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memse - estimate power spectrum using maximum entropy (all poles) method


memse [ options ... ] input-file


memse transforms a real-valued time series (from the specified input-file, or from the standard input if input-file is specified as ‘‘-’’; input-file must be in text form) into a power spectrum (on the standard output). memse is designed to be used in much the same way as fft(1) ; it accepts the same input, produces output in the same format, and accepts many of the same options used with fft.

Unlike fft, which bases its spectral estimates on the discrete Fourier transform, memse uses the maximum entropy (all poles) method, also known as autoregressive (AR) spectral estimation. This method models the spectrum by a series expansion in which the free parameters are all in the denominators of its terms; hence each term may represent a pole (corresponding to infinite power spectral density within an infinitely narrow frequency band). By contrast, Fourier analysis models the spectrum by a series expansion in which the free parameters are all in the numerators; hence each term in a Fourier series may represent a zero. All-poles models are particularly useful for analysis of spectra which have discrete peaks (in the terminology of optical spectra, ‘‘lines’’).

In order to use memse, you should have some idea of the order of the model you wish to use (i.e., the number of poles). Although this may be any number up to the number of input points, the number of poles generally should not exceed the square root of the number of input points, and usually should be considerably less than that number. Large numbers of poles lead to lengthy computations (much slower than the FFT) in which accumulated roundoff error becomes a serious problem. This problem may also occur if the length of the input series becomes excessive. The recommended way to use memse is to begin by using fft, in order to estimate the model order. Typically this should be a small multiple of the number of peaks which you believe are present. Beware! memse will produce smooth spectral estimates for whatever model order you choose -- and they may be totally bogus if you choose incorrectly. Varying the model order can help to weed out some spurious features, but use extreme care when interpreting memse output given noisy input.

Options are:

-b low high [ low high ... ]
Print power in the specified bands. Each low and high pair specifies the low and high frequency boundaries of the band of interest, in Hz. Multiple bands may be specified following a single -b option; only the last -b option has any effect. Also see -s below.
-f frequency
Show the center frequency for each bin in the first column. The frequency argument specifies the input sampling frequency; the center frequencies are given in the same units.
Print a usage summary.
-n n
Produce exactly n power estimates, evenly spaced in frequency from 0 up to half the input sampling frequency inclusive. The default depends on the length of the input series; it is designed to match fft’s defaults, to make it easy to compare outputs. You may wish to use values of n which are higher than the default in order to improve your estimates of the locations of sharp features in the spectrum; since this is not possible using fft, this feature is one of the main advantages of memse.
-o n
Use an nth order model (i.e., up to n poles). Default: the square root of the number of input samples.
Generate a power spectrum (print squared magnitudes).
Print power in a standard set of frequency bands of interest for HRV analysis.
-w window-type
Apply the specified window to the input data. window-type may be one of: ‘Bartlett’, ‘Blackman’, ‘Blackman-Harris’, ‘Hamming’, ‘Hanning’, ‘Parzen’, ‘Square’, and ‘Welch’. The ‘Square’ window type is equivalent to using no window at all; this is also variously known as a rectangular or Dirichlet window.
Add a constant to each input sample, chosen such that the mean value of the entire series is zero.
Set the mean value of the inputs to zero as for -z, and detrend the series (set its mean first derivative to zero). This is equivalent to subtracting a best-fit (by least squares) line from the input data.


Versions of memse released prior to September 1999 did not support the -P option, and did not normalize amplitudes with respect to the number of output points.

See Also

fft(1) , hrfft(1) , lomb(1)


George B. Moody (


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