Signal Processing Utilities¶
Functions¶
signals.corrvis()
... Visualization for cross and autocorrelationsignals.pSpect()
... Simple power spectrum from FFTsignals.savgol()
... SavitzkyGolay filtersignals.show_se()
... Show mean and standard error, of a dataset in column form.
Details¶
Utilities for signal processing

signals.
corrvis
(x, y)[source]¶ Visualize correlation, by calculating the crosscorrelation of two signals. The aligned signals and the resulting cross correlation value are shown, and advanced when the user hits a key or clicks with the mouse.
Parameters: X : array (N,)
Comparison signal
Y : array (M,)
Reference signal
Notes
Based on an idea from dpwe@ee.columbia.edu
Examples
>>> x = np.r_[0:2*pi:10j] >>> y = np.sin(x) >>> corrvis(y,y)

signals.
pSpect
(data, rate)[source]¶ Power spectrum and frequency
Parameters: data : array, shape (N,)
measurement data
rate : float
sampling rate [Hz]
Returns: powerspectrum : array, shape (N,)
frequency : array, shape (N,)

signals.
savgol
(x, window_size=3, order=2, deriv=0, rate=1)[source]¶ Smooth (and optionally differentiate) data with a SavitzkyGolay filter. The SavitzkyGolay filter removes high frequency noise from data. It has the advantage of preserving the original shape and features of the signal better than other types of filtering approaches, such as moving averages techhniques.
Parameters: y : array_like, shape (N,) or (N,m)
the values of the time history of the signal.
window_size : int
the length of the window. Must be an odd integer number.
order : int
the order of the polynomial used in the filtering. Must be less then window_size  1.
deriv : int
the order of the derivative to compute (default = 0 means only smoothing)
rate : sampling rate (in Hz; only used for derivatives)
Returns: ys : ndarray, shape same as y
the smoothed signal (or it’s nth derivative).
Notes
The SavitzkyGolay is a type of lowpass filter, particularly suited for smoothing noisy data. The main idea behind this approach is to make for each point a leastsquare fit with a polynomial of high order over a oddsized window centered at the point.
The data at the beginning / end of the sample are deterimined from the best polynomial fit to the first / last datapoints. This makes the code a bit more complicated, but avoids wild artefacts at the beginning and the end.
Cutofffrequencies For smoothing (deriv=0), the frequency where the amplitude is reduced by 10% is approximately given by:
f_cutoff = sampling_rate / (1.5 * look)
For the first derivative (deriv=1), the frequency where the amplitude is reduced by 10% is approximately given by:
f_cutoff = sampling_rate / (4 * look)
References
[R1] A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 1964, 36 (8), pp 16271639. [R2] Numerical Recipes 3rd Edition: The Art of Scientific Computing W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery Cambridge University Press ISBN13: 9780521880688 [R3] Siegmund Brandt, Datenanalyse, pp 435 Examples
>>> t = np.linspace(4, 4, 500) >>> y = np.exp( t**2 ) + np.random.normal(0, 0.05, t.shape) >>> ysg = savgol(y, window_size=31, order=4) >>> import matplotlib.pyplot as plt >>> plt.plot(t, y, label='Noisy signal') >>> plt.plot(t, np.exp(t**2), 'k', lw=1.5, label='Original signal') >>> plt.plot(t, ysg, 'r', label='Filtered signal') >>> plt.legend() >>> plt.show()

signals.
show_se
(raw)[source]¶ Show mean and standard error, of a dataset in column form.
Parameters: raw : array (N,M)
input data, M sets of N data points
Returns: avg : array (N,)
average value
se : array (N,)
standard error
Notes
Examples
>>> t = np.arange(0,20,0.1) >>> x = np.sin(t) >>> data = [] >>> for ii in range(10): >>> data.append(x + np.random.randn(len(t))) >>> show_se(np.array(data).T)