Linear frequency modulation

Keywords continuous wave radar linear frequency modulation noise radar noise ... 

Linear Frequency Modulated Continuous Wave Radar... 

Having defined the utility of a waveform library we go on to investigate the utilities of a few libraries. Specifically, we consider libraries generated from a fixed waveform 4>o, usually an unmodulated pulse of some fixed duration, by symplectic transformations. Such transformations form a group of unitary transformations on L2(R) and include linear frequency modulation as well as the Fractional Fourier transform (FrFT) in a sense that we shall make clear. 

This section describes a new waveform design for automotive applications based on CW transmit signals which lead to an extremely short measurement time. The basic idea is a combination of linear frequency modulation (LFM) and FSK CW waveforms in an intertwined technique. Unambiguous range and velocity measurement with high resolution and accuracy can be required in this case even in multi-target situations. After introductions to FSK and LFM waveform design techniques in sections 2.1 and 2.2 the combined and intertwined waveform is described in detail in section 2.3. 

The most common frequency modulated continuous wave-form employs a linear frequency pattern (Richards, 2005), where B is the swept bandwidth, f o is the starting frequency, T is the sweep duration and //the linear frequency modulation coefficient. 

Figure 2. Linear frequency modulated continuous waveform.

Linear frequency modulation (LFM) pulse compression Doppler filtering SAR/ISAR imaging... 

The linear frequency modulated (LFM) waveform is one of well-known and most useful radar pulse compression waveforms due to its high range resolution (depended of the waveform bandwidth) and its tolerance to Doppler shift and easy for the receiver processing. 

Lewis B.L., Kretschmer F.F., Linear frequency modulation derived polyphase pulse compression codes, IEEE Trans, on Aerospace and Electronic Systems Vol. AES-18, N5, Sept. 1982, pp. 637-641. 

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

It should be noted that there is a considerable difference between rotational structure narrowing caused by pressure and that caused by motional averaging of an adiabatically broadened spectrum [158, 159]. In the limiting case of fast motion, both of them are described by perturbation theory, thus, both widths in Eq. (3.16) and Eq (3.17) are expressed as a product of the frequency dispersion and the correlation time. However, the dispersion of the rotational structure (3.7) defined by intramolecular interaction is independent of the medium density, while the dispersion of the vibrational frequency shift (5 12) in (3.21) is linear in gas density. In principle, correlation times of the frequency modulation are also different. In the first case, it is the free rotation time te that is reduced as the medium density increases, and in the second case, it is the time of collision tc p/ v) that remains unchanged. As the density increases, the rotational contribution to the width decreases due to the reduction of t , while the vibrational contribution increases due to the dispersion growth. In nitrogen, they are of comparable magnitude after the initial (static) spectrum has become ten times narrower. At 77 K the rotational relaxation contribution is no less than 20% of the observed Q-branch width. If the rest of the contribution is entirely determined by... 

As a consequence of the spectral modulation, the temporal width of the laser pulse is modified and a linear frequency sweep (chirp) is introduced. The modulated pulse duration is... 

We can divide synthesis techniques into four basic categories Additive (Linear), Subtractive, Nonlinear and Physical modeling. Synthesis algorithms depend critically on the implementation of oscillators. For example, in the implementation of Frequency Modulation (F.M.), the output of one oscillator will serve as the input to another. Since the number of real time oscillators depends on the number of simple oscillators, it is important to efficiently and speedily implement the realizations. 

A Kubo analysis was attempted as a first approach to interpreting these data (61,63). The dephasing is attributed to a single frequency modulation process characterized by a magnitude A0J and a correlation time tr . The decay at each temperature was fit to Equation (7) to find these parameters. The results are plotted in Fig. 16. As expected, the magnitude of the frequency perturbations is independent of temperature. However, the correlation time shows a linear correlation to the viscosity of the solution. This... 

Figure 8 Simplified diagram of the FM NMOR setup. The balanced polarimeter incorporating the polarizer, analyzer, and photodiodes PD1 and PD2 detects signals due to the time-dependent optical rotation of linearly polarized frequency-modulated light.

In an FM MMW spectrometer the spectral source frequency is modulated at a certain rate /, typically 1 kHz. This gives rise to sidebands of the spectral source frequency above and below the carrier frequency. The frequency modulated MMW carrier has in its modulation envelope phase and amplitude relationships to the carrier. Mixing in the non-linear junction of the detector yields the modulation signals altered by their interaction with the cavity and gas inside it, with their preserved amplitude and phase relationship to the original modulation signals. Those properties are measured by passing the heterodyne mixer output and the thermal noise contribution from the mixer, to a filtered phase-sensitive detection system, with the original modulation as reference. 

Automatic tuning can be substituted for manual firequency variation. Instruments employing such frequency modulated signals have been in use for many years for measuring thickness by ultrasonic resonance. This resonance electric equipment usually does not provide a linear amplitude vs frequency readout and is therefore only suitable for the detection of resonance peaks in spectra. 

FIGURE 20 The pulse compression experiment of Grischkowsky et al., in which self-phase modulation and group velocity dispersion of a pulse in an optical fiber are balanced to produce a linear frequency chirp in the output pulse. The two passes off the diffraction grating constitute a dispersive delay time, which compresses this pulse to one-twelfth the width of the input pulse. [Reprinted with permission from Nikolaus, B., and Grischkowsky, D. (1983). Appl. Phys. Lett. 42, 1.]... 

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