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DESCRIPTION

Estimates a sum of sinusoidal signals by separable least squares with Levenberg damping.

 

USAGE

lsfreq(y,x=NULL,freq,constant=F,trace=F)

 

REQUIRED ARGUMENTS

y		numeric vector of observations. Missing values not allowed.
freq		numeric vector of starting values for the frequencies.

 

OPTIONAL ARGUMENTS

x		numeric vector of time points. The default is 0:(length(y)-1).
constant		logical constant. True if a constant term or intercept is to be included in the model.
trace		logical constant. If true frequencies and residual sum of squares are printed at each iteration.

 

VALUE

freq		numeric vector of estimated frequencies.
coef		numeric vector of estimated coefficients.
fitted		numeric vector of same length as y of fitted values.
residuals		numeric vector of same length as y of residuals.

 

DETAILS

If constant = T then the assumed model is

y = a[1] + a[2]*cos(x*f[1]) + ... + a[p+1]*cos(x*f[p]) + a[p+2]*sin(x*f[1]) + ... + a[2*p+1]*sin(x*f[p])

where coef = a, freq = f and p = length(f). If constant = F then the model is

y = a[1]*cos(x*f[1]) + ... + a[p]*cos(x*f[p]) + a[p+1]*sin(x*f[1]) + ... + a[2*p]*sin(x*f[p])

The estimation algorithm is a Gauss-Newton algorithm in which the linear coefficients a[] are set to their known values conditional on the frequencies. Levenberg damping is used to ensure that each iteration reduces the residual sum of squares.

 

REFERENCES

Smyth, G. K. (1996). Partitioned algorithms for maximum likelihood and other nonlinear estimation. Statistics and Computing, 6, 201-216. (PDF).

 

SEE ALSO

mmfreq, robfreq

 

EXAMPLES

Estimate the signal for the Variable Star data set. The pronyfreq function is used to obtain starting values. In this case the starting values are good enough!

> ora <- pronyfreq(star,nfreq=2)
> ora$freq
[1] 0.2166596 0.2617983
> ora$coef
[1] 17.0857822411  7.6477245734  0.0009274355  6.4906186247  7.0845674915
> out.ls <- lsfreq(star,freq=ora$freq,constant=T)
> out.ls$freq
[1] 0.2166595 0.2617983
> out.ls$coef
[1] 17.085781788  7.647776911  0.001107758  6.490566875  7.084562954

Gordon Smyth. Copyright © 1996-2016. Last modified: 10 February 2004