Dynamic measurement implies determining the content of signals having spectral structure and energy changing with time, sometimes on very short time scales. Dynamic measurements can present challenges to determine sufficient information in both the time and frequency domains. High resolution in frequency prevents finding short-term peak levels and recognizing true crest factors, and vice versa. The human ear/brain system exceeds the simultaneous time and frequency recognition of conventional measurement methods, further complicating the challenge. People have at least three times better time/frequency resolution than the familiar Fourier transform moved across the time axis, although quite often a compromise block size can be found that gives time/frequency measurement agreeing with human sound perception of both factors. Unlike technical measuring systems, human hearing is also very sensitive to patterns. The presence of tones, varying tones (amplitude and/or frequency), clicks, rattles, splashing sounds, etc., even at low levels in the presence of other less structured noise of considerably higher level, can dominate perception. Human consciousness effectively performs the opposite of averaging, ignoring the absolute value of slowly varying or stationary signals and focusing on things differing at short time bases from their surroundings in both time and frequency. In dynamic measurement, it can be difficult to withdraw an important pattern from the absolute whole. Case studies will be given comparing conventional techniques with three high-resolution time/frequency methods useful in general engineering although developed to model the processes of human sound perception: a hearing model with very rapid time resolution at all frequencies (Sottek, R., 1993, “Modelle zur Signalverarbeitung im menschlichen Gehör,” dissertation, RWTH Aachen), a relative (pattern) measurement technique subtracting a sliding average in both time and frequency from a running instantaneous spectrum (Genuit, K., 1996, “A New Approach to Objective Determination of Noise Quality Based on Relative Parameters,” Proceedings of InterNoise, Liverpool, UK), and a Fourier-based window deconvolution method giving pure spectral lines regardless of signal-to-block synchronization and permitting multiplication of frequency resolution for a given block length and time resolution (Sottek, R., 1993, “Modelle zur Signalverarbeitung im menschlichen Gehör,” dissertation, RWTH Aachen;Bray, W. R., 2004, “Perceptually Related Analysis of Time-Frequency Patterns via a Hearing Model (Sottek), a Pattern-Measurement Algorithm (“Relative Approach”) and a Window-Deconvolution Algorithm,” 147th Meeting, New York, May, Acoustical Society of America, 5aPPb7). Types of noise which particularly benefit from the techniques we will discuss include, but are by no means limited to, time-varying emissions from information technology devices (printers, hard disk drives, servosystems), appliances, HVAC (compressors and controls), hydraulic systems including direct high-pressure fuel injection internal combustion engines, tonal orders from rotating machinery, and environmental noise in workplaces and residences. The three analytic tools presented here are well suited in matching the time-frequency, tonal, and pattern recognition capabilities of human hearing, and offer general engineering capabilities especially involving the fine time-structured behavior of transient and tonal events.
Superlets: time-frequency super-resolution using wavelet sets