FM Pulse Research Articles

Frequency-modulated radiofrequency pulses in spin-echo and stimulated-echo experiments.

Frequency-modulated rf pulses based on a linear frequency sweep are studied experimentally in spin-echo and stimulated-echo sequences. It turns out that these FM pulses generate a quadratic phase perpendicular to the selected slice and that the quadratic phases of the FM pulses in a spin-echo or stimulated-echo sequence may compensate each other if sweep velocity and gradients are suitably chosen. For a complete rephasing, a formula is given and supported by measured slice profiles. Slice profiles of excellent rectangularity are obtained. Finally, it is shown that with this technique images can be obtained using pulses of increased bandwidth and reduced peak power compared with the AM situation.

Digital beamforming of a linear FM pulse array

A digital beamforming technique utilising a long linear FM pulse in a sonar array is described. The difficulties of the beat frequency deviation at various sensors are overcome by sampling and phase correction. Theoretical discussions and computer simulations show that this technique may give improved detection with high angular resolution as well as high range resolution.

Use of rectangular vandermonde matrix decomposition to resolve damped sinusoidal oscillation components

Signals that are sums of decaying sinusoids arise frequently in passive and active sonar applications, both as spontaneous acoustic transients and as echoes from elastic objects. When the oscillations are highly damped, identification of component frequencies and damping factors is more amenable to least‐squares Prony analysis than to Fourier analysis, and is particularly suited to a related technique that we call “rectangular Vandermonde matrix decomposition.” Our results indicate that the Vandermonde method is robust in the presence of noise, but not in the presence of distortions created by ideal bandpass filters. On the other hand, analysis of simulated replica‐correlated echoes of FM pulses bounced off an object having a pair of heavily damped resonances give different results. Surprisingly, the Vandermonde method identified the resonant frequencies even without replica correlation, despite the fact that the analyzed waveform looked not at all like a sum of decaying sinusoids. [Work supported by the ONR.]

Generating analogue FM pulses using a 1 bit digital technique

A method of generating sinusoidal frequency-modulated pulses using a 1 bit digital technique is developed. The method utilises the information in the zero crossings of the signal, rather than sampling and voltage quantisation, to reconstruct the signal. An intuitive view of the spectrum of a frequency-modulated square wave (FMSW) is derived, and confirmed by mathematical analysis. The spectrum consists of a series of harmonics of the form associated with the modulation law used. The bandwidth and TB product of the harmonics increase in direct proportion to the order of the harmonic. The effect of the time quantisation of the zero crossings necessary to generate a FMSW using digital logic is analysed. The relationship between the time quantisation, signal bandwidth and clock frequency is discussed. The generation of nonlinear FM pulses is illustrated using a truncated Gaussian 15 dB spectrum, and the effect of the time quantisation on the compressed pulse sidelobe levels is computed. The effect of Doppler shift on the sidelobe levels is also illustrated. Hardware for generating FMSWs is described, and the effect of the logic risetime on the spectrum is analysed. The concept of the FMSW is verified using a simple TTL circuit to generate a LFM pulse.

CHIRP Doppler radar

The idea of combining the clinical procedure known as Reconstruction Tomography, and the radar processing for linear FM pulse compression, in order to map radar backscatter energy, is explained. A possible configuration is described.

Possible neural mechanisms of target distance coding in auditory system of the echolocating bat Myotis lucifugus.

1. In order to investigate the possible neural mechanisms underlying delay-dependent facilitation in the bat's auditory cortex (18), the responses to single FM pulses of varying amplitude were examined. Analysis of amplitude-spike count functions revealed three distinct types: monotonic, simple nonmonotonic, and complex nonmonotonic. The complex nonmonotonic function had two separate amplitude peaks, with a clear notch or worst amplitude between them. Other units had spike count functions that were mainly monotonic or nonmonotonic, but showed some evidence for a second response region. 2. Examination of response latency revealed another novel response property, which has been termed the paradoxical latency shift. Units with this response property responded at a shorter latency to sounds of low amplitude than to sounds of high amplitude. The paradoxical latency shift also appears to be related to the twin-peaked complex nonmonotonic response function. Units with the most prominent twin-peaked response functions also had the clearest latency shifts. In these units, the high-amplitude peak corresponded to the long-latency response and the low-amplitude peak to the short-latency-response. 3. These curious spike count and latency observations can be explained if they are considered in relation to the temporal and amplitude pattern of the acoustic input during echolocation. In echolocation, a loud orientation pulse is followed by a weaker echo. In delay-dependent facilitation, this pulse-echo sequence is followed by a neural response if the pulse-echo delay is appropriate. The simplest model for delay-dependent facilitation assumes that a synchronization of excitatory inputs from the pulse and echo is needed for facilitation. Since the weaker echo occurs after the pulse, it is closer in time to the postulated synchronization point. Therefore, in order for this model to work, the echo input must reach the summation place with less of a time lag than the pulse input. This is exactly what is seen with the paradoxical latency shift; the loud "pulse" response is delayed relative to the weak "echo" response.

Effect of Fresnel ripples on sidelobe suppression in low time-bandwidth product linear FM pulse compression

Effect of Fresnel ripples on sidelobe suppression in low time-bandwidth product linear FM pulse compression

Suppression of sidelobes in rectangular linear FM pulse compression radar

Application of a cubic phase predistortion function to the rectangular transmitted pulse significantly reduces the peak time side-lobe level of Hamming weighted linear FM pulse compression radars with time-bandwidth (TB) products less than about 60 and yields a more rapid falloff of far sidelobes.

Subglottic pressure and the control of phonation by the echolocating bat,Eptesicus

1. The respiratory dynamics of phonation, particularly the relationship between subglottic pressure and the sound pressure level (SPL), frequency and duration of vocalizations by nine bats (Eptesicus fuscus) is described. 2. Subglottic pressure rises to about 30 or 40 cm H2O immediately prior to emission of a single FM pulse or group of pulses, respectively, and drops 5 to 20 cm H2O during the course of each pulse (Fig. 2). 3. The maximum SPL of the echolocative pulse is positively correlated with the magnitude of the subglottic pressure at the onset of phonation in eight bats. The unusually high subglottic pressure in bats is an adaptation for the production of high intensity orientation pulses, thus increasing the range of echolocation. 4. The maximum SPL was proportional to the subglottic pressure at the pulse onset raised to a power which ranged from a mean of 0.4 to 1.36 for individualEptesicus (Fig. 3 and Table 1). The approximately linear relationship between sound pressure level and onset subglottic pressure in several bats suggests the vocal tract has a minimal effect on pulse intensity. 5. Within a given vocalization, upward sweeping FM is usually associated with either constant or increasing subglottic pressure (Figs. 4 and 5), but the absolute value of the subglottic pressure at pulse onset is correlated with the initial frequency of vocalization in only four of these bats (Table 2). 6. Subglottic pressure drops most rapidly during short pulses, but during long vocalizations (exceeding 20 ms) it attains a minimum rate of decline of about 0.2 cm H2O/ms (Fig. 6 and Table 2), which may be determined by the maximum glottal resistance at which phonation can occur. 7. The relatively non-compliant lung ofEptesicus (mean static compliance = 0.021 ±0.002 ml/cm H2O) may be an adaptation for the production of the unusually high subglottic pressures needed to produce high intensity echolocative pulses.

FM pulses in stratified isotropic plasma

A study of signals excited by FM pulses in an infinite inhomogeneous cold isotropic plasma is presented. The medium is assumed to vary arbitrarily with position, though sufficiently slowly with respect to all wavelengths contained in the source spectrum. For simplicity only one spatial dimension is considered, but the development may be extended to include more space variables. After deducing integral representations that are evaluated asymptotically, the theory is applied to a particular plasma inhomogeneity characterized by an exponential variation of plasma frequency. Space-time rays associated with an impulsive source are shown to justify the use of time-inversion in establishing the required phase of an FM pulse capable of producing an optimally compressed signal at a particular space-time point. Since ordinary asymptotic methods fail in the neighborhood of such a focal point, a theory that in a prior study described signals in the focal region of a homogeneous plasma is applied to signals in a plasma with exponentially varying plasma frequency. Computed results based on this theory display the character of optimally compressed signals in focal regions.

Array Dispersion Effects on Matched Filter Output for a Linear FM Signal

The response of a matched filter to a linear FM pulse transmitted and received through a linear phased array after return from a stationary target is studied with the matched filter assumed to be matched to the undistorted pulse. The investigation is carried out for three different feed arrangements: the parallel feed, the series end-feed, and the series center-feed. The results are presented in a general manner so as to apply to an arbitrary linear array.

Modulation Diversity for Pulse-Compressing Radars

Radars using wideband FM pulses in the same band are less likely to interfere if one of them uses linear FM and the other uses hyperbolic FM. This can be done without sacrificing Doppler tolerance and without separate software to accommodate the range-Doppler coupling.

A SAW planar piezoelectric convolver

An increase of the dynamic range of a surface-wave piezo-electric convolver can be obtained by increasing its bilinear factor. We show that this can be done by reducing the acoustic beamwidth in the interaction region. A lower limit of beamwidth is found through the study of the guided modes in the convolver plate. A 600-BT product device using nonsymmetrical couplers to obtain the beamwidth reduction is described. The main characteristics-bandwidth, dynamic range, spurious signals-are given and we show a linear FM pulse autocorrelation performed in this device.

Fast acousto-optic lens Q switch

A fast acousto-optic Q switch has been demonstrated which relies on a linear FM pulse of acoustic energy to act as a moving lens. While one corrdinate of the focus of the lens is fixed by the rate of frequency sweep, the other coordinate is ’’swept’’ in time by the frequency variation of the pulse. The on time of the switch is proportional to the reciprocal of the pulse bandwidth. Experiments have been conducted which verify the characteristics of this technique. A TeO2 Bragg cell was used in a successful attempt to Q switch a Nd/YAG laser with the acousto-optic lens approach.

Experimental studies of the ontogeny of ultrasonic vocalizations in bats.

The ontogeny of FM pulses emitted by bats is a process of maturation that is not easily altered by experimental manipulation during early development. Infants that were hand-raised and infants that were raised by mothers with altered voices (the superior laryngeal nerves were cauterized pre- and postpartum) emitted normal adult calls. Effects of pinching the superior laryngeal nerves of young bats with a cold forcepts on their vocalizations suggest that the development of this nerve and its associated musculature occurs early in the bat's postnatal life.

Digital matched filtering with pipelined floating point fast Fourier transforms (FFT's)

A special floating point arithmetic technique for fast Fourier transform (FFT) processors has been developed. The implementation of a high-speed pipeline FFT matched filter using the method employs significantly fewer components than a fixed-point processor with an equivalent performance level. The special floating point process avoids the nonlinear effects of fixed-point processors while achieving performance levels of traditional floating point arithmetic. Computer simulations were used to examine the performance of the system for linear FM pulse compression under a variety of conditions. In a specific case, with 8 bits plus sign quantization of the complex I- and Q-mantissa words in the processor and a 12-stage (4096-coefficient) FFT convolver, the mean square error (MSE) of the sidelobes relative to the peak from a single point target was less than -70 dB. Changes in waveform duration and sampling rate had negligible effect on the error level. This error characteristic can be treated as a computational or self noise, added to the input thermal noise of the radar receiver. Quantization artifacts or noise peaks which occur at levels consistent with the mantissa quantization are below levels (-50 dB for 8 bits plus sign) which would normally cause difficulty in an operational system.

Coherence of Sea Surface Reflected Pulses

Forward reflected undersea pulses are known to fluctuate and undergo severe distortion from arrival to arrival. The coherence of high-frequency surface reflected pulses has been measured by cross correlating the transmitted pulse with the reflected arrival. Both pulsed CW and linear FM pulses were utilized, with bandwidths ranging from 50 to 2000 Hz. Considerable care was taken to resolve the surface path from direct and bottom arrivals, thus enabling one to compute a normalized cross-correlation coefficient versus bandwidth. Data strongly shows that the normalized coefficient decreases with increasing bandwidth. Temporal elongation of the reflected pulse appears to be the major cause of decorrelation of the wider bandwidth signals. A statistical model of the sea surface is adopted based upon known properties such as the dependence of mean-square slopes and correlation lengths upon wind speed. Ray theory is used to compute the expected number of ray paths from facets and their attendant travel times. The problem is tractable, assuming Gaussian surface statistics. Woodward cross-ambiguity theory then allows one to predict signal coherence loss due to time spreading from the foregoing analysis, resulting in good agreement with experiment.

On the derivation of Zone I spectra for a pulsed finite-amplitude source operating in a nonviscous nondispersive fluid medium

A mathematical procedure for deriving the complex spectral amplitudes generated by nonlinear interaction of the frequency components of a pulsed finite-amplitude source in a nonviscous nondispersive fluid medium, within a distance prior to shock formation, is established. In order to illustrate the procedure, the nonlinear propagation spectra of a dual frequency pulse and a dual sweep linear FM pulse are derived.

Response of Deep-Ocean Sound Channels to Wide-Band Pulses

Wide-band signals received at long range in a SOFAR channel are distorted and dispersed during transmission. In addition to temporal dispersion explained by ray theory, there is frequency structure that is best explained by mode theory. Explicit prediction of the time-frequency structure of the received waveform given the projected pressure pulse can be made for arbitrary sound-velocity profiles by using the WKB approximation. The response of deep-ocean sound channels to various pressure pulses including an impulse, an impulse pair, and a linear FM pulse has been investigated. It is shown that observed phenomena such as combined ray and mode propagation, and bubble pulse modulation of the spectrum, can be predicted by WKB mode theory.

Neural processing mechanisms in echolocating bats, correlated with differences in emitted sounds.

Bats that emit pulses containing constant wavelength (CW) components preceding an FM sweep show neural adaptations that differ conspicuously from those of bats emitting purely FM pulses. In contrast to “FM bats,” which have sharply tuned units distributed broadly throughout the range of their emitted pulses, “CW bats” have auditory systems tuned predominantly to a much smaller range corresponding to the restricted range of emitted frequencies. There is an “off”-response sharply tuned to the emitted CW frequencies. “On” response sensitivity is greater at just lower frequencies (CW component of less than 8-msec duration) or on either side of the “off”-frequency, with a null at that point (CW component of 10–20 msec or longer). The “off”-response, which is present at the level of the auditory nerve, apparently represents rebound excitation following non-neural suppression peripheral to the primary afferent fibers. It reflects a mechanism for increasing frequency discrimination and has the effect as well of enhancing response to the FM portion of the emitted pulses. High sensitivity to frequencies above that of the emitted CW, in “long CW” bats, is apparently tied to a use of the Doppler-shifted echo CW to detect and determine the angle and/or relative velocity of echo sources. CW bats show much less dramatic temporal resolution ability than FM bats, although it seems probable that the same mechanism of distance determination—measurement of elapsed time between emitted and returning FM sweeps—is used by both. CW bats, on the other hand, appear to have more units that are sharply sensitive to signal angle, showing strong binaural interaction. The consistent and conspicuous differences in neurophysiology in different species indicates not only that central analytic mechanisms are highly adaptable, but that these adaptations are important and closely tied to the types of orientation sounds used.