Smooth response data
yy = smooth(y)
gpuarrayYY = smooth(gpuarrayY)
yy = smooth(y,span)
yy = smooth(y,method
)
yy = smooth(y,span,method
)
yy = smooth(y,'sgolay',degree)
yy = smooth(y,span,'sgolay',degree)
yy = smooth(x,y,...)
yy = smooth(y)
smooths the
data in the column vector y
using a moving average
filter. Results are returned in the column vector yy
.
The default span for the moving average is 5
.
The first few elements of yy
are given by
yy(1) = y(1) yy(2) = (y(1) + y(2) + y(3))/3 yy(3) = (y(1) + y(2) + y(3) + y(4) + y(5))/5 yy(4) = (y(2) + y(3) + y(4) + y(5) + y(6))/5 ...
Because of the way endpoints are handled, the result differs
from the result returned by the filter
function.
gpuarrayYY = smooth(gpuarrayY)
performs
the operation on a GPU. The input gpuarrayY
is
a gpuArray column vector. The output gpuarrayYY
is
a gpuArray column vector. This syntax requires the Parallel Computing Toolbox™.
Note:
You can use gpuArray x and y inputs with the smooth function,
but this is only recommended with the default |
yy = smooth(y,span)
sets
the span of the moving average to span
. span
must
be odd.
yy = smooth(y,
smooths
the data in method
)y
using the method method
and
the default span. Supported values for method
are
listed in the table below.
| Description |
---|---|
| Moving average (default). A lowpass filter with filter coefficients equal to the reciprocal of the span. |
| Local regression using weighted linear least squares and a 1st degree polynomial model |
| Local regression using weighted linear least squares and a 2nd degree polynomial model |
| Savitzky-Golay filter. A generalized moving average with filter coefficients determined by an unweighted linear least-squares regression and a polynomial model of specified degree (default is 2). The method can accept nonuniform predictor data. |
| A robust version of |
| A robust version of |
yy = smooth(y,span,
sets
the span of method
)method
to span
.
For the loess
and lowess
methods, span
is
a percentage of the total number of data points, less than or equal
to 1. For the moving average and Savitzky-Golay methods, span
must
be odd (an even span
is automatically reduced by 1
).
yy = smooth(y,'sgolay',degree)
uses
the Savitzky-Golay method with polynomial degree specified by degree
.
yy = smooth(y,span,'sgolay',degree)
uses
the number of data points specified by span
in
the Savitzky-Golay calculation. span
must be odd
and degree
must be less than span
.
yy = smooth(x,y,...)
additionally
specifies x
data. If x
is not
provided, methods that require x
data assume x
= 1:length(y)
. You should specify x
data
when it is not uniformly spaced or sorted. If x
is
not uniform and you do not specify method
, lowess
is
used. If the smoothing method requires x
to be
sorted, the sorting occurs automatically.
Load the data in count.dat
:
load count.dat
The 24-by-3 array count
contains traffic
counts at three intersections for each hour of the day.
First, use a moving average filter with a 5-hour span to smooth all of the data at once (by linear index) :
c = smooth(count(:)); C1 = reshape(c,24,3);
Plot the original data and the smoothed data:
subplot(3,1,1) plot(count,':'); hold on plot(C1,'-'); title('Smooth C1 (All Data)')
Second, use the same filter to smooth each column of the data separately:
C2 = zeros(24,3); for I = 1:3, C2(:,I) = smooth(count(:,I)); end
Again, plot the original data and the smoothed data:
subplot(3,1,2) plot(count,':'); hold on plot(C2,'-'); title('Smooth C2 (Each Column)')
Plot the difference between the two smoothed data sets:
subplot(3,1,3) plot(C2 - C1,'o-') title('Difference C2 - C1')
Note the additional end effects from the 3-column smooth.
Create noisy data with outliers:
x = 15*rand(150,1); y = sin(x) + 0.5*(rand(size(x))-0.5); y(ceil(length(x)*rand(2,1))) = 3;
Smooth the data using the loess
and rloess
methods
with a span of 10%:
yy1 = smooth(x,y,0.1,'loess'); yy2 = smooth(x,y,0.1,'rloess');
Plot original data and the smoothed data.
[xx,ind] = sort(x); subplot(2,1,1) plot(xx,y(ind),'b.',xx,yy1(ind),'r-') set(gca,'YLim',[-1.5 3.5]) legend('Original Data','Smoothed Data Using ''loess''',... 'Location','NW') subplot(2,1,2) plot(xx,y(ind),'b.',xx,yy2(ind),'r-') set(gca,'YLim',[-1.5 3.5]) legend('Original Data','Smoothed Data Using ''rloess''',... 'Location','NW')
Note that the outliers have less influence on the robust method.