Frequency and power content using eigenvector method
[w,pow] = rooteig(x,p)
[f,pow] = rooteig(...,fs)
[w,pow] = rooteig(...,'corr
')
[w,pow] = rooteig(x,p)
estimates
the frequency content in the time samples of a signal x
,
and returns w
, a vector of frequencies in rad/sample,
and the corresponding signal power in the vector pow
in
units of power, such as volts^2. The input signal x
is
specified either as:
A row or column vector representing one observation of the signal
A rectangular array for which each row of x
represents
a separate observation of the signal (for example, each row is one
output of an array of sensors, as in array processing), such that x'*x
is
an estimate of the correlation matrix
Note
You can use the output of |
You can specify the second input argument p
as
either:
A scalar integer. In this case, the signal subspace
dimension is p
.
A two-element vector. In this case, p(2)
,
the second element of p
, represents a threshold
that is multiplied by λ_{min}, the smallest
estimated eigenvalue of the signal's correlation matrix. Eigenvalues
below the threshold λ_{min}*p(2)
are
assigned to the noise subspace. In this case, p(1)
specifies
the maximum dimension of the signal subspace.
The extra threshold parameter in the second entry in p
provides
you more flexibility and control in assigning the noise and signal
subspaces.
The length of the vector w
is the computed
dimension of the signal subspace. For real-valued input data x
,
the length of the corresponding power vector pow
is
given by
length(pow) = 0.5*length(w)
For complex-valued input data x
, pow
and w
have
the same length.
[f,pow] = rooteig(...,fs)
returns
the vector of frequencies f
calculated in Hz.
You supply the sampling frequency fs
in Hz. If
you specify fs
with the empty vector []
,
the sampling frequency defaults to 1 Hz.
[w,pow] = rooteig(...,'
forces
the input argument corr
')x
to be interpreted as a correlation
matrix rather than a matrix of signal data. For this syntax, you must
supply a square matrix for x
, and all of its eigenvalues
must be nonnegative.
Note
You can place |
The eigenvector method used by rooteig
is
the same as that used by peig
.
The algorithm performs eigenspace analysis of the signal's correlation
matrix in order to estimate the signal's frequency content.
The difference between peig
and rooteig
is:
peig
returns the pseudospectrum
at all frequency samples.
rooteig
returns the estimated discrete
frequency spectrum, along with the corresponding signal power estimates.
rooteig
is most useful for frequency estimation
of signals made up of a sum of sinusoids embedded in additive white
Gaussian noise.