sddsnaff

description: sddsnaff is an implementation of Laskar’s Numerical Analysis of Fundamental Frequencies (NAFF) algorithm. This algorithm determines the frequency components of a signal more accurately than Fast Fourier Transforms (FFT). FFTs are used as part of the analysis, so if an FFT is sufficient for an application, sddsfft() should be used as it will be much faster. The algorithm starts by removing the average value of the signal and applying a Hanning window. Next, the signal is FFT’d and the frequency at which the maximum FFT amplitude occurs is found. This is taken as the starting frequency for a numerical optimization of the “overlap” between the signal and e^iωt, which allows determining ω to resolution greater than the frequency spacing of the FFT. Once ω is determined, the overlap is subtracted from the original signal and the process is repeated, if desired.

examples: Find the first fundamental frequency for each of the BPM signals in par.bpm.

sddsnaff par.bpm par.naff -column=Time,’P?P?x’ -terminateSearch=frequencies=1

synopsis:

sddsnaff [inputfile] [outputfile]
  [-pipe=[input][,output]]
  [-columns=indep-variable[,depen-quantity[,...]]]
  [-pair=<column1>,<column2>]
  [-exclude=depen-quantity[,...]]
  [-terminateSearch={changeLimit=fraction[,maxFrequencies=number] | frequencies=number}]
  [-iterateFrequency=[cycleLimit=number][,accuracyLimit=fraction]]
  [-truncate] [-noWarnings]

files: inputFile contains the data to be NAFF’d. One column must be chosen as the independent variable. If inputFile contains multiple pages, each is treated separately and delivered to a separate page of outputFile. outputFile contains two columns for each selected column in inputFile. These columns have names like origColumnFrequency and origColumnAmplitude, giving the frequency and amplitude for origColumn.

switches:

-pipe[=input][,output] — The standard SDDS Toolkit pipe option.
-columns=indepVariable[,depenQuantityList] — Specifies the name of the independent variable column. Optionally, if no -pair options are given, this specifies a comma-separated list (optionally with wildcards) of dependent quantities to be NAFF’d as a function of the independent variable. By default, all numerical columns except the independent column are NAFF’d.
-pair=<column1>,<column2> — Specifies the names of conjugate pairs to give double the frequency range. column1 is used to obtain the basic frequency and column2 is used to obtain the phase at the frequency of the first column. The relative phase expands the resulting frequency from 0–Fn to 0–2Fn. Multiple -pair options may be provided. The independent column is provided by -columns, while dependent columns may be provided by either -columns or -pair.
-exclude=depenQuantity,... — Specifies optionally wildcarded names of columns to exclude from analysis.
-terminateSearch={changeLimit=fraction[,maxFrequencies=number] | frequencies=number} — Specifies when to stop searching for frequency components. If changeLimit is given, the program stops when the RMS change in the signal is less than the specified fraction of the original RMS value. The maximum number of frequencies returned in this mode is set with maxFrequencies (default is 4). If frequencies is given, the program finds the specified number of frequencies, if possible. By default, one frequency is found for each signal.
-iterateFrequency=[cycleLimit=number][,accuracyLimit=fraction] — Controls the optimization procedure that searches for the best frequency. By default, the procedure executes 100 passes and attempts to determine the frequency to a precision of 0.00001 of the Nyquist frequency. cycleLimit changes the number of passes, while accuracyLimit specifies the desired precision.
-truncate — Specifies that the data should be truncated so that the number of points is the largest product of primes from 2 to 19 not greater than the original number of points. In some cases, this results in significantly greater speed by making the FFTs faster.
-noWarnings — Suppresses warning messages.

4.74 sddsnaff