smoothdata
Smooth noisy data
Syntax
Description
smooths entries of B
= smoothdata(A
)A
using a moving average.
smoothdata
determines the moving window size from the
entries in A
. The window slides down the length of the
vector, computing an average over the elements within each window.
If
A
is a matrix, thensmoothdata
computes the moving average down each column ofA
.If
A
is a multidimensional array, thensmoothdata
operates along the first dimension ofA
whose size does not equal 1.If
A
is a table or timetable with numeric variables, thensmoothdata
operates on each variable ofA
separately.
specifies additional parameters for smoothing using one or more namevalue
arguments. For example, if B
= smoothdata(___,Name,Value
)t
is a vector of time values, then
smoothdata(A,"SamplePoints",t)
smooths the data in
A
relative to the times in t
.
[
also returns the moving window size.B
,winsize
]
= smoothdata(___)
Alternative
You can use smoothdata
functionality interactively by
adding the Smooth
Data task to a live script.
Examples
Smooth Data Using Moving Average
Create a vector containing noisy data, and smooth the data with a moving average.
x = 1:100;
rng(0,"twister")
A = cos(2*pi*0.05*x+2*pi*rand) + 0.5*randn(1,100);
B = smoothdata(A);
Plot the original and smoothed data.
plot(x,A) hold on plot(x,B) legend("Input Data","Smoothed Data")
Matrix of Noisy Data
Create a matrix whose rows represent three noisy signals. Smooth the three signals using a moving average, and plot the smoothed data.
x = 1:100; rng(0,"twister") s1 = cos(2*pi*0.03*x+2*pi*rand) + 0.5*randn(1,100); s2 = cos(2*pi*0.04*x+2*pi*rand) + 0.4*randn(1,100) + 5; s3 = cos(2*pi*0.05*x+2*pi*rand) + 0.3*randn(1,100)  5; A = [s1; s2; s3]; B = smoothdata(A,2); plot(x,B(1,:)) hold on plot(x,B(2,:)) plot(x,B(3,:)) legend("s1","s2","s3")
Gaussian Filter
Smooth a vector of noisy data with a Gaussianweighted moving average filter. Display the window size used by the filter.
x = 1:100; rng(0,"twister") A = cos(2*pi*0.05*x+2*pi*rand) + 0.5*randn(1,100); [B,winsize] = smoothdata(A,"gaussian"); winsize
winsize = 4
Smooth the original data with a larger window containing 20 elements. Plot the smoothed data for both window sizes.
C = smoothdata(A,"gaussian",20); plot(x,B) hold on plot(x,C) legend("Small Window","Large Window")
Smoothing Involving Missing Values
Create a noisy vector containing NaN
values, and smooth the data ignoring NaN
values.
rng(0,"twister")
A = [NaN randn(1,48) NaN randn(1,49) NaN];
B = smoothdata(A);
Smooth the data including NaN
values. The average in a window containing any NaN
value is NaN
.
C = smoothdata(A,"includenan");
Plot the smoothed data in B
and C
.
plot(1:100,B,"o") hold on plot(1:100,C,"x") legend("Ignore Missing","Include Missing")
Smooth Data with Sample Points
Create a vector of noisy data that corresponds to a time vector t
. Smooth the data relative to the times in t
, and plot the original data and the smoothed data.
x = 1:100; rng(0,"twister") A = cos(2*pi*0.05*x+2*pi*rand) + 0.5*randn(1,100); t = datetime(2017,1,1,0,0,0) + hours(0:99); B = smoothdata(A,"SamplePoints",t); plot(t,A) hold on plot(t,B) legend("Input Data","Smoothed Data")
Input Arguments
A
— Input data
vector  matrix  multidimensional array  table  timetable
Input data, specified as a vector, matrix, multidimensional array, table,
or timetable. If A
is a table or timetable, then either
the variables must be numeric, or you must use the
DataVariables
namevalue argument to list numeric
variables explicitly. Specifying variables is useful when you are working
with a table that also contains nonnumeric variables.
Data Types:
double
 single

int8
 int16

int32
 int64

uint8
 uint16

uint32
 uint64

logical
 table

timetable
Complex Number Support: Yes
dim
— Dimension to operate along
positive integer scalar
Dimension to operate along, specified as a positive integer scalar. If you do not specify the dimension, then the default is the first array dimension of size greater than 1.
Consider an m
byn
input matrix,
A
:
smoothdata(A,1)
smooths the data in each column ofA
and returns anm
byn
matrix.smoothdata(A,2)
smooths the data in row ofA
and returns anm
byn
matrix.
For table or timetable input data, dim
is not supported
and operation is along each table or timetable variable separately.
method
— Smoothing method
"movmean"
(default)  "movmedian"
 "gaussian"
 "lowess"
 "loess"
 "rlowess"
 "rloess"
 "sgolay"
Smoothing method, specified as one of these values:
"movmean"
— Average over each window ofA
. This method is useful for reducing periodic trends in data."movmedian"
— Median over each window ofA
. This method is useful for reducing periodic trends in data when outliers are present."gaussian"
— Gaussianweighted average over each window ofA
."lowess"
— Linear regression over each window ofA
. This method can be computationally expensive, but results in fewer discontinuities."loess"
— Quadratic regression over each window ofA
. This method is slightly more computationally expensive than"lowess"
."rlowess"
— Robust linear regression over each window ofA
. This method is a more computationally expensive version of the method"lowess"
, but it is more robust to outliers."rloess"
— Robust quadratic regression over each window ofA
. This method is a more computationally expensive version of the method"loess"
, but it is more robust to outliers."sgolay"
— SavitzkyGolay filter, which smooths according to a quadratic polynomial that is fitted over each window ofA
. This method can be more effective than other methods when the data varies rapidly.
window
— Window size
positive integer or duration
scalar  twoelement vector of nonnegative integer or duration
values
Window size, specified as a positive integer or
duration
scalar or twoelement vector of nonnegative
integer or duration
values.
smoothdata
defines the window relative to the
sample points.
When
window
is a positive integer scalar, then the window has lengthwindow
and is centered about the current element.When
window
is a twoelement vector of nonnegative integers[b f]
, the window contains the current element,b
preceding elements, andf
succeeding elements.
When A
is a timetable or
SamplePoints
contains datetime
or
duration
values, window
must be of
type duration
.
For more information about the window position, see Moving Window Size.
Example: smoothdata(A,"movmean",4)
Example: smoothdata(A,"movmedian",[2 3])
nanflag
— Missing value condition
"omitmissing"
(default)  "omitnan"
 "includemissing"
 "includenan"
Missing value condition, specified as one of these values:
"omitmissing"
or"omitnan"
— IgnoreNaN
values inA
when smoothing. If all elements in the window areNaN
, then the corresponding elements inB
areNaN
."omitmissing"
and"omitnan"
have the same behavior."includemissing"
or"includenan"
— IncludeNaN
values inA
when smoothing. If any element in the window isNaN
, then the corresponding elements inB
areNaN
."includemissing"
and"includenan"
have the same behavior.
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue arguments must appear after other arguments, but the order of the
pairs does not matter.
Example: smoothdata(A,SmoothingFactor=0.5)
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: smoothdata(A,"SmoothingFactor",0.5)
SamplePoints
— Sample points
vector  table variable name  scalar  function handle  table vartype
subscript
Sample points, specified as a vector of sample point values or one of
the options in the following table when the input data is a table. The
sample points represent the xaxis locations of the
data, and must be sorted and contain unique elements. Sample points do
not need to be uniformly spaced. The vector [1 2 3
...]
is the default.
When the input data is a table, you can specify the sample points as a table variable using one of these options:
Indexing Scheme  Examples 

Variable name:


Variable index:


Function handle:


Variable type:


Note
This namevalue argument is not supported when the input data is a
timetable
. Timetables use the vector of row times as the sample
points. To use different sample points, you must edit the timetable so that the row times
contain the desired sample points.
Moving windows are defined relative to the sample points. For example,
if t
is a vector of times corresponding to the input
data, then smoothdata(rand(1,10),3,"SamplePoints",t)
has a window that represents the time interval between
t(i)1.5
and t(i)+1.5
.
When the sample points vector has data type
datetime
or duration
, the
window size must have type duration
.
Example: smoothdata(A,"SamplePoints",0:0.1:10)
Example: smoothdata(T,"SamplePoints","Var1")
Data Types: double
 single
 datetime
 duration
DataVariables
— Table variables to operate on
table variable name  scalar  vector  cell array  pattern  function handle  table vartype
subscript
Table variables to operate on, specified as one of the options in this
table. The DataVariables
value indicates which
variables of the input table to smooth.
Other variables in the table not specified by
DataVariables
pass through to the output without
being smoothed.
Indexing Scheme  Examples 

Variable names:


Variable index:


Function handle:


Variable type:


Example: smoothdata(T,"DataVariables",["Var1" "Var2"
"Var4"])
ReplaceValues
— Replace values indicator
true
or
1
(default)  false
or 0
Replace values indicator, specified as one of these values when
A
is a table or timetable:
true
or1
— Replace input table variables with table variables containing smoothed data.false
or0
— Append input table variables with table variables containing smoothed data.
For vector, matrix, or multidimensional array input data,
ReplaceValues
is not supported.
Example: smoothdata(T,"ReplaceValues",false)
SmoothingFactor
— Window size factor
scalar ranging from 0 to 1
Window size factor, specified as a scalar ranging from 0 to 1. Generally, the value of
SmoothingFactor
adjusts the level of smoothing by
scaling the window size that smoothdata
determines
from the entries in A
. Values near 0 produce smaller
moving window sizes, resulting in less smoothing. Values near 1 produce
larger moving window sizes, resulting in more smoothing. In some cases,
depending on the entries that smoothdata
uses to
determine the window size, the value of
SmoothingFactor
may not have a significant impact
on the window size.
SmoothingFactor
is 0.25 by default. You can only specify
SmoothingFactor
when you do not specify
window
.
Degree
— SavitzkyGolay degree
nonnegative integer
SavitzkyGolay degree, specified as a nonnegative integer. This namevalue argument can only
be specified when "sgolay"
is the specified smoothing
method. The value of Degree
corresponds to the degree
of the polynomial in the SavitzkyGolay filter that fits the data within
each window, which is 2 by default.
The value of Degree
must be less than the window size for uniform sample
points. For nonuniform sample points, the value must be less than the
maximum number of points in any window.
Output Arguments
B
— Smoothed data
vector  matrix  multidimensional array  table  timetable
Smoothed data, returned as a vector, matrix, multidimensional array, table, or timetable.
B
is the same size as A
unless the
value of ReplaceValues
is false
. If
the value of ReplaceValues
is false
,
then the width of B
is the sum of the input data width
and the number of data variables specified.
winsize
— Window size
positive integer or duration
scalar  twoelement vector of nonnegative integer or duration
values
Window size, returned as a positive integer or duration
scalar or a twoelement vector of nonnegative integer or
duration
values.
If you specify window
as an input argument, then
winsize
is the same as window
. If
you do not specify window
as an input argument, then
smoothdata
determines the window size from the
entries in A
.
More About
Moving Window Size
This table illustrates the window position across the default
uniformly spaced sample points vector [1 2 3 4 5 6 7]
.
Description  Window Size and Location  Sample Points in Window  Diagram 

For a scalar window size, the leading edge of the window is included and the trailing edge of the window is excluded. 
Current sample point = 4  3, 4, 5 

Current sample point = 4  2, 3, 4, 5 
 
For a vector window size, the leading edge and the trailing edge are included. 
Current sample point = 4  2, 3, 4, 5, 6 

For sample points near the endpoints of the input data, these moving statistic smoothing methods truncate the window so it begins at the first sample point or ends at the last sample point.

Current sample point = 2  1, 2, 3, 4 

For sample points near the endpoints of the input data, these local regression smoothing methods shift the window to include the first or last sample point.

Current sample point = 2  1, 2, 3, 4, 5 

Algorithms
When the window size for the smoothing method is not specified, smoothdata
computes
a default window size based on a heuristic. For a smoothing factor τ,
the heuristic estimates a moving average window size that attenuates
approximately 100*τ percent of the energy of the input data.
Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
Usage notes and limitations:
Tall timetables are not supported.
The
"rlowess"
and"rloess"
methods are not supported.Multiple outputs are not supported.
You must specify the window size.
smoothdata
heuristically determining the window size is not supported.The
SamplePoints
andSmoothingFactor
namevalue arguments are not supported.The value of
DataVariables
cannot be a function handle.
For more information, see Tall Arrays.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
dim
must be constant.For complex input
A
, thewindow
argument must be specified.Variablesize
window
arguments are not supported.For fixedsize code generation, all input arguments other than
A
must be constant.For datetime
SamplePoints
values or timetable input data with datetimeRowTimes
, a window size must be specified.
ThreadBased Environment
Run code in the background using MATLAB® backgroundPool
or accelerate code with Parallel Computing Toolbox™ ThreadPool
.
This function fully supports threadbased environments. For more information, see Run MATLAB Functions in ThreadBased Environment.
Version History
Introduced in R2017aR2023a: Specify missing value condition
Omit or include missing values in the input data when smoothing by using the
"omitmissing"
or "includemissing"
options.
These options have the same behavior as the "omitnan"
and
"includenan"
options, respectively.
R2022a: Append smoothed values
For table or timetable input data, append, instead of replace, input table
variables with table variables containing smoothed data by setting the
ReplaceValues
namevalue argument to
false
.
R2021b: Specify sample points as table variable
For table input data, specify the sample points as a table variable using the
SamplePoints
namevalue argument.
See Also
Functions
smoothdata2
fillmissing
fillmissing2
movmean
movmedian
movmad
filter
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