Fourier Spectral Analysis Object and Template – Peak-Hold Spectrum (Spectral Analysis Option)
The Peak-Hold spectral procedure forms the maximum across several frequency spectra, which are formed via the Fourier Transform of multiple (and usually overlapping) segments of the data stream. The segmenting results in a smaller size data record, and consequently in a reduced spectral resolution. This procedure is suitable for evaluating non-stationary signals, since temporarily occurring spectral components of a high amplitude, such as resonances during ramp-up, are included in the result without being weakened by averaging. The time reference, i.e., the information about when a high level occurred, is lost.
Spectrum Type
The frequency domain information can be output in a variety of formats. In the following table, Re is the real component of a given segment's real (single sided) FFT at a given frequency, Im is the imaginary component, δF is the frequency spacing of the spectrum, n is the data set size, δX is the sampling interval, and σ² is the data set variance.
Spectrum Type |
Formula/Description |
|---|---|
Amplitude |
sqrt(Re² + Im²) / n |
RMS Amplitude |
sqrt((Re² + Im²) / 2) / n |
Amplitude² |
(Re² + Im²) / n² |
dB |
20 * log10(sqrt(Re² + Im²) / n / Aref) Aref = Reference amplitude which is assigned 0 dB |
Normalized dB |
20 * log10(sqrt(Re² + Im²) / n) - dBmax dBmax = dB value of the spectral line with maximum amplitude |
PSD - Power Spectral Density |
(Re² + Im²) / n² / δF / 2 |
TISA - Time Integral Amplitude² |
δX * (Re² + Im²) / n / 2 |
MSA - Mean Amplitude² |
(Re² + Im²) / n² / 2 |
SSA - Sum Amplitude² |
(Re² + Im²) / n / 2 |
Variance |
(Re² + Im²) / (n * σ²) / 2 |
Magnitude² |
Re²+Im² |
Magnitude |
sqrt(Re² + Im²) |
Third octaves (mean values) |
The mean of the amplitudes in a third octave band is formed. |
Third octaves (sums) |
The amplitudes in a third octave band are summed up. |
Third octaves (RMS) |
The square mean or RMS for each third octave band is calculated, i.e. the squared amplitudes are averaged and from this the square root is calculated. |
Third octaves (quadratic mean) |
The square amplitudes in a third octave band are summed up. |
Octaves (mean values) |
The mean of the amplitudes in an octave band is formed. |
Octaves (sums) |
The amplitudes in an octave band are summed up. |
Octaves (RMS) |
The square mean or RMS for each octave band is calculated, i.e. the squared amplitudes are averaged and from this the square root is calculated. |
Octaves (quadratic mean) |
The square amplitudes in an octave band are summed up. |
In an amplitude plot, you see the actual amplitude of sine components. In a normalized decibel plot, the highest peak is at 0 dB, a peak at -3 dB would have half the power and a peak at -6 dB would have half the amplitude. The PSD TISA (time-integral squared amplitude power) is the actual integral under the curve defined by the square of the raw data.
For the third octaves and octaves spectral types an amplitude spectrum is computed first, which is then evaluated with the ThirdOctaveAnalysis or OctaveAnalysis FPScript functions respectively.
Windows
FlexPro offers a variety of tapering windowsto reduce the spectral leakage. The Window adjustment field is used to set the spectral width, and thus the dynamic range, of adjustable windows. This field will be disabled for fixed windows.
The list box Normalization offers two options to normalize after applying the window. Selecting Amplitude normalizes to the gain of the used window function, i.e. the sum of all values is divided by their number. This compensates the damping of the amplitudes caused by applying the window. This is especially useful to measure peaks within the spectrum. If you select Power the loss of power is compensated. The ratio of the sum of the squared data before and after applying the window is used as a normalization factor. The total power within the spectrum therefore always corresponds to the power of the data before applying the window.
Parameters
The Best Exact N composite algorithm is used for the FFT.
The length of individual data segments, Segment Length and the amount of overlap, Overlap % can be specified. You should set the segment size based on the resolution needed. The default value of 0 sets the segment length to the double of the square root of the data length, rounded up to the next power of two. With the default overlap of 50% this leads to about double as much frequencies than time values.
To accommodate zero padding, the FFT Length can be specified separately. Zero padding occurs when you set the FFT length to a value greater than the segment length. You can enter 0 for the FFT length to set it to the segment length. When a data tapering window is used, then zero-padding causes very little spectral leakage. Zero-padding is especially useful for interpolating peak frequencies with this algorithm, given the loss in resolution incurred by the reduced size of the segments.
Options - Set/Clear Reference (Analysis Wizard Only)
This function lets you compare various spectral procedures and settings. You can view a copy of the currently displayed spectrum in the lower pane by pressing Set Reference. Next, you can adjust additional settings that affect the display in the upper pane. With Clear Reference you can remove the copy and the time signal will appear again.