Low-pass Noise Research Articles

Influence of bandwidth on some nonlinear transformations of a Gaussian random process

Predictions of the response probability density function for bandlimited white noise excitation of nonlinear systems often employ the so-called Fokker-Planck technique. While these predictions are exact for white noise, there exist no general criteria for assessing their accuracy in physical situations. This paper endeavors to shed some light on the problem and perhaps point the way toward better understanding of the inherent difficulties involved. First, a brief discussion of more typical response functions for a first-order nonlinear system is presented on the basis of a very narrow-band low-pass excitation and on a very wide-band low-pass excitation spectrum. Such limiting cases generally exhibit substantially different behavior. Next, some experimental results for the same system driven by variable-bandwidth low-pass Gaussian noise is presented. These results indicate substantial deviation from the Fokker-Planck predictions when the excitation bandwidth is comparable with an equivalent system bandwidth. Moreover, it was found that the data at high response levels were bounded by the Fokker-Planck predictions on one hand and by a prediction based on a pointwise transformation of an extremely low-pass excitation process on the other. Bandwidths ranging between three and fifteen times the system's equivalent bandwidth are required for validity of the Fokker-Planck approximation depending on the nature of the non-linearity and the response level in question.

Olivocochlear Bundle: Relationships to Signal Discrimination in Noise.

Monkeys, trained to discriminate between human speech sounds presented at 70 dB SPL in 2400-Hz low-pass noise of different intensities, were found significantly impaired in their performance following surgical section of the crossed OCB. There is absolutely no loss in the ability to discriminate between the signals in the absence of noise. The deficit is related to “perceptual” (as opposed to physical) signal-to-noise ratio: high intensity noise per se is insufficient to cause performance decrement if its passband provides inadequate masking of the speech stimuli (e.g., 2400 Hz high pass). The magnitude of the postoperative deficit is apparently related to the extent of destruction of the fibers of the OCB.

Pitch of noise bands.

Ten subjects were asked to produce octave judgments, i.e., one octave above and one octave below a standard stimulus, with bands of low-pass and high-pass noise as well as sinusoids. For example, given a specific low-pass noise band as a standard, subjects adjusted the cutoff frequency of a second low-pass noise band so that its pitch was 1 oct above that of the standard. Results indicate that bands of noise have a pitch and that the pitch is correlated with cutoff frequency. For low-pass noise, there seemed to be a relatively linear relation between pitch and cutoff frequency from 80- to 10 000-Hz cutoff, whereas the linear relation for high-pass noise holds only for a restricted frequency range, 600–10 000 Hz. The pitch of both types of noise stimuli degenerates above 10 kHz, possibly because of limited earphone response and a rising threshold of hearing. More difficult to explain is the static and vague pitch of high-pass noise at low cutoff frequencies. A discussion of several mechanisms is included.

YIG Filters as Envelope Limiters

Envelope limiters are used in such applications as FM demodulation and power leveling. Recently, the envelope-limiting properties of yttrium-iron-garnet (YIG) filters were reported for the special cases of unmodulated and pulsed input signals. Measured data is presented hereon the response of a YIG limiter to AM carriers having modulation index of the order of 50 percent. Sinusoidal, square-wave, and low-pass noise modulating signals were used in the measurements. It was found that a YIG filter will give good envelope Iimiting for modulating frequencies in the submegacycle range. At these low frequencies the carrier and the side frequencies are not limited selectively. At higher modulating frequencies where the limiting is frequency selective, the YIG filter will not remove the variations. In fact, in the particular filter tested, the modulation index was increased, rather than decreased, at modulating frequencies greater than about 750 kc/s. A graph is given showing the measured factor of reduction (or increase) of modulation index, as a function of modulating frequency. The response of the limiter as a function of carrier frequency, modulating frequency, and input power is shown by oscilloscope displays produced by sweeping the carrier frequency or input power. In addition, selected photographs of output envelope waveforms are given.

Binaural Lateralization of Cophasic and Antiphasic Clicks

Results from a computational model for middle ear and basilar-membrane operation suggest several binaural phenomena. The effects are sought experimentally in tests on the binaural lateralization of pulses. The interaural times for producing centered images are measured as functions of pulse polarity and noise masking. To a large extent. the interaural disparities appear explicable in terms of the mechanical response of the basilar membrane together with simple hypotheses about the mechanical-to-neural transduction in the inner ear. The time disparity can be manipulated by symmetrically masking with high-pass or low pass noise. By this means, the coherent neural information is elicited from a restricted place on the membrane and reflects the mechanical properties of that place. Similarly, asymmetrical masking (for example, high pass in one ear and low pass in the other) yields interaural times that reflect the transit times to specific membrane places. Calculations from the mathematical model for the middle ear and basilar membrane are used to interpret the psychoacoustic behavior in terms of physiological response. The results are discussed in the context of related findings, and an effort is made to assess the relative influence of mechanical and neural factors.

Tracking Systems Employing the Delay-Lock Discriminator

The delay-lock discriminator is a statistically optimum device for measuring the delay between two correlated waveforms. Its theory of operation and the performance of an experimental model have been described by Spilker and Magill.1 The application of this device to range-and angle-measuring systems is discussed herein. Utilization of the delay-lock discriminator can lead to substantial simplification as compared to tracking systems relying exclusively on phase-lock loops. Such improvements result because the delay-lock loop is free of the ambiguities inherent in phase-lock measurements. The characteristics of presently available delay lines, an essential component of the delay-lock loop, and, in particular, the limited accuracy of which they are capable at present prohibits the immediate exploitation of the full capability of the delay-lock technique. For this reason, an attractive possibility for an immediate implementation is a hybrid system in which a delay-lock measurement is made to resolve ambiguities, while a phase-lock measurement determines the ultimate accuracy. A combined range- and angle-tracking system employing this hybrid concept is described herein, in which the delay-lock measurement is made on a low-pass noise waveform which, for transmission purposes, is applied as amplitude modulation to a stable carrier. The precise measurement is made by phase-locking onto the carrier. The phase-lock output is also used to synchronously detect the low-pass modulation. The characteristics of this system are discussed and expressions are given which show the dependence of threshold SNR and rms delay error upon system parameters. Its theoretical performance is illustrated in tracking a cooperative (i.e.

THE AUTOCORRELATION FUNCTION OF SYMMETRICALLY FOLDED GAUSSIAN NOISE

Noise with a uniform distribution of amplitudes and frequency of level crossings can be obtained by passing Gaussian noise through a symmetrical folder. A nonlinear device is required to do this. The input–output amplitude characteristic of this device has a positive unity slope between certain voltage (folding) levels which are symmetrical with respect to zero. The characteristic assumes a negative slope, called the folding slope, for voltages above and below the respective folding levels. The autocorrelation function of symmetrically folded noise is calculated. Curves are presented showing the power spectrum of symmetrically folded low-pass Gaussian noise for various degrees of folding and various values of folding slopes.

Effect of Masking on the Pitch of Periodic Pulses

Pitch-matching experiments were performed with stimuli and procedure similar to those employed by Flanagan and Guttman [J. Acoust. Soc. Am. 32, 1308–1328 (1960)] to determine whether selective masking alters the transition region between the pulse rate and pattern-rate modes of perception. In the unmasked condition, for pulse repetition rates below approximately 150 pps, listeners essentially match the pulse repetition rates of the comparison and standard signals; for fundamental frequencies higher than approximately 150 cps (and below 800 cps), listeners match the fundamental frequencies of the comparison and standard signals, even if the fundamental has been removed from the standard by filtering. Present results indicate that if to standard signals in or near the transition region high-pass noise (1000 cps) is added, the “buzz” quality associated with the pulse rate judgment can be masked and a pattern-rate judgment favored. Conversely, low-pass noise (1000 cps) can mask the “tonal” quality associated with pattern-rate judgments and favor pulse-rate judgments. Equally effective narrow-band noise or sinusoidal maskers seem to lie at about 5000 cps for masking pulse-rate pitch and 500 cps for masking pattern-rate pitch.

Serendipitous Effects of Masking Noise upon Sensations Produced by the Dentist's Drill

The observations to be reported were made in a dentist's chair. Part of the sensory stimulation was generated by the dentist and his dental equipment, particulary his drill, during the course of routine dental operations. Part was generated by apparatus consisting of random noise generator, low-pass filter, stereophonic tape playback, patient-operated faders and attenuators, power amplifiers, and earphones. The initial observations concerned masking of the drilling noise. Low-pass random noise sufficiently intense to mask the drilling noise completely turned out not to be itself objectionable. Not only the sound of the drill, but also much of the massive complex of tension, anxiety, and pain was drowned in the masking noise. One patient {JCRL) made subjective observations, during a single drilling, alternately with and without the masking noise. During the masking noise, there was only a “small, thin sensation of pain.” When the masking noise was off, the noise and vibration of the drill accrued to the core pain and made it seem larger and more noxious. Further tests were made with music, and with music and noise in combination. Music is less effective than noise as a masker, but it is very effective in inducing relaxation. The combination of music and noise, alternating under the patient's control, appears to provide a practicable dental analgesia. Observations on more than 170 patients will be described, and applications outside the field of dentistry will be mentioned.