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Showing papers on "Chirp published in 1969"


Journal ArticleDOI
TL;DR: Applications discussed include: enhancement of poles in spectral analysis, high resolution narrow-band frequency analysis, interpolation of band-limited waveforms, and the conversion of a base 2 fast Fourier transform program into an arbitrary radix fast Fouriers transform program.
Abstract: We discuss a computational algorithm for numerically evaluating the z-transform of a sequence of N samples. This algorithm has been named the chirp z-transform algorithm. Using this algorithm one can efficiently evaluate the z-transform at M points in the z-plane which lie on circular or spiral contours beginning at any arbitrary point in the z-plane. The angular spacing of the points is an arbitrary constant; M and N are arbitrary integers. The algorithm is based on the fact that the values of the z-transform on a circular or spiral contour can be expressed as a discrete convolution. Thus one can use well-known high-speed convolution techniques to evaluate the transform efficiently. For M and N moderately large, the computation time is roughly proportional to (N + M) log 2 (N + M) as opposed to being proportional to N · M for direct evaluation of the z-transform at M points. Applications discussed include: enhancement of poles in spectral analysis, high resolution narrow-band frequency analysis, interpolation of band-limited waveforms, and the conversion of a base 2 fast Fourier transform program into an arbitrary radix fast Fourier transform program.

349 citations


Journal ArticleDOI
14 Nov 1969-Science
TL;DR: Snowy tree crickets synchronize their chirps by responding to the preceding chirp of their neighbors, which may advance their phase of chirping 160� and retard it 200�.
Abstract: Snowy tree crickets synchronize their chirps by responding to the preceding chirp of their neighbors. If a neighbor9s chirp precedes his own, a cricket shortens his chirp and the following interval. If it follows his own, he lengthens his chirp interval and sometimes the following chirp. A single response of the first type may advance his phase of chirping 160° and one of the second type may retard it 200°.

310 citations


Journal ArticleDOI
01 Jul 1969
TL;DR: The optimum frequency-modulation law is shown to be the linear period modulation (it can be with equal rights called hyperbolic frequency modulation or logarithmic phase modulation).
Abstract: In applications where large time-bandwidth products and high target speeds combine, linear FM pulse-compression systems used in radar or sonar suffer considerable losses in performance. This paper deals with the problem of wide-band signal optimizintion for the purpose of minimizing signal degradation resulting from Doppler distortion effects. The equation for the instantaneous frequency of a Doppler-transformed signal is derived. The optimum frequency-modulation law is then shown to be the linear period modulation (it can be with equal rights called hyperbolic frequency modulation or logarithmic phase modulation). It is interesting to note that some kinds of bats use this type of signal in their "sonar." Exact and approximate expressions for the spectrum of a linear-period-modulated rectangular pulse are given, and the shape of the compressed output pulse is considered. Signal degradation due to Doppler distortion is shown to be negligible in the case of linear-period-modulation pulses. The influence of pulse envelope on the compressed signal waveform is discussed, and envelope-optimization examples are presented. A possibility for active generation of the optimum signal is mentioned. Significant properties of linear FM and linear-period-modulation pulse compression systems are compared.

148 citations


Journal ArticleDOI
J. Armstrong1, E. Courtens1
TL;DR: In this paper, a steady-state solution for a homogeneously broadened laser amplifier embedded in a dispersive lossy host is found. But the model of dispersion in the host group velocity causes a large frequency sweep during the pulse.
Abstract: A steady-state solution describing \Pi -pulse propagation in a homogeneously broadened laser amplifier embedded in a dispersive lossy host is found. For a given model of dispersion, the solution satisfies exactly the second-order wave equation together with the equations of motion for the density matrix of the two-level resonant system. The salient feature of the solution is that a small amount of dispersion in the host group velocity causes a large monotonic frequency sweep during the pulse. The effects of this chirp on the pulse properties are described in detail, and the relation of the theory to experiments is discussed.

43 citations


Journal ArticleDOI
TL;DR: In this paper, a theory of laser mode locking due to saturable absorbers when the dispersive property of the active material is taken into account is developed. And the authors show that, owing to dispersion, the phase φ l of the modes ( l running from -N to +N ) has a term that is proportional to l 2 and a term (smaller than the previous one) that is proportionally to l 4.
Abstract: A theory is developed of laser mode locking due to saturable absorbers when the dispersive property of the active material is taken into account. The electric field within the cavity is expanded in terms of cavity modes, the problem is treated under the rate-equation approximation, and only third-order nonlinear polarization terms of the dye are considered. The field is assumed to be made of 2N + 1 oscillating modes. It is shown that, owing to dispersion, the phase φ l of the modes ( l running from -N to +N ) has a term that is proportional to l2and a term (smaller than the previous one) that is proportional to l4. In agreement with the experimental results, the term proportional to l2increases the pulsewidth of the total electric field over the case of perfect mode-locking and it also gives a positive linear sweep of the field frequency. The pulsewidth increase is expressed by a factor γ that is proportional to the fourth power of the oscillating bandwidth, to the square of the relaxation time T 1 of the dye, and to the product of the length of the active material times a quantity e that is related to dispersion of the material.

34 citations


Journal ArticleDOI
TL;DR: In this article, a selfconsistent analysis of pulse propagation inside a laser cavity containing, in addition to an amplifying medium, some material displaying the optical Kerr effect, yields ultrashort pulses.
Abstract: A self‐consistent analysis of pulse propagation inside a laser cavity containing, in addition to an amplifying medium, some material displaying the optical Kerr effect, yields ultrashort pulses. These pulses become stable in the limit of high line‐center excess gain with the stabilization provided by an interplay between strong chirping in the Kerr medium and bandlimiting in the laser medium.

21 citations


Journal ArticleDOI
TL;DR: In this article, the authors investigate optical pulse propagation in homogeneously broadened absorbers with an optical Kerr effect nonlinearity and show that the presence of the Kerr effect requires pulse chirping.

17 citations


Patent
16 Sep 1969
TL;DR: In this paper, a laser echo ranging system utilizing a unique modulator for providing an audio signal corresponding to the distance to the target and a simplified inexpensive method of reading the distances is described.
Abstract: The invention disclosed in this application concerns itself with a laser echo ranging system utilizing a unique modulator for providing an audio signal corresponding to the distance to the target and a simplified inexpensive method of reading the distances.

13 citations


Patent
07 May 1969
TL;DR: In this article, the product functions of the sine and the cosine components of the antenna position angle times the radar-sweep function are generated in respective multipliers, each multiplier consists of a first differential amplifier pair coupled push-pull to a second differential amplifier.
Abstract: To display radar data on the face of a cathode-ray tube or other display device, it is necessary to generate product functions of the sine and the cosine components of the antenna position angle times the radar-sweep function. Both the sine product function and the cosine product function are electronically generated in respective multipliers. Each multiplier consists of a first differential amplifier pair coupled push-pull to a second differential amplifier pair. To minimize the effect of line voltage variation on the product functions, the sweep voltage is corrected prior to multiplication with the sine and cosine components in accordance with line voltage variation.

13 citations


Journal ArticleDOI
TL;DR: In this paper, the synthesis of such L-band delay equalizers using a general purpose successive approximation computer program, SUPROX is described, and Linear as well as certain higher order delay characteristics have been synthesized with a high degree of accuracy.
Abstract: The folded-tape meander-line configuration that has been used in the design of compression filters for chirp RADAR applications can also be used in the design of microwave delay equalizers for communication systems. Specifically, it can be utilized in the design of delay equalizers for use in the repeaters of a long distance waveguide transmission system. In this paper, the synthesis of such L-band delay equalizers using a general purpose successive approximation computer program, SUPROX is described. In this procedure, both the locations of the resonant frequencies and the number of meander-line turns at each of these resonant frequencies are optimized to give the final design. Linear as well as certain higher order delay characteristics have been synthesized with a high degree of accuracy. Experimental results show excellent agreement with the theoretical designs.

9 citations


Journal ArticleDOI
TL;DR: In this article, an analytical expression for the frequency sweep (chirp) and pulse width for externally-locked laser with host dispersion was obtained using a self-consistent circulating pulse method.
Abstract: Analytic expressions for the frequency sweep (chirp) and pulse width are given for externally‐locked lasers with host dispersion. The expressions have been obtained using a self‐consistent circulating pulse method. For both phase and amplitude modulation, the pulse is broadened by the host dispersion. However, only phase modulation can give the large frequency sweeps which allow the pulse to be compressed outside the laser. This result helps one to understand some conflicting observations on chirping in the Nd:glass laser.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the results in the above on pulse transmission of saturable absorbers are amenable to analysis by the dynamic transmission model, which is the same model used in this paper.
Abstract: It is shown that the results in the above on pulse transmission of saturable absorbers are amenable to analysis by the dynamic transmission model.

Journal ArticleDOI
R. Abrams1
TL;DR: In this paper, the frequency-swept CO 2 laser pulses generated with an offset rotating mirror have been found to be frequencyswept (chirped) with rates as high as 120 MHz/μs.
Abstract: Q -switched CO 2 laser pulses generated with an offset rotating mirror have been found to be frequency-swept (chirped). Chirp rates as high as 120 MHz/μs have been observed.