Signal Processing and Generation (signals)

Signal processing, creation and plotting.

Analysis of data and generation of simulated experiments.

signals.asd(x, t, windowname='hanning', ave=True)[source]

Return autospectrum (power spectrum) density of a signal x.

Parameters:

x : float array

Data array (n x N x m) where n is the number of sensors, m the number of experiments.

t : float array

Time array (1 x N)

windowname : string

Name of windowing function to use. See window.

ave : bool, optional(True)

Average result or not?
Returns:

f : float array

Frequency vector (1 x N)

Pxx : float array

Autospectrum (n x N) or (n x N x m) if not averaged.

Examples

(Source code, png, hires.png, pdf)

../_images/signal-1.png
signals.blackwin(x)[source]

Return the n point Blackman window.

Returns x as the Blackman windowing array x_window The windowed signal is then x*x_window

signals.boxwin(x)[source]

Return the n point box window (uniform).

Returns x as the boxwin windowing array x_windowed The windowed signal is then x*x_window

signals.crsd(x, y, t, windowname='hanning', ave=True)[source]

Calculate the cross spectrum (power spectrum) density between two signals.

Parameters:

x, y : arrays

Data array (n x N x m) where n is the number of sensors, m the number of experiments.

t : array

Time array (1 x N)

windowname : string

Name of windowing function to use

ave : bool, optional

Average result or not?
Returns:

f : array

Frequency vector (1 x N)

Pxy : array

Autospectrum (n x N) or (n x N x m) if not averaged.

Examples

(Source code, png, hires.png, pdf)

../_images/signal-2.png
signals.decimate(t, in_signal, sample_frequency)[source]

Decimate a signal to mimic sampling anti-aliased signal.

Returns the signal down-sampled to sample_frequency with an anti-aliasing filter applied at 45% of ` sample_frequency`.

Parameters:

t : float array

time array, size (N,)

signal : float array

signal array, size (N,), (m,N), or (m,N,n)

sample_frequency : float

new sampling frequency
Returns:

time : float array

decimated_signal : float array

Examples

>>> time = np.linspace(0,4,4096)
>>> u = np.random.randn(1,len(time))
>>> ttime, signal_out = decimate(time, u, 100)
signals.expwin(x, ts=0.75)[source]

Return the n point exponential window.

Returns x as the expwin windowing array x_windowed The windowed signal is then x*x_window The optional second argument set the 5% “settling time” of the window. Default is ts=0.75

signals.flatwin(x)[source]

Return the n point flat top window.

x_windows=flatwin(x) Returns x as the flat top windowing array x_windowed The windowed signal is then x*x_window McConnell, K. G., “Vibration Testing: Theory and Practice,” Wiley, 1995.

signals.frfest(x, f, dt, windowname='hanning', ave=True, Hv=False)[source]

Return freq, H1, H2, coh, Hv.

Estimates the \(H(j\omega)\) Frequency Response Functions (FRFs) between \(x\) and \(f\).

Parameters:

x : float array

output or response of system

f : float array

input to system

dt : float

time step of samples

windowname : string

name of leakage window to use

ave : bool, optional(True)- currently locked

whether or not to average PSDs and ASDs or calculate raw FRFs

Hv : bool, optional(False)

calculate the \(H_v\) frequency response function
Returns:

freq : float array

frequency vector (1xN)

H1 : float array

Frequency Response Function \(H_1\) estimate, (nxN) or (nxNxm)

H2 : float array

Frequency Response Function \(H_2\) estimate, (nxN) or (nxNxm)

coh : float array

Coherance Function \(\gamma^2\) estimate, (nxN)

Hv : float array

Frequency Response Function \(H_v\) estimate, (nxN) or (nxNxm)

Currently windowname and ave are locked to default values.

Notes

Note

Not compatible with scipy.signal functions

See also

asd(), crsd(), frfplot().

Warning

hanning window cannot be selected yet. Averaging cannot be unslected yet.

Todo

Fix averaging, windowing, multiple input.

Examples

(Source code)

signals.frfplot(freq, H, freq_min=0, freq_max=None, type=1, legend=[])[source]

Frequency Response function pretty plotting.

Plots frequency response functions in a variety of formats

Parameters:

freq : float array

Frequency vector (rad/sec), (1xN)

H : float array

Frequency response functions (nxN)

freq_min : float, optional

Low frequency for plot (default 0)

freq_min : float, optional

High frequency for plot (default max frequency)

legend : string array

Array of string for use in legend.

type : int, optional

Plot type. See notes.
Returns:

ax : axis objects

allows manipulation of plot parameters (xlabel, title…)

Notes

type Plot style
1 (def) Magnitude and Phase versus F
2 Magnitude and Phase versus log10(F)
3 Bodelog (Magnitude and Phase versus log10(w))
4 Real and Imaginary
5 Nyquist (Imaginary versus Real)
6 Magnitude versus F
7 Phase versus F
8 Real versus F
9 Imaginary versus F
10 Magnitude versus log10(F)
11 Phase versus log10(F)
12 Real versus log10(F)
13 Imaginary versus log10(F)
14 Magnitude versus log10(w)
15 Phase versus log10(w)

See also

frfest

Copyright J. Slater, Dec 17, 1994 Updated April 27, 1995 Ported to Python, July 1, 2015

Examples

(Source code, png, hires.png, pdf)

../_images/signal-4.png
signals.hammer_impulse(time, imp_time=None, imp_duration=None, doublehit=False, dh_delta=None)[source]

Generate simulated hammer hit (half sine).

Parameters:

time : float array

1 x N time array. Suggest using np.linspace(0,10,1000).reshape(1,-1) for example

imp_time : float (optional)

Time of onset of impulse. Default is 0.1 time end time- which traditionally works well for impact testing

imp_duration : float (optional)

Duration of impulse. Default is 0.01 of total record

doublehit : Boolean (optional)

Allows repeat of hit to emulate a bad strike. Default is False

dh_delta : float (optional)

Time difference between primary strike and accidental second strike Default is 0.02 of record.
Returns:

force : float array

Examples

>>> import vibrationtesting as vt
>>> time = np.linspace(0,10,1024).reshape(1,-1)
>>> force = vt.hammer_impulse(time, doublehit=True)
>>> plt.plot(time.T, force.T)
[<matplotlib.lines.Line2D object...
signals.hammwin(x)[source]

Return the n point hamming window.

Returns x as the hamming windowingarray x_windowed The windowed signal is then x*x_window

signals.hanning(x, normalize=False)[source]

Return hanning window.

Create a hanning window of length \(x\), or a hanning window sized to match \(x\) that \(x\times w\) is the windowed result.

Parameters:

x: integer, float array

If integer- number of points in desired hanning windows.
If array- array provides size of window returned.

windowname: string

One of: hanning, hamming, blackman, flatwin, boxwin

normalize: bool, optional(False)

Adjust power level (for use in ASD) to 1
Returns:

w: float array

window array of size x
window array. Windowed array is then \(x\times w\)

Examples

(Source code, png, hires.png, pdf)

../_images/signal-5.png
signals.hannwin(*args, **kwargs)[source]

Alternative for function hanning.

signals.window(x, windowname='hanning', normalize=False)[source]

Create leakage window.

Create a window of length \(x\), or a window sized to match \(x\) that \(x\times w\) is the windowed result.

Parameters:

x: integer, float array

If integer- number of points in desired hanning windows.
If array- array provides size of window returned.

windowname: string

One of: hanning, hamming, blackman, flatwin, boxwin

normalize: bool, optional(False)

Adjust power level (for use in ASD) to 1
Returns:

w: float array

window array of size x
window array. Windowed array is then \(x\times w\)

Examples

(Source code, png, hires.png, pdf)

../_images/signal-6.png
signals.xcorr(t, x, y, zeropad=True)[source]

Sorry, no docs or tests yet.