Calculating RMS Noise from Sensor Spectral Noise Density Datasheet Specifications
Root-mean-square noise equals spectral density multiplied by the square root of equivalent noise bandwidth, adjusted for flicker corner frequency integration.
Hann Window Normalization
Leakage Correction
Discrete Fourier transform pre-processing applies cosine-tapered weighting windows to time-series data records to reduce spectral leakage. The adjustment process termed Hann window normalization scales output spectrum amplitudes to compensate for window power reduction. Weighting time samples reduces edge discontinuities but alters calculated signal peak amplitudes and total integrated energy.
Scaling factors restore true physical units to spectrum magnitude displays.
Scale Adjustment
Cosine bell window weighting reduces side lobe levels in discrete spectral transforms to minus thirty-two decibels per octave. Multiplying time domain samples by the window function reduces effective record energy by fifty percent. Coherent gain correction multiplies peak amplitudes by two to restore single-tone sinusoid amplitudes.
Equivalent noise bandwidth correction multiplies power values by one point five for broadband noise power calculations.
FFT Processing
Digital signal processing blocks in acoustic analyzers apply window functions before computing FFT spectrums. Executing Hann window normalization ensures accurate voltage or acceleration amplitude measurements across all frequency bins. Peak amplitude estimation accuracy improves to within zero point one decibel for dynamic signal monitoring.
Spectrum analyzer software scales both coherent peak values and power spectral density arrays using appropriate window factors. Energy conservation laws require distinct normalization factors for narrowband tonal components versus broadband random noise. Continuous spectral integration yields correct root-mean-square amplitude values only when window normalization factors apply correctly.
Resolution Boundary
Reference single-tone calibrators verify amplitude scaling accuracy after window application. Main lobe broadening inherent to Hann windowing reduces frequency resolution compared to rectangular windowing. Scallop loss introduces up to one point four decibels of amplitude uncertainty for frequencies falling between bin centers.
Overlapping processing buffers recover time-domain information lost at window edges.