RMS Signal Research Articles

The use of spectral analysis to assess the performance of shock absorbing footwear.

Spectral analysis methods have been used to examine the influence of shock absorbing inserts on heel strike transients in normal gait. The data were obtained from a piezoelectric accelerometer mounted on a custom moulded splint fitting around the malleoli which was found to eliminate unwanted resonances. The peak accelerations measured with this system were similar to those obtained in earlier studies. Examination of the gait of one subject in four different types of footwear showed that a reduction of rms acceleration could be achieved by the use of a shock absorbing insert. The efficiency of the insert was measured by its ability to reduce the rms acceleration in the 10–150 Hz band and to reduce the rms signal in the 50–150 Hz band as a proportion of the total. This second measure was defined as the ‘Shock Factor’.

Direct inversion of slant-stacked seismic data. Part I. Synthetic seismogram results

Abstract Bube and Burridge (1983) have investigated direct inverse methods in the time domain for solving the acoustic equation in one space dimension for the impedance profile. Since every slowness in a proper slant stack is a rescaled plane wave component, the technique can legitimately be applied to each trace individually. We have developed a robust estimation procedure that combines the (overdetermined) set of solutions in the τ − p domain to invert not just the impedance profile but the density and wave velocity separately. We have successfully applied the method to synthetic seismogram data for which neither the density, the wave velocity, nor the impedance are monotone functions of depth. Satisfactory results have been obtained after convolution of the model seismograms with a variety of source wavelets and after addition of random noise of amplitude comparable in level to the rms signal. We note that our method and results are for an acoustic equation model which may be inappropriate for physical models which generate significant shear waves from interface conversions.

Optimal design of a foil electret earphone for use in telephony

This paper describes the optimal design of a foil electret earphone for use in telephony. The sensitivity (ratio of the sound pressure generated to the signal supplied) was maximized while meeting material, geometric, and performance constraints. First, a generalized reduced gradient optimization scheme based on the leading order approximations to the diaphragm motions was used. Second, the region of the approximate optimum was examined and an exhaustive search conducted for the optimal design based on exact numerical solution for the diaphragm motion. The results indicate that it is theoretically possible to design a foil electret earphone suitable for telephony which produces a sound pressure level of just over 90 dB in response to a 1‐V rms signal. The optimum earphone has a center circular portion surrounded by an annulus and uses thin, highly tensioned Mylar as a diaphragm. The electret material is mounted on the back electrode.

Measurement of intrinsic signal to noise ratios for high performance rigid recording media (abstract)

Measurement of the noise spectrum of high performance oxide, thin-film longitudinal and perpendicular rigid recording media have been made in order to establish the frequency dependence of the noise, the intrinsic media signal-to-noise ratio, and the practical recording density limit set by error rate considerations. For the oxide media tested, the noise spectrum was flat with frequency at 0.7 μV rms/100 μV rms signal indicating it was close to the particle size determined noise limit. For plated Co-P and sputtered Co-Re thin-film longitudinal media the noise spectrum increases with frequency. At D70 (18 KFCI) the noise was 1.25 and 1 μV per 100 μV rms signal, respectively. For the vertical media the noise contribution came from shouldering around the fundamental frequency and was 2.5 μV/10 μV rms signal at D70 (22 KFCI) and increased with frequency. The measurements were made with both inductive and magnetoresistive heads (improved sensitivity) at 900 TPI and over a 20-MHz bandwidth. D70 for the oxide media was 13 KFCI. The flying height was maintained at 9μ in. Measurements were made at narrower trackwidths to confirm the square root dependence of S/N on trackwidth. Comparisons of both dc erase and high-frequency noise spectrums are presented and contrasted for oxide and metallic media. Evidence supporting proposed theories for the source of the media noise is discussed and the implications with respect to maximum achievable areal densities (without error correction) are presented.

Dynamics of a digital automatic gain control for Gaussian signals

A simple digital automatic gain control loop, suitable for stabilizing the level of a slowly varying Gaussian signal in single-channel or multichannel applications is described. The probabilities of the excursion levels of the feedback control signal are derived and presented in normalized charts. These enable tradeoff between the signal level accuracy and the magnitude of the gain change steps to be readily accomplished and the corresponding increase in signal rms deviation due to the control signal to be determined.

A first-order scattering solution for modelling elastic wave codas -- I. The acoustic case

Summary A corrected, first-order solution for modelling acoustic wave scattering in layered halfspaces containing random inhomogeneities is derived. Energy lost to higher order scattering and intrinsic attenuation is included in the correction, which is constructed so that energy is conserved to first order. The complex propagation effects of the layering are overcome by representing the motion as a sum of normal modes. This approach renders the kinematic description of the scattering two dimensional, with the wave vectors of incident and scattered modes lying parallel to the layering. At each level in the halfspace, the inhomogeneities are resolved into two-dimensional Fourier spectra also parallel to the layering. The root mean square (rms) motion of a scattered mode depends on the correlation between spectra at different levels and the group velocity of the mode. To simplify the solution, it is assumed that the inhomogeneity spectra are piecewise constant and that the energy of a normal model propagates only at its group velocity. The final step of the theory establishes a criterion for the source—receiver separations over which the results are accurate. Numerical calculations have been carried out for a single layer of inhomogeneities over a halfspace. The spectra of the inhomogeneities were assumed band limited, and several different spectra were examined. The results suggest the existence of a diagonal selection rule whereby a wavelet of mode order n scatters mostly to wavelets of the same order. Moreover, a resonant frequency of scattering occurs, causing the rms signal to appear monochromatic. The frequency of the resonance is controlled by the inhomogeneity spectra band limits. With the aid of the diagonal selection rule, the simplified solution allows for both rapid computation of synthetic signals and inversion of data for scattering cross-section. Existing data suggest the theory may be applied to obtain approximate models of local earthquake codas. The synthetic signals of the single layer cases, for example, have codas similar to published observations. To illustrate the inversion of data with the theory, a preliminary scattering cross-section for the lunar crust is presented.

Theory of an Adaptive Quantizer

In an adaptive quantizer that has been used for speech encoding, the entire amplitude range expands or contracts by a multiplicative constant after each input sample. The constant M i depends only on the magnitude of the current quantizer output. Assuming independent identically distributed input samples, we show that the sequence of quantizer ranges is a stochastically stable process. Furthermore, we derive a key design equation, \Sigma p_{i}x logM_{i} = O , where p_{i}(x) is the probability that an input sample is in the i th magnitude interval when the ratio of quantizer range to rms signal level is x . A designer may specify x and solve this equation for multipliers that provide the desired steady-state performance. There are many such sets of multipliers and we show that the adaptation time constant associated with each set decreases as the ratio of the largest multiplier to the smallest multiplier is increased. On the other hand, the spread of the steady-state range distribution about the operating point can be made as small as desired by making this ratio sufficiently small. A bound is obtained for the tradeoff between responsiveness to changing input level and steady-state range accuracy.

Comparison of radio transmission at X-band frequencies in suburban and urban areas

Measurements were made at a frequency of 11.2 GHz of the signal strength received by a fixed-base station from a mobile transmitter. Distributions of the instantaneous and rms signal levels are compared for data taken in New York City and suburban New Providence, N. J.

Stark-Effect Modulation of a CO2 Laser by NH2 D

The molecular Stark effect in NH2D was used to modulate the 10. 6-μ P(20) line of a CO2 laser yielding a modulation depth of 40% from a 200-V cm−1 rms signal applied to a 19. 7-cm gas cell external to the laser. NH2D was prepared by mixing ND3 and NH3. The absorption coefficient of the M=4 Stark-split line was measured as a function of mixing ratio and pressure. The observed pressure-broadening coefficient was 32. 5 MHz/Torr.

The Biquad: Part I-Some practical design considerations

The use of active elements in linear networks offers new degrees of freedom to both network and system designers. A comprehensive report on the Biquad, an active topology based on analog computer concepts, is given. We describe the electrical characteristics of the Biquad that make it a manufacturable realization for precision networks. Analysis and experimental data describe the dependence of Biquad performance on nonideal operational amplifiers. Compensation techniques are derived which allow high- <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> operation at several hundred kilohertz with existing devices. The 8-V rms signal capacity and 80-dB dynamic range of the voice-frequency Biquad are illustrated.

Germanium Bolometer Detector of Millimeter Wavelength Thermal Energy

This paper describes the construction and evaluation of a Ka band bolometer receiver using a highly temperature-resistance dependent (at 4.2°K) doped germanium bolometer of Texas Instruments, Inc. The receiver noise equivalent power (NEP) of approximately 10−9 W and input bandwidth exceeding 12 Gc has a rms signal level indicating uncertainty equivalent to 90 C° per cycle of output filtering. Evaluation of the germanium bolometer as a millimeter wavelength radiometer detector was performed at Ka band to utilize existing apparatus and to facilitate fabrication of the receiver. With the increased sensitivity anticipated for smaller bolometer elements, short millimeter and submillimeter wavelength scaled models of the receiver appear promising as detectors for radio telescopes.