smoothdata
Smooth noisy data
Syntax
Description
returns
a moving average of the elements of a vector using a fixed window
length that is determined heuristically. The window slides down the
length of the vector, computing an average over the elements within
each window.B
= smoothdata(A
)
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
.
Examples
Smooth Data with Moving Average
Create a vector containing noisy data, and smooth the data with a moving average. Plot the original and smoothed data.
x = 1:100; A = cos(2*pi*0.05*x+2*pi*rand) + 0.5*randn(1,100); B = smoothdata(A); plot(x,A,'o',x,B,'x') legend('Original 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; 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,:),x,B(2,:),x,B(3,:))
Gaussian Filter
Smooth a vector of noisy data with a Gaussianweighted moving average filter. Display the window length used by the filter.
x = 1:100;
A = cos(2*pi*0.05*x+2*pi*rand) + 0.5*randn(1,100);
[B,window] = smoothdata(A,'gaussian');
window
window = 4
Smooth the original data with a larger window of length 20. Plot the smoothed data for both window lengths.
C = smoothdata(A,'gaussian',20); plot(x,B,'o',x,C,'x') legend('Small Window','Large Window')
Vector with NaN
Create a noisy vector containing NaN
values, and smooth the data ignoring NaN
, which is the default.
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 NaN
is NaN
.
C = smoothdata(A,'includenan');
Plot the smoothed data in B
and C
.
plot(1:100,B,'o',1:100,C,'x') legend('Ignore NaN','Include NaN')
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; 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,'o',t,B,'x') legend('Original 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
— Operating dimension
positive integer scalar
Operating dimension, specified as a positive integer scalar. If no value is specified, then the default is the first array dimension whose size does not equal 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'
— Moving average over each window ofA
. This method is useful for reducing periodic trends in data.'movmedian'
— Moving median over each window ofA
. This method is useful for reducing periodic trends in data when outliers are present.'gaussian'
— Gaussianweighted moving 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 length
positive integer scalar  twoelement vector of positive integers  positive duration scalar  twoelement vector of positive durations
Window length, specified as a positive integer scalar, a twoelement vector of positive integers, a positive duration scalar, or a twoelement vector of positive durations.
When window
is a positive integer scalar, then the window is centered about
the current element and contains window1
neighboring
elements. If window
is even, then the window is centered
about the current and previous elements.
When window
is a twoelement vector of positive
integers [b f]
, the window contains the current element,
b
elements backward, and f
elements forward.
When A
is a timetable or SamplePoints
is specified as a
datetime
or duration
vector,
window
must be of type duration
,
and the window is computed relative to the sample points.
When the window length is also specified as an output argument, the output value matches the input value.
nanflag
— NaN
condition
'omitnan'
(default)  'includenan'
NaN
condition, specified as one of these values:
'omitnan'
— IgnoreNaN
values in the input. If a window contains allNaN
values, thensmoothdata
returnsNaN
.'includenan'
— IncludeNaN
values when computing within each window, resulting inNaN
.
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.
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 sampled. 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:
Option for Table Input  Description  Examples 

Variable name  A character vector or scalar string specifying a single table variable name 

Scalar variable index  A scalar table variable index 

Logical vector  A logical vector whose elements each correspond to a table variable, where


Function handle  A function handle that takes a table variable as input and returns a logical scalar,
which must be 

vartype subscript  A table subscript generated by the 

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
moving window length 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  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.
Option  Description  Examples 

Variable name  A character vector or string scalar specifying a single table variable name 

Vector of variable names  A cell array of character vectors or string array, where each element is a table variable name 

Scalar or vector of variable indices  A scalar or vector of table variable indices 

Logical vector  A logical vector whose elements each correspond to a table variable, where


Function handle  A function handle that takes a table variable as input and returns a logical scalar 

vartype subscript  A table subscript generated by the 

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 heuristic window size. Values near 0 produce smaller moving
window lengths, resulting in less smoothing. Values near 1 produce
larger moving window lengths, resulting in more smoothing. In some
cases, depending on the input data from which the heuristic window size
is determined, the value of SmoothingFactor
may not
have a significant impact on the window size used by
smoothdata
.
SmoothingFactor
is 0.25 by default and can only be specified when
window
is not specified.
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 length 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.
window
— Window length
positive integer scalar  twoelement vector of positive integers  positive duration scalar  twoelement vector of positive durations
Window length, returned as a positive integer scalar, a twoelement vector of positive integers, a positive duration scalar, or a twoelement vector of positive durations.
When window
is specified as an input argument,
the output value matches the input value. When window
is
not specified as an input argument, then its value is the scalar heuristically
determined by smoothdata
based on the input data.
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. Automatic selection of 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:
The
ReplaceValues
namevalue argument is not supported.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 R2017aR2022a: 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.
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