An angular velocity sensor includes a vibrator. A differential amplifier circuit outputs a differential signal including a Coriolis component from the vibrator. The differential signal is converted into a digital signal by an A/D converter. A Hilbert transformer shifts the differential signal by .pi./2. Two multipliers squares the original differential signal and the .pi./2-phase-shifted differential signal, respectively, and an adder computes the sum of the squares. A square root circuit computes the square root of the sum and outputs a magnitude signal proportional to Coriolis force.

A coprocessor (15) for synthesizing a signal from the sum of sinusoids preferably includes an electronic system (20) having a host processor (12) that forwards frame boundary parameters to the coprocessor (15). Parameter registers (26) in coprocessor (15) store synthesis parameters for iteratively deriving amplitude and phase values for each sample point within a data frame. Adders (28, 30, 32) generate current amplitude from one addition, and current phase value from two additions, with the results stored back into parameter registers (26). A sine function calculator circuit (34), which may use a CORDIC technique, receives the current amplitude and phase values, and generates a digital component signal for the current sample point for one of the sinusoids. Digital component signals are accumulated at the sample point in a data sample buffer (40) and output at an output (44).

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal.

Two current outputs are converted into voltage outputs by I/V converters, and further converted into digital outputs D1 and D2 by binarizing circuits. The outputs are added by an adder in a phase shifter, and converted into an output like a triangular wave by an integrator. The output like a triangular wave is compared with a reference in a binarizing circuit and, therefore, it is possible to shift the phase from the median of the phase differential between the two signals by 90 deg with high precision.

A computer implemented physical signal analysis method includes four basic steps and the associated presentation techniques of the results. The first step is a computer implemented Empirical Mode Decomposition that extracts a collection of Intrinsic Mode Functions (IMF) from nonlinear, nonstationary physical signals. The decomposition is based on the direct extraction of the energy associated with various intrinsic time scales in the physical signal. Expressed in the IMF's, they have well-behaved Hilbert Transforms from which instantaneous frequencies can be calculated. The second step is the Hilbert Transform which produces a Hilbert Spectrum. Thus, the invention can localize any event on the time as well as the frequency axis. The decomposition can also be viewed as an expansion of the data in terms of the IMF's. Then, these IMF's, based on and derived from the data, can serve as the basis of that expansion. The local energy and the instantaneous frequency derived from the IMF's through the Hilbert transform give a full energy-frequency-time distribution of the data which is designated as the Hilbert Spectrum. The third step filters the physical signal by combining a subset of the IMFs. In the fourth step, a curve may be fitted to the filtered signal which may not have been possible with the original, unfiltered signal.