The spectral analysis techniques can be broadly classified into nonparametric, i.e. Fourier analysis based methods and parametric, i.e. model based methods. DART XP Pro offers both ways of frequency analysis.
The basis for this method is the Fourier transform of the analyzed sequence - the fast Fourier transform (FFT) algorithm is used for the purpose of transform evaluation.
Periodogram can yield very 'bumpy' spectral plots, especially if the analyzed signal is noiselike. On the other hand it guarantees high spectral resolution, i.e. the ability to distinguish between the closely spaced frequency components.
By default the spectral analysis is performed on a block of 1024 samples centered at the current cursor position. You can change the size of the analysis frame by picking another value from the Frame list placed inside the FFT group.
In order to improve consistency of spectral estimates it is recommended that the Fourier transforms are weighted prior to periodogram evaluation - the Goodman-Enochson-Otnes (GEO) window is used for this purpose. If the Windowing box is not checked the results of spectral analysis may be overly sensitive to the position and size of the analysis frame. Without windowing they may also be inconsistent with the results of parametric analysis, especially in the region of high frequencies.
The parametric spectral evaluation techniques are model based. This means the parameters of the mathematical model of the analyzed time series are the basis for spectrum estimation. DART XP Pro adopts the so-called autoregressive (AR) model for this purpose. The Burg lattice algorithm is used for estimation of autoregressive coefficients.
The parametric approach yields spectral graphs that are smooth and therefore easy to interpret. Since the number of resonant peaks the method is capable of distinguishing depends on the number of model coefficients (at least 2k parameters are needed to match spectrum with k peaks) it is important to make the right choice of the order of the adopted AR model. Low order models may yield spectral plots that do not reflect all details of the true spectrum. On the other hand, if the order of the AR model is too high, the corresponding graphs will tend to show spurious peaks. To choose the preferred order of autoregression pick the Order list placed inside the AR group and select the available values (4, 8, 12, 16, 20) - 12 should be fine in most cases. If you want DART XP Pro to make this decision for you choose Auto from the top of the list. The applied procedure of automatic order selection is based on the Akaike's information criterion (AIC).
Since the parametric approach gives satisfactory results even if the analyzed data segments are relatively short the default size of the analysis frame was set to 256 - you can change it by choosing another value from the Frame list placed inside the AR group.
There is no clear-cut answer to this question. Each of the approaches described above has both advantages and limitations. Due to a large number of degrees of freedom the nonparametric estimates form pretty ragged patterns which may be difficult to interpret. The plots obtained using the parametric approach are smooth and therefore easy to analyze. On the other hand periodogram, as all FFT-based methods, yields “unprejudiced” spectral estimates in the sense that the number of resonant peaks is not limited a priori. In contrast with this, the results of parametric analysis may strongly depend on the order of the adopted model.
DART XP Pro allows you to use both methods of spectral analysis simultaneously - the plots are superimposed. Whenever you like to inspect the results of parametric or nonparametric analysis alone, uncheck the corresponding boxes (FFT or AR, respectively) in the extended spectral dialog.
In most cases the superimposed plots stay in a good agreement. Whenever discrepancies occur remember that
Only the dominant periodogram peaks correspond to spectral resonances.
The graphs obtained using the parametric approach tend to show too many spectral peaks if the order of autoregression is too high; if the order of the AR model is too low, some resonances might be overlooked.
The AR estimates have a tendency to match spectral peaks (resonances) better than spectral valleys (antiresonances).
Both approaches may give different and/or dubious results if the processed signal is not locally stationary, e.g., if you analyze a fast speech transient - we recommend you use short analysis frames in all such situations.