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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 corrmtx to generate such an array x. |
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(...,'corr') forces the input argument 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.