detrend
Subtract offset or trend from time-domain signals contained in
iddata
objects
Syntax
Description
detrend
subtracts offsets or linear trends from
time-domain input-output data represented in iddata
objects.
detrend
either computes the trend data to subtract, or
subtracts the trend that you specify.
For a more general detrending function that does not require
iddata
objects, see detrend
.
computes and subtracts the piecewise-linear trends for data with segmented
trends, using the breakpoints that you define with
data_d
= detrend(data
,1,brkpt
)brkpt
.
The second argument, which corresponds to Type
, must be
1
.
With this syntax, you cannot retrieve the resulting piecewise-linear trend information as an output.
Examples
Remove Biases from Signals
Remove biases from steady-state signals in an iddata
object by using detrend
to compute and subtract the mean values of the input and output.
Load the input and output time series data y2
and u2
. Construct the iddata
object data2
, using the data and a sample time of 0.08 seconds.
load dryer2 y2 u2 data2 = iddata(y2,u2,0.08);
Use detrend
to both compute the mean values and subtract them from input and output signals. Use the input argument Tr
to store the computed trend information. Plot the original data and detrended data together.
[data2_d,Tr] = detrend(data2); plot(data2,data2_d) legend('Original Data','Detrended Data')
The detrended data has shifted by about 5 units. Inspect Tr
to obtain the precise mean values that detrend
computed and subtracted. These values are returned in the InputOffset
and OutputOffset
properties.
Tr
Trend specifications for data "data2" with 1 input(s), 1 output(s), 1 experiment(s): DataName: 'data2' InputOffset: 5.0000 OutputOffset: 4.8901 InputSlope: 0 OutputSlope: 0
The mean of the original input is higher than the mean of the original output.
Remove Linear Trend from a Signal
Remove the linear trend from a signal in an iddata
object, and overlay the trendline on a before-and-after data plot.
Load and plot signal data from the file lintrend2
. For this example, only output data is provided in iddata
object dataL
.
load lintrend2 dataL plot(dataL,'b')
The plot shows a clear linear trend in the data. Use detrend
linear option (Type
= 1) to subtract the trend from the data. detrend
fits the data and determines the linear trend to subtract. Include the TrendInfo
object Tr
as an output argument so you can see what detrend
subtracts.
[dataL_d,Tr] = detrend(dataL,1);
Plot the detrended data against the original data.
hold on plot(dataL_d,'g') legend('Original','Detrended','Location','northwest')
The linear trend has been removed. Inspect Tr
to get more information about the removed trend.
Tr
Trend specifications for data "dataL" with 0 input(s), 1 output(s), 1 experiment(s): DataName: 'dataL' InputOffset: [1x0 double] OutputOffset: 0.8888 InputSlope: [1x0 double] OutputSlope: 19.3830
The OutputOffset
and the OutputSlope
properties provide the parameters of the line that detrend
removed. You can reconstruct this line, and then overlay it on the before-and-after data plot. The SamplingInstants
property of DataL
provides the timepoints associated with the data.
m = Tr.OutputSlope
m = 19.3830
b = Tr.OutputOffset
b = 0.8888
t = dataL.SamplingInstants; TrLn = m*t+b; plot(t,TrLn,'r') legend('Original','Detrended','Trendline','Location','northwest')
Remove Specified Offsets from Signals
Remove known offsets from an input-output signal pair contained in an iddata object
.
Detrend
can compute and subtract the mean values for input and output signals, resulting in zero-mean detrended signals. However, if you already know you have specific data offsets beforehand, you can have detrend
subtract these from your signals instead. Specifying the offsets also allows you to retain a non-zero operating point in the detrend
result.
Load SISO data containing vectors u2
and y2
. For this example, suppose that you know both signals have an offset of 4 from the expected operating point of 1. Combine these vectors into an iddata object
, using a sample time of 0.08 seconds, and plot it.
load dryer2 u2 y2 data = iddata(y2,u2,0.08); plot(data)
The known offset of 4 (from operating point 1) is visible in the plots. You can construct a TrendInfo
object to capture this offset, using the function getTrend
.
Create the TrendInfo
object, and then set its offset properties.
T = getTrend(data); T.InputOffset = 4; T.OutputOffset = 4
Trend specifications for data "data" with 1 input(s), 1 output(s), 1 experiment(s): DataName: 'data' InputOffset: 4 OutputOffset: 4 InputSlope: 0 OutputSlope: 0
Use detrend
to subtract the offset from the data. Plot it alongside the original data.
data_d = detrend(data,T); hold on plot(data_d) legend('Original','Detrended')
The offset of 4 has been removed.
Remove Segmented Linear Trends from Signals by Using Breakpoints
Detrend data with segmented piecewise-linear trends by specifying breakpoints to delimit the segments.
Most of the detrend
syntaxes assume and compute a single trend for each of the signals. However, in some cases there are discontinuities in the linear trends, caused by test configuration changes, environmental conditions, or other influences. When the signal displays such segmentation, you can have detrend
operate on the test segments independently. To do so, specify breakpoints in the brkpt
input argument. These are the indices to the timepoints in the signal at which linear trends change slope.
You may know these breakpoints up front, based on changes that you know occurred during data collection. Alternatively, you may need to approximate them by inspecting the data itself.
Load the data, inspect its structure and contents, and plot it. This data consists of output data only in the iddata
object dataLb2
.
load brkTrend dataLb2 dataLb2
dataLb2 = Time domain data set with 512 samples. Sample time: 0.00390625 seconds Outputs Unit (if specified) y1
plot(dataLb2)
For this example, the data has known breakpoints at indices [100 300]. Applying the sample time (property Ts
), these breakpoints correspond to the actual timepoints as follows:
brkpt=[100 300]; brkpt_time = brkpt*dataLb2.Ts
brkpt_time = 1×2
0.3906 1.1719
Detrend the data using brkpt
.
dataLb2_d = detrend(dataLb2,1,brkpt);
Plot the original and detrended data.
plot(dataLb2,dataLb2_d) legend('Original Data','Detrended Data')
The linear trend segments have been removed.
Detrend Multiexperiment Signals Using Multiple-Breakpoint Sets
Apply a unique set of breakpoints to each experiment when you detrend a Multiexperiment dataset.
Experiments within a multiexperiment dataset may contain unique linear trending discontinuities. You can apply a unique set of breakpoints to each experiment by expressing them in a cell array.
Load the data, which consists of:
datmult
, a multiexperimentiddata
object containing three experiments (output only)bp
n vectors, which provide known breakpoints for each experiment in the form of indices to timepoints
load multiexpdt datmult bp1 bp2 bp3 datmult
datmult = Time domain data set containing 3 experiments. Experiment Samples Sample Time exp1 250 1 exp2 320 1 exp3 350 1 Outputs Unit (if specified) y1
bp1,bp2,bp3
bp1 = 1×2
50 200
bp2 = 100
bp3 = []
Plot the data. There are significant differences among the streams, and they drift at different rates from zero mean.
plot(datmult) legend
For this set of experiments, it is known that there is unique trending for each run and unique discontinuities indicated by the bp
vectors.
detrend
can incorporate these unique characteristics if the bp
information is provided as a cell array.
Construct the cell array.
bpcell = {bp1;bp2;bp3}
bpcell=3×1 cell array
{[ 50 200]}
{[ 100]}
{0x0 double}
Apply detrend
and plot the result, using the same scale as the original plot.
datmult_d = detrend(datmult,1,bpcell); figure plot(datmult_d) axis([0,inf,-15,30]) legend
The experimental data are now better aligned, and do not drift significantly away from zero mean.
Detrend Input and Output Signals Separately
Apply different trend types to the input and output signals contained in an iddata
object.
Detrend
assumes that the same type of trend applies to both input and output signals. In some cases, there may be a trend type that is present in only one signal. You can perform detrend
individually on each signal by extracting the signals into separate iddata
objects. Apply detrend
to each object using its individual signal trend type. Then reassemble the results back into a single detrended iddata
object.
Load, examine, and plot the data in iodatab
.
load septrend iodatab; iodatab
iodatab = Time domain data set with 1000 samples. Sample time: 0.08 seconds Outputs Unit (if specified) y1 Inputs Unit (if specified) u1
plot(iodatab)
hold on
Both input and output plots show a bias. However, the output plot also shows an inverted V-shape trend that is not present in the input data.
Separate the input data and the output data into separate objects for detrending, using the iddata
general data-selection form (see Representing Time- and Frequency-Domain Data Using iddata Objects):
data(samples,outputchannels,inputchannels)
idatab = iodatab(:,[],:); odatab = iodatab(:,:,[]);
Remove the bias from the input data, using detrend
to calculate and subtract the mean.
idatab_d = detrend(idatab,0);
Remove the bias and the inverted-V trend from the output data, using the midpoint index 500 as a breakpoint.
odatab_d = detrend(odatab,1,500);
Combine the detrended input and output data into a single iddata
object.
iodatab_d = [odatab_d,idatab_d];
Overlay the detrended data on the original data.
plot(iodatab_d) legend('original','detrended')
The input and output data now contain neither bias nor V-shape trend.
Input Arguments
data
— Time-domain input-output data
iddata
object
Time-domain input-output data, specified as an iddata
object containing one or more sets of time-domain signals. The
iddata
object can contain SISO, MIMO, or
multiexperiment data. The signal sets can contain either input and output
data, or output data only.
Type
— Trend type to be subtracted
0 (default) | 1 | TrendInfo
object
Trend type to be subtracted, specified as one of:
0 — Compute and subtract the mean value
1 — Compute and subtract the linear trend (least-squares fit)
TrendInfo
object — subtract the trend you specify in theTrendInfo
object. UsegetTrend
to create aTrendInfo
object. For an example, see Remove Specified Offsets from Signals.
brkpt
— Timepoint locations of trending discontinuities
integer row vector | cell array of integer vectors
Timepoint locations of trending discontinuities (breakpoints), specified as:
An integer row vector — For single-experiment SISO and MIMO datasets. Doing so applies a single set of breakpoints to all input and output signals. For an example, see Remove Segmented Linear Trends from Signals by Using Breakpoints.
A cell array containing individually-sized integer row vectors — For multiple-experiment datasets. Doing so applies a unique set of breakpoints to the output and input signals for each experiment. For an example, see Detrend Multiexperiment Signals Using Multiple-Breakpoint Sets.
Output Arguments
data_d
— Detrended signals
iddata
object
Detrended signals, returned as an iddata
object.
Dimensions of the contents are the same as dimensions of the contents of
data
.
Version History
Introduced before R2006a
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