smoothdata

Smooth noisy data

Syntax

B = smoothdata(A)

B = smoothdata(A,dim)

B = smoothdata(___,method)

B = smoothdata(___,method,window)

B = smoothdata(___,nanflag)

B = smoothdata(___,Name,Value)

[B,winsize] = smoothdata(___)

Description

B = smoothdata(A) smooths entries of 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, then smoothdata computes the moving average down each column of A.

• If A is a multidimensional array, then smoothdata operates along the first dimension of A whose size does not equal 1.

• If A is a table or timetable with numeric variables, then smoothdata operates on each variable of A separately.

B = smoothdata(A,dim) specifies the dimension of A to operate along. For example, if A is a matrix, then smoothdata(A,2) smooths the data in each row of A.

B = smoothdata(___,method) specifies the smoothing method for either of the previous syntaxes. For example, smoothdata(A,"sgolay") uses a Savitzky-Golay filter to smooth the data in A.

B = smoothdata(___,method,window) specifies the smoothing method window size. For example, smoothdata(A,"movmedian",5) smooths the data in A by taking the median over a five-element sliding window.

B = smoothdata(___,nanflag) specifies whether to omit or include NaN values in A. For example, smoothdata(A,"includenan") includes all NaN values when smoothing. By default, smoothdata ignores NaN values.

B = smoothdata(___,Name,Value) specifies additional parameters for smoothing using one or more name-value arguments. For example, if t is a vector of time values, then smoothdata(A,"SamplePoints",t) smooths the data in A relative to the times in t.

[B,winsize] = smoothdata(___) also returns the moving window size.

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 Gaussian-weighted 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 name-value 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 whose size does not equal 1.

Consider an m-by-n input matrix, A:

• smoothdata(A,1) smooths the data in each column of A and returns an m-by-n matrix.

  

• smoothdata(A,2) smooths the data in row of A and returns an m-by-n 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 of A. This method is useful for reducing periodic trends in data.

• "movmedian" — Median over each window of A. This method is useful for reducing periodic trends in data when outliers are present.

• "gaussian" — Gaussian-weighted average over each window of A.

• "lowess" — Linear regression over each window of A. This method can be computationally expensive, but results in fewer discontinuities.

• "loess" — Quadratic regression over each window of A. This method is slightly more computationally expensive than "lowess".

• "rlowess" — Robust linear regression over each window of A. 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 of A. This method is a more computationally expensive version of the method "loess", but it is more robust to outliers.

• "sgolay" — Savitzky-Golay filter, which smooths according to a quadratic polynomial that is fitted over each window of A. This method can be more effective than other methods when the data varies rapidly.

window — Window size

positive integer or duration scalar | two-element vector of nonnegative integer or duration values

Window size, specified as a positive integer or duration scalar or two-element 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 length window and is centered about the current element.

• When window is a two-element vector of nonnegative integers [b f], the window contains the current element, b preceding elements, and f 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" — Ignore NaN values in A when smoothing. If all elements in the window are NaN, then the corresponding elements in B are NaN. "omitmissing" and "omitnan" have the same behavior.

• "includemissing" or "includenan" — Include NaN values in A when smoothing. If any element in the window is NaN, then the corresponding elements in B are NaN. "includemissing" and "includenan" have the same behavior.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value 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)

Data Options

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 x-axis 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: A string scalar or character vector	"A" or 'A' — A variable named A
Variable index: An index number that refers to the location of a variable in the table A logical vector. Typically, this vector is the same length as the number of variables, but you can omit trailing 0 or false values	3 — The third variable from the table [false false true] — The third variable
Function handle: A function handle that takes a table variable as input and returns a logical scalar	@isnumeric — One variable containing numeric values
Variable type: A vartype subscript that selects one variable of a specified type	vartype("numeric") — One variable containing numeric values

Note

This name-value 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	Values to Specify	Examples
Variable name	A string scalar or character vector A string array or cell array of character vectors A pattern object	"A" or 'A' — A variable named A ["A" "B"] or {'A','B'} — Two variables named A and B "Var"+digitsPattern(1) — Variables named "Var" followed by a single digit
Variable index	An index number that refers to the location of a variable in the table A vector of numbers A logical vector. Typically, this vector is the same length as the number of variables, but you can omit trailing 0 (false) values.	3 — The third variable from the table [2 3] — The second and third variables from the table [false false true] — The third variable
Function handle	A function handle that takes a table variable as input and returns a logical scalar	@isnumeric — All the variables containing numeric values
Variable type	A vartype subscript that selects variables of a specified type	vartype("numeric") — All the variables containing numeric values

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 or 1 — Replace input table variables with table variables containing smoothed data.

• false or 0 — 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)

Smoothing Options

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 — Savitzky-Golay degree

nonnegative integer

Savitzky-Golay degree, specified as a nonnegative integer. This name-value 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 Savitzky-Golay 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 | two-element vector of nonnegative integer or duration values

Window size, returned as a positive integer or duration scalar or a two-element 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.	window = 3 Current sample point = 4	3, 4, 5
	window = 4 Current sample point = 4	2, 3, 4, 5
For a vector window size, the leading edge and the trailing edge are included.	window = [2 2] 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. "movmean" "movmedian" "gaussian"	window = [2 2] 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. "lowess" "loess" "rlowess" "rloess" "sgolay"	window = [2 2] 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.

The smoothdata function supports tall arrays with the following 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 and SmoothingFactor name-value 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, the window argument must be specified.

• Variable-size window arguments are not supported.

• For fixed-size code generation, all input arguments other than A must be constant.

• For datetime SamplePoints values or timetable input data with datetime RowTimes, a window size must be specified.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced in R2017a

R2023a: 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 name-value 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 name-value argument.