Root MUSIC algorithm
W
= rootmusic(X
,P
)
[W
,POW
]
= rootmusic(X
,P
)
[F
, POW
]
= rootmusic(...,Fs
)
[W
,POW
]
= rootmusic(...,'corr')
returns
the frequencies in radians/sample for the W
= rootmusic(X
,P
)P
complex
exponentials (sinusoids) that make up the signal X
.
The input X
is specified either as:
A row or column vector representing one realization of 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
[
returns
the estimated absolute value squared amplitudes of the sinusoids at
the frequencies W
,POW
]
= rootmusic(X
,P
)W
.
The second input argument, P
is the number
of complex sinusoids in X
. You can specify P
as
either:
A positive 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.
[
returns
the vector of frequencies F
, POW
]
= rootmusic(...,Fs
)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.
[
forces the input argument W
,POW
]
= rootmusic(...,'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. You can place the 'corr'
option
anywhere after the P
input argument.
Note
You can use the output of |
If the input signal, x
is real and an odd
number of sinusoids, p
is specified, the following
error message is displayed:
Real signals require an even number p of complex sinusoids.
The MUSIC algorithm used by rootmusic
is
the same as that used by pmusic
.
The algorithm performs eigenspace analysis of the signal's correlation
matrix in order to estimate the signal's frequency content.
The difference between pmusic
and rootmusic
is:
pmusic
returns the pseudospectrum
at all frequency samples.
rootmusic
returns the estimated
discrete frequency spectrum, along with the corresponding signal power
estimates.
rootmusic
is most useful for frequency estimation
of signals made up of a sum of sinusoids embedded in additive white
Gaussian noise.