Python numpy.blackman() Examples

def run_mgc_example():
    import matplotlib.pyplot as plt
    fs, x = wavfile.read("test16k.wav")
    pos = 3000
    fftlen = 1024
    win = np.blackman(fftlen) / np.sqrt(np.sum(np.blackman(fftlen) ** 2))
    xw = x[pos:pos + fftlen] * win
    sp = 20 * np.log10(np.abs(np.fft.rfft(xw)))
    mgc_order = 20
    mgc_alpha = 0.41
    mgc_gamma = -0.35
    mgc_arr = win2mgc(xw, order=mgc_order, alpha=mgc_alpha, gamma=mgc_gamma, verbose=True)
    xwsp = 20 * np.log10(np.abs(np.fft.rfft(xw)))
    sp = mgc2sp(mgc_arr, mgc_alpha, mgc_gamma, fftlen)
    plt.plot(xwsp)
    plt.plot(20. / np.log(10) * np.real(sp), "r")
    plt.xlim(1, len(xwsp))
    plt.show() 

def run_mgc_example():
    import matplotlib.pyplot as plt
    fs, x = wavfile.read("test16k.wav")
    pos = 3000
    fftlen = 1024
    win = np.blackman(fftlen) / np.sqrt(np.sum(np.blackman(fftlen) ** 2))
    xw = x[pos:pos + fftlen] * win
    sp = 20 * np.log10(np.abs(np.fft.rfft(xw)))
    mgc_order = 20
    mgc_alpha = 0.41
    mgc_gamma = -0.35
    mgc_arr = win2mgc(xw, order=mgc_order, alpha=mgc_alpha, gamma=mgc_gamma, verbose=True)
    xwsp = 20 * np.log10(np.abs(np.fft.rfft(xw)))
    sp = mgc2sp(mgc_arr, mgc_alpha, mgc_gamma, fftlen)
    plt.plot(xwsp)
    plt.plot(20. / np.log(10) * np.real(sp), "r")
    plt.xlim(1, len(xwsp))
    plt.show() 

def find_peak(fname):
    """Find the signal frequency and maximum value"""
    #print("find_peak",fname)
    Fs, x = wavfile.read(fname)
    f,s = periodogram(x, Fs,'blackman',8192,'linear', False, scaling='spectrum')
    threshold = max(s)*0.8  # only 0.4 ... 1.0 of max value freq peaks included
    maxtab, mintab = peakdet(abs(s[0:int(len(s)/2-1)]), threshold,f[0:int(len(f)/2-1)] )
    try:
        val = maxtab[0,0]
    except:
        print("Error: {}".format(maxtab))
        val = 600.
    return val

# Fs should be 8000 Hz 
# with decimation down to 125 Hz we get 8 msec / sample
# with WPM equals to 20 => Tdit = 1200/WPM = 60 msec   (time of 'dit')
# 4 seconds equals 256 samples ~ 66.67 Tdits 
# word 'PARIS' is 50 Tdits 

def init(self, lo=0, hi=125, bins=256, yrange=750, ratio=False):
        self.widget = pg.PlotWidget()
        self.widget.setLabel('bottom', 'Frequency', units='Hz')

        self.bars = pg.BarGraphItem()

        self.win = np.hanning(bins)
        self.win = np.blackman(bins)
        #self.win = np.ones(bins)
        self.lo, self.hi = lo, hi
        self.ratio = ratio
        
        FS = self.input.sample_rate

        self.gr_block.set_history(bins)

        #num_bars = int(round((self.bins - 1) * (self.hi - self.lo) / FS))
        # This is total bullshit:
        num_bars = len(np.zeros(bins)[lo: hi])

        x = np.linspace(self.lo, self.hi, num_bars)

        self.bars = pg.BarGraphItem(x=x, height=range(num_bars), width=1.0)
        
        self.bars.setOpts(brushes=[pg.hsvColor(float(x) / num_bars) for x in range(num_bars)])
        self.widget.addItem(self.bars)

        # TODO: Better autoranging features
        #self.plot.enableAutoRange('xy', False)
        
        self.widget.setYRange(0, yrange)
        self.widget.enableAutoRange('y', 0.95)

        self.buffer = np.zeros(bins)

        self.timer = pg.QtCore.QTimer()
        self.timer.timeout.connect(self.updateGUI)
        self.timer.start(10) 

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 design_windowed_sinc_lpf(fc, bw):
        N = Filter.get_filter_length_from_bandwidth(bw)

        # Compute sinc filter impulse response
        h = np.sinc(2 * fc * (np.arange(N) - (N - 1) / 2.))

        # We use blackman window function
        w = np.blackman(N)

        # Multiply sinc filter with window function
        h = h * w

        # Normalize to get unity gain
        h_unity = h / np.sum(h)

        return h_unity 

def impulse_response(self, sampling_frequency):
        dt = 1 / sampling_frequency
        if self.impulse_window in ['hanning', 'blackman']:
            t_start = 0
            t_stop = int(self.impulse_cycles / self.center_frequency * sampling_frequency) * dt  # int() applies floor
            t_num = int(self.impulse_cycles / self.center_frequency * sampling_frequency) + 1  # int() applies floor
            t = np.linspace(t_start, t_stop, t_num)
            impulse = np.sin(2 * np.pi * self.center_frequency * t)
            if self.impulse_window == 'hanning':
                win = np.hanning(impulse.shape[0])
            elif self.impulse_window == 'blackman':
                win = np.blackman(impulse.shape[0])
            else:
                raise NotImplementedError('Window type {} not implemented'.format(self.impulse_window))
            return impulse * win
        elif self.impulse_window == 'gauss':
            # Compute cutoff time for when the pulse amplitude falls below `tpr` (in dB) which is set at -100dB
            tpr = -60
            t_cutoff = scipy.signal.gausspulse('cutoff', fc=int(self.center_frequency), bw=self.bandwidth, tpr=tpr)
            t = np.arange(-t_cutoff, t_cutoff, dt)
            return scipy.signal.gausspulse(t, fc=self.center_frequency, bw=self.bandwidth, tpr=tpr)
        else:
            raise NotImplementedError('Window type {} not implemented'.format(self.impulse_window)) 

def spectrum(signal, fs, taper=True):
        if taper:
            windowed = signal * np.blackman(len(signal))
        else:
            windowed = signal
        a = abs(np.fft.rfft(windowed))
        f = np.fft.rfftfreq(len(signal), 1/fs)

        db = 20 * np.log10(a)
        sig = db - np.amax(db) + 20
        indices = ((sig[1:] >= 0) & (sig[:-1] < 0)).nonzero()
        crossings = [z - sig[z] / (sig[z+1] - sig[z]) for z in indices]
        mi, ma = np.amin(crossings), np.amax(crossings)
        x = np.arange(0, len(f))  # for back-interpolation
        f_min = np.interp(mi, x, f)
        f_max = np.interp(ma, x, f)

        return f, a, f_min, f_max 

def transform(self, X_indices, y_indices):
        X_indices, y_indices = super(IndexBatchIterator, self).transform(X_indices, y_indices)
        [count] = X_indices.shape
        # Use preallocated space
        X = self.Xbuf[:count]
        Y = self.Ybuf[:count]
        window = np.blackman(SAMPLE_SIZE//DOWNSAMPLE)[None,:]
        for i, ndx in enumerate(X_indices):
            if ndx == -1:
                ndx = np.random.randint(len(self.source.events))
            augmented = self.augmented[:,ndx:ndx+SAMPLE_SIZE]
            X[i] = augmented[:,::-1][:,::DOWNSAMPLE]
            if y_indices is not None:
                Y[i] = self.source.events[ndx]
        Y = None if (y_indices is None) else Y
        return X, Y 

def run_mgc_example():
    import matplotlib.pyplot as plt
    fs, x = wavfile.read("test16k.wav")
    pos = 3000
    fftlen = 1024
    win = np.blackman(fftlen) / np.sqrt(np.sum(np.blackman(fftlen) ** 2))
    xw = x[pos:pos + fftlen] * win
    sp = 20 * np.log10(np.abs(np.fft.rfft(xw)))
    mgc_order = 20
    mgc_alpha = 0.41
    mgc_gamma = -0.35
    mgc_arr = win2mgc(xw, order=mgc_order, alpha=mgc_alpha, gamma=mgc_gamma, verbose=True)
    xwsp = 20 * np.log10(np.abs(np.fft.rfft(xw)))
    sp = mgc2sp(mgc_arr, mgc_alpha, mgc_gamma, fftlen)
    plt.plot(xwsp)
    plt.plot(20. / np.log(10) * np.real(sp), "r")
    plt.xlim(1, len(xwsp))
    plt.show() 

def _plot_multiple_spectrum(signals, fs, labels, colors):
    """
    plot the signals spectrum
    """
    s = Spectrum(block_length=min(2048, signals[0].size), fs=fs,
                 wfunc=np.blackman)
    for sig in signals:
        s.periodogram(sig, hold=True)
    s.plot(labels=labels, colors=colors, fscale='lin') 

def _design(self):
        """Designs the FIR filter"""
        # the length of the filter
        order = self._get_order()
        half_order = (order - 1) // 2

        w = np.blackman(order)
        t = np.linspace(-half_order, half_order, order)
        phase = (2.0 * np.pi * self.fc / self.fs) * t

        car = np.cos(phase)
        fir = w * car

        # the filter must be symmetric, in order to be zero-phase
        assert np.all(np.abs(fir - fir[::-1]) < 1e-15)

        # remove the constant component by forcing fir.sum() = 0
        if self.zero_mean:
            fir -= fir.sum() / order

        gain = np.sum(fir * car)
        self.fir = fir * (1.0 / gain)

        # add the imaginary part to have a complex wavelet
        if self.extract_complex:
            car_imag = np.sin(phase)
            fir_imag = w * car_imag
            self.fir_imag = fir_imag * (1.0 / gain)
        return self 

def test_fft_peaks():
    fig, ax = plt.subplots()
    t = np.arange(65536)
    p1 = ax.plot(abs(np.fft.fft(np.sin(2*np.pi*.01*t)*np.blackman(len(t)))))

    path = p1[0].get_path()
    transform = p1[0].get_transform()
    path = transform.transform_path(path)
    simplified = path.cleaned(simplify=True)

    assert simplified.vertices.size == 36 

def test_fft_peaks():
    fig, ax = plt.subplots()
    t = np.arange(65536)
    p1 = ax.plot(abs(np.fft.fft(np.sin(2*np.pi*.01*t)*np.blackman(len(t)))))

    path = p1[0].get_path()
    transform = p1[0].get_transform()
    path = transform.transform_path(path)
    simplified = path.cleaned(simplify=True)

    assert simplified.vertices.size == 36 

def get_specgram(signal, rate):
    arr2D, freqs, bins = specgram(
        signal,
        window=np.blackman(nfft),
        Fs=rate,
        NFFT=nfft,
        noverlap=overlap,
        pad_to=32 * nfft,
    )
    return arr2D, freqs, bins 

def iFFT(Y, output_length=None, window=False):
    """ Inverse real-valued Fourier Transform

    Parameters
    ----------
    Y : array_like
       Frequency domain data [Nsignals x Nbins]
    output_length : int, optional
       Length of returned time-domain signal (Default: 2 x len(Y) + 1)
    window : boolean, optional
       Window applied to the resulting time-domain signal

    Returns
    -------
    y : array_like
       Reconstructed time-domain signal
    """
    Y = _np.atleast_2d(Y)
    y = _np.fft.irfft(Y, n=output_length)

    if window:
        no_of_samples = y.shape[-1]

        if window == 'hann':
            window_array = _np.hanning(no_of_samples)
        elif window == 'hamming':
            window_array = _np.hamming(no_of_samples)
        elif window == 'blackman':
            window_array = _np.blackman(no_of_samples)
        elif window == 'kaiser':
            window_array = _np.kaiser(no_of_samples, 3)
        else:
            raise ValueError('Selected window must be one of hann, hamming, blackman or kaiser')

        y *= window_array

    return y


# noinspection PyUnusedLocal 

def __init__(self, sf=16000, fl=400, fs=80, fftl=512, mfbsize=80):
        self.sf = sf
        self.fl = fl
        self.fs = fs
        self.fftl = fftl
        self.mfbsize = mfbsize
        winpower = numpy.sqrt(numpy.sum(numpy.square(numpy.blackman(self.fl).astype(numpy.float32))))
        self.window = numpy.blackman(self.fl).astype(numpy.float32) / winpower
        self.melfb = self._melfbank() 

def get_normalized_templates(template_streams):
    templates = []
    for ts in template_streams:
        t = data_conversion.stream2array(ts)
        t = t.astype(np.float32)
        t -= np.mean(t, axis=1, keepdims=True)
        template_max = np.amax(np.abs(t))
        t /= template_max
        t *= np.blackman(ts[0].stats.npts)
        templates.append(t)
    return templates 

def kde_sklearn(x, x_grid, bandwidth):
    """Kernel Density Estimation with Scikit-learn"""
    n_samples, = x.shape
    if n_samples == 0:
        return np.zeros_like(x_grid)

    window = np.blackman(bandwidth) * bandwidth
    return np.convolve(x, window, 'same') 

def _plot_activation(z_k, info, ax, color, n_times_atom, t_min=0,
                     plot="density"):
    sfreq = int(info.get('sfreq', 1))
    z_k = z_k.mean(axis=0)  # Average over the epochs
    t = np.arange(len(z_k)) / sfreq + t_min
    if plot == "density":
        blob = np.blackman(n_times_atom)  # bandwidth of n_times_atom
        z_k_smooth = np.convolve(z_k, blob, mode='same')
        ax.fill_between(t, z_k_smooth, color=color, alpha=.5)
    elif plot == "logratio":
        eps = 1e-4
        baseline = z_k[:sfreq]  # Take the first second a a baseline
        mean_baseline = max(baseline.mean(), eps)

        patch = np.ones(sfreq)
        energy = np.maximum(np.convolve(z_k, patch, mode='same'), eps)
        logratio = np.log10(energy / mean_baseline)
        # logratio /= np.std(logratio[:sfreq])
        ax.plot(t[sfreq // 2:-sfreq // 2], logratio[sfreq // 2:-sfreq // 2])
    elif plot == "whiskers":
        # Take 1s at the beginning of the epochs as a baseline
        # Take 1s starting from stim as evoked
        # Take 1s starting 1s after the stim as induced
        baseline = z_k[:sfreq]
        evoked = z_k[(0 < t) * (t < 1)]
        induced = z_k[(1 < t) * (t < 2)]

        ax.boxplot([baseline, evoked, induced], sym='',
                   labels=["baseline", "evoked", "induced"])

        # raise NotImplementedError("Not yet!")
    else:
        raise NotImplementedError("No plot '{}' for activations".format(plot)) 

def init(self):
        self.canvas = Canvas()
        self.widget = self.canvas.native

        self.gr_block.set_history(bins)
        self.win = np.blackman(bins) 

def init(self, lo=0, hi=125, bins=256, yrange=750, ratio=False):
        self.widget = pg.PlotWidget()
        self.widget.setLabel('bottom', 'Frequency', units='Hz')

        self.bars = pg.BarGraphItem()

        self.win = np.hanning(bins)
        self.win = np.blackman(bins)
        #self.win = np.ones(bins)
        self.lo, self.hi = lo, hi
        self.ratio = ratio
        
        FS = self.input.sample_rate

        self.gr_block.set_history(bins)

        #num_bars = int(round((self.bins - 1) * (self.hi - self.lo) / FS))
        # This is total bullshit:
        num_bars = len(np.zeros(bins)[lo: hi])

        x = np.linspace(self.lo, self.hi, num_bars)

        self.bars = pg.BarGraphItem(x=x, height=range(num_bars), width=1.0)
        
        self.bars.setOpts(brushes=[pg.hsvColor(float(x) / num_bars) for x in range(num_bars)])
        self.widget.addItem(self.bars)

        # TODO: Better autoranging features
        #self.plot.enableAutoRange('xy', False)
        
        self.widget.setYRange(0, yrange)
        self.widget.enableAutoRange('y', 0.95)

        self.buffer = np.zeros(bins)

        self.timer = QtCore.QTimer()
        self.timer.timeout.connect(self.updateGUI)
        self.timer.start(10) 

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 blackman(M):
    """Returns the Blackman window.

    The Blackman window is defined as

    .. math::
        w(n) = 0.42 - 0.5 \\cos\\left(\\frac{2\\pi{n}}{M-1}\\right)
        + 0.08 \\cos\\left(\\frac{4\\pi{n}}{M-1}\\right)
        \\qquad 0 \\leq n \\leq M-1

    Args:
        M (:class:`~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.blackman`
    """
    if M == 1:
        return cupy.ones(1, dtype=cupy.float64)
    if M <= 0:
        return cupy.array([])
    alpha = numpy.pi * 2 / (M - 1)
    out = cupy.empty(M, dtype=cupy.float64)
    return _blackman_kernel(alpha, out) 

def test_fft_peaks():
    fig, ax = plt.subplots()
    t = np.arange(65536)
    p1 = ax.plot(abs(np.fft.fft(np.sin(2*np.pi*.01*t)*np.blackman(len(t)))))

    path = p1[0].get_path()
    transform = p1[0].get_transform()
    path = transform.transform_path(path)
    simplified = path.cleaned(simplify=True)

    assert simplified.vertices.size == 36 

def __init__(self, sf=16000, fl=400, fs=80, fftl=1024, mfbsize=80):
        self.sf = sf
        self.fl = fl
        self.fs = fs
        self.fftl = fftl
        self.mfbsize = mfbsize
        winpower = np.sqrt(np.sum(np.square(np.blackman(self.fl).astype(np.float32))))
        self.window = np.blackman(self.fl).astype(np.float32) / winpower
        self.melfb = self._melfbank() 

def smooth(y, box_pts, window='flat'):
  # https://scipy-cookbook.readthedocs.io/items/SignalSmooth.html
  if window is 'flat':
    box = np.ones(box_pts)
  elif window is 'blackman':
    box =  np.blackman(box_pts)
  else:
    raise ValueError('unknown window')
  box /= np.sum(box)
  y_smooth = astroconv.convolve(y, box, boundary='extend') # also: None, fill, wrap, extend
  return y_smooth 

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 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]