Signal Processing

Requirement: plugin-processing-1.0.0+, plugin-spectrum-1.0.0+

Live provides pipe functions to improve signal data processing helping make business decisions.

Filters

The pipe function for filtering signals enables removing unwanted harmonic component to have a more clear curve using low/band/high pass filters.

Signal filter pipe function

Sine Wave Combined with Multiple Frequencies and Gaussian White Noise

def sine_wave(x, f=60, amp=1, theta=0): amp * sin(2*pi()*f*x + theta);

=> over all every sec
=> count() as x, normrandom(0, 2) as noise over all every item
=> sine_wave(x, 1/60, 10)
  + sine_wave(x, 1/30, 5)
  + sine_wave(x, 1/15, 2.5)
  + noise as y, x every item

Sine noised wave

Generate FFT of Original Signal

def sine_wave(x, f=60, amp=1, theta=0): amp * sin(2*pi()*f*x + theta);

=> over last min every sec
=> count() as x, normrandom(0, 2) as noise over all every item
=> sine_wave(x, 1/60, 10)
  + sine_wave(x, 1/30, 5)
  + sine_wave(x, 1/15, 2.5)
  + noise as y, x every item

=> signal.FFT(x, y#, 1, false) as result over last 5 min every min
=> result->magnitudes:seq:get(0) as mag, result->frequencies:seq as freq
=> @for range(freq:len()) as i, mag, freq
=> mag[i] as y, freq[i] as x

FFT of the original sine

Applying Low Pass IIR Butterworth Filter

def sine_wave(x, f=60, amp=1, theta=0): amp * sin(2*pi()*f*x + theta);

=> over all every sec
=> count() as x, normrandom(0, 2) as noise over all every item
=> sine_wave(x, 1/60, 10)
  + sine_wave(x, 1/30, 5)
  + sine_wave(x, 1/15, 2.5)
  + noise as y, x every item
 
=> signal.filter(x, y, 0, 1/60, 1, 1, "low", "butterworth") as result, 
y over all every min
=> res->result:seq:get(0) as yArr, res->timestamps:seq as xArr
=> @for range(xArr:len()) as x, yArr
=> yArr[x] as y_filtered, x as x

Low pass filter on noised sine

FFT of the Filtered Signal

def sine_wave(x, f=60, amp=1, theta=0): amp * sin(2*pi()*f*x + theta);

=> over last min every sec
=> count() as x, normrandom(0, 2) as noise over all every item
=> sine_wave(x, 1/60, 10)
  + sine_wave(x, 1/30, 5)
  + sine_wave(x, 1/15, 2.5)
  + noise as y, x every item
 
=> signal.filter(x, y, 0, 1/60, 1, 1, "low", "butterworth") as result, 
y over all every 10 sec
=> res->result:seq:get(0) as yArr, res->timestamps:seq as xArr
=> @for range(xArr:len()) as x, yArr
=> yArr[x] as y, x as x

=> signal.FFT(x, y#, 1, false) as fftResultData over last 5 min every min
=> fftResultData:json():jsonparse() as result
=> result->magnitudes:seq as mag, result->frequencies:seq as freq
=> @for range(freq:len()) as i, mag, freq
=> mag[i] as y, freq[i] as x

FFT of the filtered signal

Peak Detection

The pipes find peaks function is used to find peaks or valleys within a given sample. The values found can be filtered within a certain range that can take into account its height, plateau size, distance, prominence and width.

Signal find peaks pipe function

Signal find troughs pipe function

Detecting Peaks and Troughs on a Channel

mnemonic:MNEMONIC => value, timestamp

=> signal.findPeaks(timestamp#, value#) as res at the end
=> res->timestamps as xArr, res->heights as yArr
=> @for range(xArr:len) as x, xArr, yArr
=> yArr[x] as peak, xArr[x] as timestamp

mnemonic:MNEMONIC => value, timestamp

=> signal.findTroughs(timestamp#, value#) as res at the end
=> res->timestamps as xArr, res->heights as yArr
=> @for range(xArr:len) as x, xArr, yArr
=> yArr[x]#:abs() as trough, xArr[x] as timestamp

Peak detection

Wave Generation

Sine Waves

=> over last 10 min every sec
=> count() as x over all every item
=> signal.generate_wave("sin", x, 0.01, 0, 0) as y_0_deg,
   signal.generate_wave("sin", x, 0.01, 45/pi(), 0) as y_45_deg,
   signal.generate_wave("sin", x, 0.01, 60/pi(), 0) as y_60_deg

Sine wave generated

Sine Wave with Noise

=> over last 10 min every sec
=> count() as x over all every item
=> signal.generate_wave("sin", x, 0.01, 0, 0.02) as y_0_deg,
   signal.generate_wave("sin", x, 0.01, 45/pi(), 0.03) as y_45_deg,
   signal.generate_wave("sin", x, 0.01, 60/pi(), 0.04) as y_60_deg

Sine noised wave generated

Square Wave

=> over last 10 min every sec
=> count() as x over all every item
=> signal.generate_wave("square", x, 0.01, 0, 0) as y_0_deg

Square wave generated

Square Wave with Noise

=> over last 10 min every sec
=> count() as x over all every item
=> signal.generate_wave("square", x, 0.01, 0, 0.05) as y_0_deg

Square Wave with Noise

Square Wave with differents Duty Cycles

=> over last 10 min every sec
=> count() as x over all every item
=> signal.generate_wave("square", x, 0.01, 0, 0, 0.10) as y_10,
   signal.generate_wave("square", x, 0.01, 0, 0, 0.50) as y_50

Square Wave with differents Duty Cycles

Outliers Removal

An outlier is an observation that is unusually far from the other values in a data set. Remove outlier is a common process to have a more clear data.

Remove outliers pipe funn

Remove the top 5% and bottom 5% values

data_with_outliers
=> signal.removeOutliers(timestamp#, value#, 'top_bottom') as filteredData over all every 10 minutes
=> filteredData->timestamps as xArr, filteredData->values as yArr
=> @for range(xArr:len) as x, xArr, yArr
=> yArr[x] as filtered, xArr[x] as timestamp

Outliers removal

Interpolation functions

We can use pipes to estimate a point using interpolation functions.

Types of interpolation

In pipes we have two types of interpolation linear and polynomial ( lagrange method )

Example of linear interpolation

def @@x: (1.0, 2.0, 4.0, 5.0);
def @@y: (4.0, 6.0, 11.0, 17.0);
def @@xi: (3.0, 4.0);

=> @@x:seq() as x,
    @@y:seq() as y,
  @@xi:seq() as xi 
at the end
=> signal.linear_interpolation(x, y, xi) as result

Example of polynomial interpolation

def @@x: (1.0, 2.0, 4.0, 5.0);
def @@y: (4.0, 6.0, 11.0, 17.0);
def @@xi: (3.0, 4.0);

=> @@x:seq() as x,
    @@y:seq() as y,
  @@xi:seq() as xi 
at the end
=> signal.polynomial_lagrange_interpolation(x, y, xi) as result

Here's an example where the linear interpolation function can be used with real time data. On pipes based chart create two layers with the snippets bellow.

def @@channels: ("PRESSURE");
def @@ INITIAL_TIMESTAMP: 0;

rigA .timestamp:adjusted_index_timestamp adjusted_index_timestamp:* mnemonic!:@@channels
  => @compress.swingingDoor value# by mnemonic
  => newmap("y", value#, "x", timestamp) as data
  
=> @yield
=> list(_["x"]# - @@INITIAL_TIMESTAMP) as x, list(_["y"]) as y at the end
=> @for range(x:len) |> (x:get(_) as x, y:get(_) as y) as res
=> res->x as x, res->y as y_original

def @@channels: ("PRESSURE");
def @@ INITIAL_TIMESTAMP: 0;

rigA .timestamp:adjusted_index_timestamp adjusted_index_timestamp:* mnemonic!:@@channels
  => @compress.swingingDoor value# by mnemonic
  => newmap("y", value#, "x", timestamp) as data
  
=> @yield
=> list(_["x"]# - @@INITIAL_TIMESTAMP) as x, list(_["y"]) as y at the end

=> range(100) |> x:get(_) + _*8000 as xi, x, y
=> signal.linear_interpolation(x, y, xi) as yi, xi
=> @for range(xi:len) |> (xi:get(_) as x, yi:get(_) as y) as res
=> res->x as x, res->y as yi_interpolated

The result should be something like the image bellow.

Example of polynomial interpolation with real data

Multi Linear Regression

Multi linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. There are several types of regression functions, including linear, polynomial, logarithmic, exponential, exponential decay, and power functions. The output of a regression analysis typically includes predicted values, coefficients, and statistical measures of goodness-of-fit.

The Multi Linear Regression pipes functions aggregate data over a certain period of time receiving the x and y values, the type of the function and, in the case of the polynomial, the degree. The return type is a row containing the predicted values, which is a sequence of numbers, the function coefficients, and, if present an error indicating what went wrong in the format of a string. These errors can be caused in case of using a invalid type or not enough data to make the regression. Therefore, their signature goes like the snippet below:

signal.regression(x, y, function_type, polynomn_degree)

For all examples (except real-time) the same base layer is used:

def @@channels: ("pressure");

event_type .timestamp:adjusted_index_timestamp adjusted_index_timestamp:* mnemonic!:@@channels
  => @compress.swingingDoor value# by mnemonic
  => value# as original

Polynomial

def @@channels: ("pressure");
def @@DEGREE: 2;

event_type .timestamp:adjusted_index_timestamp adjusted_index_timestamp:* mnemonic!:@@channels
  => @compress.swingingDoor value# by mnemonic
  => value# as y, timestamp# as x
  => signal.regression(x, y, "poly", @@DEGREE) as res, list(x) as xArr at the end
  => @for range(xArr:len) |> (xArr:get(_) as x, res->pred:get(_) as y) as r
  => r->x as timestamp, r->y as yPredOrder2

Example of polynomial regression

Logarithmic

def @@channels: ("pressure");

event_type .timestamp:adjusted_index_timestamp adjusted_index_timestamp:* mnemonic!:@@channels
  => @compress.swingingDoor value# by mnemonic
  => value# as y, timestamp# as x
  => signal.regression(x, y, "log") as res, list(x) as xArr at the end
  => @for range(xArr:len) |> (xArr:get(_) as x, res->pred:get(_) as y) as r
  => r->x as timestamp, r->y as yPredOrder2

Example of logarithmic regression

Exponential

def @@channels: ("pressure");

event_type .timestamp:adjusted_index_timestamp adjusted_index_timestamp:* mnemonic!:@@channels
  => @compress.swingingDoor value# by mnemonic
  => value# as y, timestamp# as x
  => signal.regression(x, y, "exp") as res, list(x) as xArr at the end
  => @for range(xArr:len) |> (xArr:get(_) as x, res->pred:get(_) as y) as r
  => r->x as timestamp, r->y as yPredOrder2

Example of exponential regression

Exponential Decay

def @@channels: ("pressure");

event_type .timestamp:adjusted_index_timestamp adjusted_index_timestamp:* mnemonic!:@@channels
  => @compress.swingingDoor value# by mnemonic
  => value# as y, timestamp# as x
  => signal.regression(x, y, "expd") as res, list(x) as xArr at the end
  => @for range(xArr:len) |> (xArr:get(_) as x, res->pred:get(_) as y) as r
  => r->x as timestamp, r->y as yPredOrder2

Example of exponential decay regression

Power

def @@channels: ("pressure");

event_type .timestamp:adjusted_index_timestamp adjusted_index_timestamp:* mnemonic!:@@channels
  => @compress.swingingDoor value# by mnemonic
  => value# as y, timestamp# as x
  => signal.regression(x, y, "pow") as res, list(x) as xArr at the end
  => @for range(xArr:len) |> (xArr:get(_) as x, res->pred:get(_) as y) as r
  => r->x as timestamp, r->y as yPredOrder2

Example of power regression

Real Time Usage

Layer 1:

def @@channels: ("pressure");

event_type .timestamp:adjusted_index_timestamp adjusted_index_timestamp:* mnemonic!:@@channels
  => @compress.swingingDoor value# by mnemonic
  => value# as original

Layer 2:

def @@channels: ("pressure");
def @@DEGREE: 2;

event_type .timestamp:adjusted_index_timestamp adjusted_index_timestamp:* mnemonic!:@@channels
  => @compress.swingingDoor value# by mnemonic
  => value# as y, timestamp# as x
 
  => signal.regression(x, y, "lin", @@DEGREE) as res, list(x) as xArr over last 10 sec every sec
  => res->pred:get(res->pred:len-1) as yPred, xArr:get(xArr:len - 1) as timestamp

Example of real time data polynomial regression

Pipeless Aggregations

Latest versions

Requirement: plugin-processing-1.2.0+, liverig-5.2.0+, liverig-vis-4.6.0+

UI improvement for the aggregations configuration

In this new update the aggregations are nested within the channel card to provide a better comprehension of what data is being used to create the modified series. To add a new aggregation to a channel click on the + button next to channel name.

Editor menu with pipeless aggregations options

Then select which aggregation is going to be created. At this point the plugin-processing provides the following aggregation types the corresponds to the pipes functions listed previously in this document: Moving Average, Signal Filtering, Peak and Through Detections and Outliers removal.

Listing all available aggregations

After adding the aggregations, the interface assumes a tree-like format.

All available aggregations activated

The follow four images shows how the configurations are now set for the aggregation functions. Each of then has their own configuration panel, where the user can even customize the plotting style.

Moving average configuration

Signal filtering configuration

Peaks detection configuration

Outliers removal configuration

The peaks detection configuration uses a different plotting style (scatter). At this point is possible to plot the aggregation to use line or scatter plot.

Plotting style options

Enabling and disabling aggregation can be done using a eye button like the channels cards.

Enable and disable aggregations

All configurations can also be done in the view mode.

Configuration in view mode

Older versions

Requirement: plugin-processing-1.1.0+, liverig-5.1.1+, liverig-vis-4.6.0+

To use a pipeless aggregation create a new temporal chart with the desired channels.

Editor menu with pipeless aggregations options

Next select which aggregations are going to be applied over the data.

Applying Moving Average aggregation over the selected channel

Applying Filter aggregation, with low pass and butterworth configuration, over the selected channel

Applying Outliers aggregation over the selected channel

Each aggregation has configuration fields that resembles the parameters passed to a correspondent pipes function.

It's possible to hide the original channel using the chart legend.

Hiding the original channel

The aggregations can also be added in the visualization mode using the new chart configuration menu.

New chart configuration menu with aggregations

It is possible to turn on the filters, moving average and outliers or on a chart to calculate it through a temporal range.

Pipeless aggregation configuration on viewmode

Pipeless aggregations on multiple curves