Transient

The amplitude-versus-time profile of the transient provides the most direct set of features. Key metrics include the rise-time variance (10% to 90% amplitude), overshoot characterization (peak excursion beyond steady-state), and settling time analysis (duration to stabilize within a tolerance). The Hilbert transform envelope is the standard method for extracting this precise amplitude contour without carrier cycle distortion. The transient attack profile and transient decay profile capture the asymmetric charging and discharging behavior of the transmitter's power amplifier and bias circuitry.

The rapid switching of a transmitter during the burst onset generates transient spectral splatter—broadband noise that momentarily spills into adjacent frequency channels. Adjacent channel splatter is a specific, measurable component of this phenomenon and serves as a key metric for assessing transmitter linearity and filtering effectiveness. Key-click analysis, a term originating from telegraphy, describes the spectral sidebands generated by the abrupt make/break of the signal. The transient spectral centroid—the center of mass of the short-time Fourier transform—indicates whether the transient energy is biased toward higher or lower frequencies.

The dynamic behavior of the carrier during the transient reveals the underlying synthesis chain. A phase discontinuity is an abrupt, unintended shift in instantaneous phase caused by non-ideal switching. The transient frequency trajectory maps the time-dependent path of the instantaneous frequency deviation as it converges to steady-state, exposing the PLL settling transient and PLL overshoot. VCO transient response artifacts, including frequency pushing and pulling, imprint a unique signature. Zero-crossing analysis is a precise time-domain technique for extracting this instantaneous frequency information.

Transient signals are inherently non-Gaussian, making higher-order statistics powerful discriminators. Transient kurtosis quantifies the peakedness and tailedness of the amplitude distribution, detecting impulsive artifacts. Transient skewness measures distribution asymmetry, revealing directional biases in hardware non-linearity. Transient bispectrum analysis reveals quadratic phase coupling while suppressing Gaussian noise. Transient cumulant analysis isolates deterministic non-linear signatures by being mathematically blind to Gaussian noise, making it highly robust for fingerprinting.

Microscopic circuit behaviors create distinct, repeatable markers. Transient DAC glitch is a momentary voltage spike from timing skews in the digital-to-analog converter. Transient IQ imbalance is a temporary gain and phase mismatch between in-phase and quadrature paths. Transient carrier feedthrough results from transient DC offset in the modulator, creating a spectral line at the carrier frequency. Transient ground bounce—a voltage spike on the internal ground reference caused by inrush current through parasitic bond wire inductance—provides a signature unique to the physical packaging of the integrated circuit.

Transient events are inherently multi-scale, requiring analysis techniques that provide simultaneous localization in time and frequency. Transient wavelet coefficients decompose the signal using a wavelet basis, capturing both short-duration, high-frequency ringing artifacts and longer-duration, low-frequency settling behaviors. The transient scattering transform cascades wavelet transforms with modulus non-linearities to produce a translation-invariant and stable representation. These methods are superior to the fixed-resolution short-time Fourier transform for characterizing the complex, non-stationary nature of turn-on and turn-off transients.