Variances for each column, and sqrt(diag(cov(X))) is a vector

of standard deviations. COV(X,Y), where X and Y are matrices with

the same number of elements, is equivalent to COV([X(:) Y(:)]).

COV(X) or COV(X,Y) normalizes by (N-1) if N>1, where N is the number of

observations. This makes COV(X) the best unbiased estimate of the

covariance matrix if the observations are from a normal distribution.

For N=1, COV normalizes by N.

COV(X,1) or COV(X,Y,1) normalizes by N and produces the second

moment matrix of the observations about their mean. COV(X,Y,0) is

the same as COV(X,Y) and COV(X,0) is the same as COV(X).

The mean is removed from each column before calculating the

result.

Class support for inputs X,Y:

float: double, single

See also corrcoef, var, std, mean.

Overloaded methods:

fints/cov

xregtwostage/cov

xregmultilin/cov

xregmodel/cov

xreglinear/cov

xregcovariance/cov

localsurface/cov

Reference page in Help browser

doc cov

<subspace> - Angle between subspaces.

SUBSPACE Angle between subspaces.

SUBSPACE(A,B) finds the angle between two subspaces specified by the

columns of A and B.

If the angle is small, the two spaces are nearly linearly dependent.

In a physical experiment described by some observations A, and a second

realization of the experiment described by B, SUBSPACE(A,B) gives a

measure of the amount of new information afforded by the second

experiment not associated with statistical errors of fluctuations.

Class support for inputs A, B:

float: double, single

Reference page in Help browser

doc subspace

Filtering and convolution

<filter> - One-dimensional digital filter.

FILTER One-dimensional digital filter.

Y = FILTER(B,A,X) filters the data in vector X with the

filter described by vectors A and B to create the filtered

data Y. The filter is a "Direct Form II Transposed"

implementation of the standard difference equation:

a(1)*y(n) = b(1)*x(n) + b(2)*x(n-1) + ... + b(nb+1)*x(n-nb)

- a(2)*y(n-1) - ... - a(na+1)*y(n-na)

If a(1) is not equal to 1, FILTER normalizes the filter

coefficients by a(1).

FILTER always operates along the first non-singleton dimension,

namely dimension 1 for column vectors and non-trivial matrices,

and dimension 2 for row vectors.

[Y,Zf] = FILTER(B,A,X,Zi) gives access to initial and final

conditions, Zi and Zf, of the delays. Zi is a vector of length

MAX(LENGTH(A),LENGTH(B))-1, or an array with the leading dimension

of size MAX(LENGTH(A),LENGTH(B))-1 and with remaining dimensions

matching those of X.

FILTER(B,A,X,[],DIM) or FILTER(B,A,X,Zi,DIM) operates along the

dimension DIM.

See also filter2 and, in the signal Processing Toolbox, filtfilt, filtic.

Overloaded methods:

timeseries/filter

gf/filter

channel.filter

LagOp/filter

mfilt.filter

adaptfilt.filter

fints/filter

fxptui.filter

sweepsetfilter/filter

sweepset/filter

dfilt.filter

Reference page in Help browser

doc filter

<filter2> - Two-dimensional digital filter.

FILTER2 Two-dimensional digital filter.

Y = FILTER2(B,X) filters the data in X with the 2-D FIR

filter in the matrix B. The result, Y, is computed

using 2-D correlation and is the same size as X.

Y = FILTER2(B,X,'shape') returns Y computed via 2-D

correlation with size specified by 'shape':

'same' - (default) returns the central part of the

correlation that is the same size as X.

'valid' - returns only those parts of the correlation

that are computed without the zero-padded

edges, size(Y) < size(X).

'full' - returns the full 2-D correlation,

size(Y) > size(X).

FILTER2 uses CONV2 to do most of the work. 2-D correlation

is related to 2-D convolution by a 180 degree rotation of the

filter matrix.

Class support for inputs B,X:

float: double, single

See also filter, conv2.

Reference page in Help browser

doc filter2

<conv> - Convolution and polynomial multiplication.

CONV Convolution and polynomial multiplication.

C = CONV(A, B) convolves vectors A and B. The resulting vector is

length MAX([LENGTH(A)+LENGTH(B)-1,LENGTH(A),LENGTH(B)]). If A and B are

vectors of polynomial coefficients, convolving them is equivalent to

multiplying the two polynomials.

C = CONV(A, B, SHAPE) returns a subsection of the convolution with size

specified by SHAPE:

'full' - (default) returns the full convolution,

'same' - returns the central part of the convolution

that is the same size as A.

'valid' - returns only those parts of the convolution

that are computed without the zero-padded edges.

LENGTH(C)is MAX(LENGTH(A)-MAX(0,LENGTH(B)-1),0).

Class support for inputs A,B:

float: double, single

See also deconv, conv2, convn, filter and,

in the signal Processing Toolbox, xcorr, convmtx.

Overloaded methods:

gf/conv

Reference page in Help browser

doc conv

<conv2> - Two-dimensional convolution.

CONV2 Two dimensional convolution.

C = CONV2(A, B) performs the 2-D convolution of matrices A and B.

If [ma,na] = size(A), [mb,nb] = size(B), and [mc,nc] = size(C), then

mc = max([ma+mb-1,ma,mb]) and nc = max([na+nb-1,na,nb]).

C = CONV2(H1, H2, A) convolves A first with the vector H1 along the

rows and then with the vector H2 along the columns. If n1 = length(H1)

and n2 = length(H2), then mc = max([ma+n1-1,ma,n1]) and

nc = max([na+n2-1,na,n2]).

C = CONV2(..., SHAPE) returns a subsection of the 2-D

convolution with size specified by SHAPE:

'full' - (default) returns the full 2-D convolution,

'same' - returns the central part of the convolution

that is the same size as A.

'valid' - returns only those parts of the convolution

that are computed without the zero-padded edges.

size(C) = max([ma-max(0,mb-1),na-max(0,nb-1)],0).

See also conv, convn, filter2 and, in the signal Processing

Toolbox, xcorr2.

Overloaded methods:

uint8/conv2

uint16/conv2

Reference page in Help browser

doc conv2

<convn> - N-dimensional convolution.

CONVN N-dimensional convolution.

C = CONVN(A, B) performs the N-dimensional convolution of

matrices A and B. If nak = size(A,k) and nbk = size(B,k), then

size(C,k) = max([nak+nbk-1,nak,nbk]);

C = CONVN(A, B, 'shape') controls the size of the answer C:

'full' - (default) returns the full N-D convolution

'same' - returns the central part of the convolution that

is the same size as A.

'valid' - returns only the part of the result that can be

computed without assuming zero-padded arrays.

size(C,k) = max([nak-max(0,nbk-1)],0).

Class support for inputs A,B:

float: double, single

See also conv, conv2.

Reference page in Help browser

doc convn

<deconv> - Deconvolution and polynomial division.

DECONV Deconvolution and polynomial division.

[Q,R] = DECONV(B,A) deconvolves vector A out of vector B. The result

is returned in vector Q and the remainder in vector R such that

B = conv(A,Q) + R.

If A and B are vectors of polynomial coefficients, deconvolution

is equivalent to polynomial division. The result of dividing B by

A is quotient Q and remainder R.

Class support for inputs B,A:

float: double, single

See also conv, residue.

Overloaded methods:

gf/deconv

Reference page in Help browser

doc deconv

<detrend> - Linear trend removal.

DETREND Remove a linear trend from a vector, usually for FFT processing.

Y = DETREND(X) removes the best straight-line fit linear trend from the

data in vector X and returns the residual in vector Y. If X is a

matrix, DETREND removes the trend from each column of the matrix.

Y = DETREND(X,'constant') removes just the mean value from the vector X,

or the mean value from each column, if X is a matrix.

Y = DETREND(X,'linear',BP) removes a continuous, piecewise linear trend.

Breakpoint indices for the linear trend are contained in the vector BP.

The default is no breakpoints, such that one single straight line is

removed from each column of X.

Class support for inputs X,BP:

float: double, single

See also mean

Overloaded methods:

timeseries/detrend