Power Spectral Density (PSD)

Power Spectral Density provides a bandwidth-independent representation of how energy is distributed across frequency. When you compute a standard FFT magnitude spectrum, the amplitude of each bin depends on the FFT size: doubling the FFT size halves the bandwidth per bin, splitting the energy and reducing per-bin amplitude by 3 dB. PSD compensates for this by dividing each bin's power by its bandwidth. This normalization is crucial for noise analysis. White noise has a flat PSD by definition, meaning equal power per Hz at all frequencies. Pink noise has a PSD that decreases at 3 dB per octave (or 10 dB per decade). Without PSD normalization, the apparent spectrum shape changes with FFT size, making it impossible to compare measurements taken with different settings. Welch's method, implemented in SonaVyx's transfer function engine, estimates PSD by averaging multiple overlapping, windowed FFT segments. This reduces spectral variance at the cost of frequency resolution. The overlap percentage (typically 50% or 75%) and number of averages determine the trade-off between resolution and statistical confidence. In practical system measurement, PSD is used for noise floor characterization, background noise analysis, and identifying tonal components in broadband noise. The environmental noise monitoring tools in SonaVyx use PSD principles to distinguish between steady-state noise (relatively flat PSD) and tonal noise (sharp peaks in PSD). Cross-Power Spectral Density between two signals is the foundation of transfer function measurement. The transfer function H(f) = Gxy(f) / Gxx(f) uses the cross-spectral density between output and input, divided by the input auto-spectral density.