as an ndarray y_mat : an ndarray whose rows are the individual overlap outputs . Notes ----- y_mat is used for diagnostics and to gain understanding of the algorithm . Examples -------- >>> n = arange ( 0 100 ) >>> x = cos ( 2 * pi * 0 . 05 * n ) >>> b = ones ( 10 ) >>> y = OS_filter ( x h N ) >>> # set mode = 1 >>> y y_mat = OS_filter ( x h N 1 )