IEEE Standard for Digitizing Waveform Recorders (IEEE Std 1057): Algorithm for least squares fit to sinewave data using matrix operations:
- three-parameter (known frequency, non-iterative) and
- four-parameter (general use, find frequency iteratively).
- Complex sinusoid fit enabled.
- Alternative 4-parameter fit by using the function fminbnd.
Marko Neitola (2019). Four-Parameter Sinefit (https://www.mathworks.com/matlabcentral/fileexchange/23214-four-parameter-sinefit), MATLAB Central File Exchange. Retrieved .
The original code does a cosine fit. If the time vector is t output parameters are [offset, amp, frq, phi], then the estimated results should be offset+amp.*cos(2*pi*frq.*t+phi).
Using the three-parameter fit disables the iterative frequency search. To enable this, use searchflag = 0.
For instance, if you want function messages (verbose), graphics (plotflag) and no iterative search, use
verbose = 1;
plotflag = 1;
searchflag = 0;
This is actually a cosine fit, I think.
Here is an example with a regular sinusoid, which may be helpful:
t = 0:0.1:1000 ; % Time must be in seconds, not Matlab time
T = 10 ; % Period (s)
f = 1/T ; % Signal frequency (not sampling frequency!)
y = 2*sin(2*pi*t./T) ; % Sinusoid
[params, yest, yres, rmserr] = sinefit(y, t, f, 1, 1, 1) ;
The program worked fine for me it was exactly what I was looking for. I use it for the estimation of the SINAD and subsequent ENOB value. The method tends to shift more signal to the residual when the signal that is used gets longer.
Improvements and bug-fixes
A feature update: fitting extended to complex sinusoids.
Fixed a bug in input parameter handling (varargin behavior).
Improved iteration convergence: the accuracy for the initial frequency guess is more relaxed.
A feature update: added a possibility to fit non-iteratively.
A minor bugfix in the plotting operation: now ALL samples are included in modulo-time plots.