Python numpy.bartlett() Examples

def bartlett(M):
    """
    An instance of this class returns the Bartlett spectral window in the
    time-domain. The Bartlett window is very similar to a triangular window,
    except that the end points are at zero. It is often used in signal
    processing for tapering a signal, without generating too much ripple in
    the frequency domain.

    .. versionadded:: 0.6

    Parameters
    ----------
    M : integer scalar
        Number of points in the output window. If zero or less,
        an empty vector is returned.

    Returns
    -------
    vector of doubles
        The triangular window, with the maximum value normalized to one
        (the value one appears only if the number of samples is odd), with
        the first and last samples equal to zero.

    """
    return bartlett_(M) 

def plotSpectrogram(data, fftWindow, fftSize, Fs):

    if fftSize == None:
        N = len(data)
    else:
        N = fftSize    
    
    if Fs == None:
        Fs = 2
    
    if fftWindow == "rectangular":
        plt.specgram(data, NFFT=N, Fs=Fs, 
        window=lambda data: data*np.ones(len(data)),  noverlap=int(N/10))
    elif fftWindow == "bartlett":
        plt.specgram(data, NFFT=N, Fs=Fs, 
        window=lambda data: data*np.bartlett(len(data)),  noverlap=int(N/10))
    elif args.fftWindow == "blackman":
        plt.specgram(data, NFFT=N, Fs=Fs, 
        window=lambda data: data*np.blackman(len(data)),  noverlap=int(N/10))
    elif fftWindow == "hamming":
        plt.specgram(data, NFFT=N, Fs=Fs, 
        window=lambda data: data*np.hamming(len(data)),  noverlap=int(N/10))
    elif fftWindow == "hanning":
         plt.specgram(data, NFFT=N, Fs=Fs, 
         window=lambda data: data*np.hanning(len(data)),  noverlap=int(N/10))

    plt.show() 

def bartlett(M):
    """
    An instance of this class returns the Bartlett spectral window in the
    time-domain. The Bartlett window is very similar to a triangular window,
    except that the end points are at zero. It is often used in signal
    processing for tapering a signal, without generating too much ripple in
    the frequency domain.

    .. versionadded:: 0.6

    Parameters
    ----------
    M : integer scalar
        Number of points in the output window. If zero or less,
        an empty vector is returned.

    Returns
    -------
    vector of doubles
        The triangular window, with the maximum value normalized to one
        (the value one appears only if the number of samples is odd), with
        the first and last samples equal to zero.

    """
    return bartlett_(M) 

def window_hann(N):
    r"""Hann window (or Hanning). (wrapping of numpy.bartlett)

    :param int N: window length

    The Hanning window is also known as the Cosine Bell. Usually, it is called
    Hann window, to avoid confusion with the Hamming window.

    .. math:: w(n) =  0.5\left(1- \cos\left(\frac{2\pi n}{N-1}\right)\right)
               \qquad 0 \leq n \leq M-1

    .. plot::
        :width: 80%
        :include-source:

        from spectrum import window_visu
        window_visu(64, 'hanning')

    .. seealso:: numpy.hanning, :func:`create_window`, :class:`Window`.
    """
    from numpy import hanning
    return hanning(N) 

def window_bartlett(N):
    r"""Bartlett window (wrapping of numpy.bartlett) also known as Fejer

    :param int N: window length

    The Bartlett window is defined as

    .. math:: w(n) = \frac{2}{N-1} \left(
              \frac{N-1}{2} - \left|n - \frac{N-1}{2}\right|
              \right)

    .. plot::
        :width: 80%
        :include-source:

        from spectrum import window_visu
        window_visu(64, 'bartlett')

    .. seealso:: numpy.bartlett, :func:`create_window`, :class:`Window`.
    """
    from numpy import bartlett
    return bartlett(N) 

def perform(self, node, inputs, out_):
        M = inputs[0]
        out, = out_
        out[0] = numpy.bartlett(M) 

def _get_window(window, wlen):
    if type(window) == str:
        # types:
        # boxcar, triang, blackman, hamming, hann, bartlett, flattop, parzen,
        # bohman, blackmanharris, nuttall, barthann
        if window == 'hamming':
            fft_window = np.hamming(wlen)
        elif window == 'bartlett':
            fft_window = np.bartlett(wlen)
        elif window == 'hann' or window == 'hanning':
            fft_window = np.hanning(wlen)
        else:
            #try:
                # scipy.signal.get_window gives non-symmetric results for hamming with even length :(
                #fft_window = scipy.signal.get_window(window, wlen)
            #except:
                #raise Exception('cannot obtain window type {}'.format(window))
            raise Exception('cannot obtain window type {}'.format(window))
        # fft_window = scipy.signal.hamming(win_length, sym=False)
    elif six.callable(window):
        # User supplied a windowing function
        fft_window = window(wlen)
    else:
        # User supplied a window vector.
        # Make it into an array
        fft_window = np.asarray(window)
        assert(len(fft_window) == wlen)

    fft_window.flatten()
    return fft_window 

def plotPSD(data,fftWindow, Fs):

    assert fftWindow in ['rectangular', 'bartlett', 'blackman', 
                         'hamming', 'hanning']
    
    N = len(data)
    
    #Generate the selected window
    if fftWindow == "rectangular":
        window = np.ones(N)
    elif fftWindow == "bartlett":
        window = np.bartlett(N)
    elif args.fftWindow == "blackman":
        window = np.blackman(N)
    elif fftWindow == "hamming":
        window = np.hamming(N)
    elif fftWindow == "hanning":
         window = np.hanning(N)         
         
    dft = np.fft.fft(data*window)    
    
    if Fs == None:
        #If the sample rate is known then plot PSD as
        #Power/Freq in (dB/Hz)
        plt.psd(data*window, NFFT=N)
        
    else:
        #If sample rate is not known then plot PSD as
        #Power/Freq as (dB/rad/sample)
        plt.psd(data*window, NFFT=N, Fs=Fs)

    plt.show() 

def voi_noise_window(length):
    return np.bartlett(length)**2.5 # 2.5 optimum # max: 4
    #return np.bartlett(length)**4

#==============================================================================
# If win_func == None, no window is applied (i.e., boxcar)
# win_func: None, window function, or list of window functions. 

def bartlett(M):
    """Returns the Bartlett window.

    The Bartlett window is defined as

    .. math::
            w(n) = \\frac{2}{M-1} \\left(
            \\frac{M-1}{2} - \\left|n - \\frac{M-1}{2}\\right|
            \\right)

    Args:
        M (int):
            Number of points in the output window. If zero or less, an empty
            array is returned.

    Returns:
        ~cupy.ndarray: Output ndarray.

    .. seealso:: :func:`numpy.bartlett`
    """
    if M == 1:
        return cupy.ones(1, dtype=cupy.float64)
    if M <= 0:
        return cupy.array([])
    alpha = (M - 1) / 2.0
    out = cupy.empty(M, dtype=cupy.float64)
    return _bartlett_kernel(alpha, out) 

def test_perform(self):
        x = tensor.lscalar()
        f = function([x], self.op(x))
        M = numpy.random.random_integers(3, 50, size=())
        assert numpy.allclose(f(M), numpy.bartlett(M))
        assert numpy.allclose(f(0), numpy.bartlett(0))
        assert numpy.allclose(f(-1), numpy.bartlett(-1))
        b = numpy.array([17], dtype='uint8')
        assert numpy.allclose(f(b[0]), numpy.bartlett(b[0])) 

def perform(self, node, inputs, out_):
        M = inputs[0]
        out, = out_
        out[0] = numpy.bartlett(M) 

def test_perform(self):
        x = tensor.lscalar()
        f = function([x], self.op(x))
        M = numpy.random.random_integers(3, 50, size=())
        assert numpy.allclose(f(M), numpy.bartlett(M))
        assert numpy.allclose(f(0), numpy.bartlett(0))
        assert numpy.allclose(f(-1), numpy.bartlett(-1))
        b = numpy.array([17], dtype='uint8')
        assert numpy.allclose(f(b[0]), numpy.bartlett(b[0])) 

def smooth(x,window_len=11,window='flat'):
    """smooth the data using a window with requested size.

    This method is based on the convolution of a scaled window with the signal.
    The signal is prepared by introducing reflected copies of the signal
    (with the window size) in both ends so that transient parts are minimized
    in the beginning and end part of the output signal.

    :param x: the input signal
    :param window_len: the dimension of the smoothing window; should be an odd integer
    :param window: the type of window from 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'
        flat window will produce a moving average smoothing.

    :return: the smoothed signal

    example::

        t=linspace(-2,2,0.1)
        x=sin(t)+randn(len(t))*0.1
        y=smooth(x)

    :see also: numpy.hanning, numpy.hamming, numpy.bartlett, numpy.blackman, numpy.convolve,
        scipy.signal.lfilter

    TODO: the window parameter could be the window itself if an array instead of a string
    """

    if x.ndim != 1:
        raise ValueError, "smooth only accepts 1 dimension arrays."

    if x.size < window_len:
        raise ValueError, "Input vector needs to be bigger than window size."

    if window_len<3:
        return x

    if not window in ['flat', 'hanning', 'hamming', 'bartlett', 'blackman']:
        raise ValueError, "Window is on of 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'"

    s=numpy.r_[2*x[0]-x[window_len:1:-1],x,2*x[-1]-x[-1:-window_len:-1]]

    #print(len(s))
    if window == 'flat': #moving average
        w=numpy.ones(window_len,'d')
    else:
        w=eval('numpy.'+window+'(window_len)')

    y=numpy.convolve(w/w.sum(),s,mode='same')

    return y[window_len-1:-window_len+1] 

def smooth(x,window_len=11,window='flat'):
    """smooth the data using a window with requested size.

    This method is based on the convolution of a scaled window with the signal.
    The signal is prepared by introducing reflected copies of the signal
    (with the window size) in both ends so that transient parts are minimized
    in the beginning and end part of the output signal.

    :param x: the input signal
    :param window_len: the dimension of the smoothing window; should be an odd integer
    :param window: the type of window from 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'
        flat window will produce a moving average smoothing.

    :return: the smoothed signal

    example::

        t=linspace(-2,2,0.1)
        x=sin(t)+randn(len(t))*0.1
        y=smooth(x)

    :see also: numpy.hanning, numpy.hamming, numpy.bartlett, numpy.blackman, numpy.convolve,
        scipy.signal.lfilter

    TODO: the window parameter could be the window itself if an array instead of a string
    """

    if x.ndim != 1:
        raise ValueError("smooth only accepts 1 dimension arrays.")

    if x.size < window_len:
        raise ValueError("Input vector needs to be bigger than window size.")

    if window_len < 3:
        return x

    if not window in ['flat', 'hanning', 'hamming', 'bartlett', 'blackman']:
        raise ValueError("Window is on of 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'")

    s=numpy.r_[2*x[0]-x[window_len:1:-1],x,2*x[-1]-x[-1:-window_len:-1]]

    #print(len(s))
    if window == 'flat': #moving average
        w = numpy.ones(window_len,'d')
    else:
        w = eval('numpy.' + window + '(window_len)')

    y = numpy.convolve(w/w.sum(), s, mode='same')

    return y[window_len-1:-window_len+1] 

def convolve(inspectral, samplingresolution,  inwinwidth,  outwinwidth,  windowtype=np.bartlett):
    """ Convolve (non-circular) a spectral variable with a window function,
    given the input resolution and input and output window widths.

    This function is normally used on wavenumber-domain spectral data.  The spectral
    data is assumed sampled at samplingresolution wavenumber intervals.
    The inwinwidth and outwinwidth window function widths are full width half-max (FWHM)
    for the window functions for the inspectral and returned spectral variables, respectively.
    The Bartlett function is used as default, but the user can use a different function.
    The Bartlett function is a triangular function reaching zero at the ends. Window function
    width is correct for Bartlett and only approximate for other window functions.

    Spectral convolution is best done in frequency domain ([cm-1] units) because
    the filter or emission line shapes have better symmetry in frequency domain than
    in wavelength domain.

    The input spectral vector must be in spectral density units of cm-1.

    Args:
        | inspectral (np.array[N,] or [N,1]):  spectral variable input  vector (e.g., radiance or transmittance).
        | samplingresolution (float): wavenumber interval between inspectral samples
        | inwinwidth (float): FWHM window width used to obtain the input spectral vector (e.g., spectroradiometer window width)
        | outwinwidth (float): FWHM window width of the output spectral vector after convolution
        | windowtype (function): name of a  numpy/scipy function for the window function

    Returns:
        | outspectral (np.array[N,]):  input vector, filtered to new window width.
        | windowfn (np.array[N,]):  The window function used.

    Raises:
        | No exception is raised.
    """

    winbins = round(2*(outwinwidth/(inwinwidth*samplingresolution)), 0)
    winbins = winbins if winbins%2==1 else winbins+1
    windowfn=windowtype(winbins)
    #np.convolve is unfriendly towards unicode strings

    if sys.version_info[0] > 2:
        cmode='same'
    else:
        cmode='same'.encode('utf-8')

    outspectral = np.convolve(windowfn/(samplingresolution*windowfn.sum()),
                        inspectral.reshape(-1, ),mode=cmode)
    return outspectral,  windowfn

###################################################################################### 

def smooth(x, window_len=11, window='flat'):
    """smooth the data using a window with requested size.

    This method is based on the convolution of a scaled window with the signal.
    The signal is prepared by introducing reflected copies of the signal
    (with the window size) in both ends so that transient parts are minimized
    in the beginning and end part of the output signal.

    :param x: the input signal
    :param window_len: the dimension of the smoothing window; should be an odd integer
    :param window: the type of window from 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'
        flat window will produce a moving average smoothing.

    :return: the smoothed signal

    example::

        t=linspace(-2,2,0.1)
        x=sin(t)+randn(len(t))*0.1
        y=smooth(x)

    :see also: numpy.hanning, numpy.hamming, numpy.bartlett, numpy.blackman, numpy.convolve,
        scipy.signal.lfilter

    TODO: the window parameter could be the window itself if an array instead of a string
    """

    if x.ndim != 1:
        raise ValueError("smooth only accepts 1 dimension arrays.")

    if x.size < window_len:
        raise ValueError("Input vector needs to be bigger than window size.")

    if window_len < 3:
        return x

    if window not in ['flat', 'hanning', 'hamming', 'bartlett', 'blackman']:
        raise ValueError(
            "Window is on of 'flat', 'hanning', 'hamming', 'bartlett', 'blackman'"
        )

    s = numpy.r_[2 * x[0] - x[window_len:1:-1], x, 2 * x[-1] - x[-1:-window_len:-1]]

    # print(len(s))
    if window == 'flat':  # moving average
        w = numpy.ones(window_len, 'd')
    else:
        w = eval('numpy.' + window + '(window_len)')

    y = numpy.convolve(w / w.sum(), s, mode='same')

    return y[window_len - 1 : -window_len + 1]