Frequency, carrier domain

In the directly acquired dimension the spectral window can be opened up to cover all frequencies of interest on both sides of the carrier with a proportional increase in the overall data size. As an alternative, it may be sufficient to open the (audio)filters to allow signals to alias to empty regions (if any) with no intensity loss. Carrier shift using time domain tools in data processing can be applied to restore a more convenient arrangement of the spectrum [10]. 

The pulse has a real-valued envelope t) and oscillates with the carrier frequency Q. Because ultrafast laser pulses are too short to be shaped directly in the time domain, the pulse is manipulated in the frequency domain. To this end, a linear spectral transfer function M co) is applied to the pulse spectrum (m), with... 

This technique can be thought of as the time-domain dual of sine-wave-based onset estimation of section 7 since the estimated slope is the carrier frequency which represents the frequency around which the spectrum of s(n) is situated. In onset-time estimation, a straight line whose slope corresponds to the onset time of the system response is fit to the measured sine-wave phases in frequency [McAulay and Quatieri, 1986a],... 

Varian VXR 500 NMR spectrometer operating at a proton frequency of 500 MHz. The spectral width was 6000 Hz with the carrier frequency at the HDO resonance. The solvent resonance was suppressed by presaturation. Each FID was composed of 16 k data points with 80 transients. The delay between successive transients was 2.8 s. The time domain data were processed by zero-filling to 32 k points, exponential multiplication (0.5 Hz) and Fourier transformation. Chemical shifts were referenced to internal sodium 3-(trimethylsilyl)-propionate-2,2,3,3-d4. The Kj values were obtained by nonlinear least square fit of the data to the equation... 

Figure 3 Sampling in the frequency domain (a) Modulated signal, x has frequency spectrum Xp (b) Harmonics of the carrier signal (c) Spectrum of modulated signal is a repetitive pattern of Xp and Xpcan be completely recovered by low pass filtering using, for example, a box filter with cut-offfrequency (d) Too low a...

Now we show you a sketch of what is happening in the frequency domain. The rf carrier frequency is at which is chosen so that the entire spectrum of interest is bracketed between and v +Av or v -Av (but not both) where 2Av is the digitizing rate. In a single phase detection experiment the folding problem is avoided by deliberately locating the carrier frequency to one side of all spectral features and ignoring the other side of There are a couple of fairly... 

Figure 4 shows the frequency domain spectra obtained with our pulsed Fourier transform spectrometer for c(13)h20 in natural abundance displayed on an oscilloscope. The formaldehyde pressure was approximately 1 mTorr. The spectra cover 25 MHz and each frequency point corresponds to 100 KHz. The displayed line corresponds to the 111 llO t otational transition of c(13)h20 at 4593.3 MHz. The carrier frequency, ff/ o, was kept at 4 MHz off-resonance in the upper spectrum and 21 MHz off-resonance in the lower spectrum. Both spectra were obtained after an averaging time of 15 sec and an optimum exponential filter was used in the digital conversion. The line has an absorption coefficient of 6 x 10 8 cm"l. The obtained signal-to-noise ratio (peak signal amplitude to rms noise amplitude) is approximately 50 1. 

The regular pulse train of a mode-locked laser with the pulse-repetition frequency / corresponds in the frequency domain to a spectrum consisting of the carrier frequency vq = col2n and sidebands vq . q f q e N) (Sect. 6.1.4). If a molecular sample with a level scheme depicted in Fig. 7.13b and a sublevel splitting An = 2qf in the lower state is irradiated by such a pulse train, where the frequency vq is chosen as vo = (vi + v2 /2, the two frequencies vi,2 = vo qf are absorbed on the two molecular transitions vi, V2. This may be regarded as the superposition of two Raman processes ([1) 2) -> 3) Stokes process) and ( 3) 2) 1) anti-Stokes process), where the population of the two sublevels 1) and 13) oscillates periodically with the frequency Av = AE/h. The level splitting AE can be obtained much more accurately from this oscillation frequency than from the difference of the two optical frequencies vi, V2. 

Figure 16 shows the results of an experimental measurement of the frequency response of the four-wave mixing process in an SOA. The experimental technique used is a frequency domain pump-probe measurement, illustrated schematically in Fig. 16(a). Two optical carriers are injected into the SOA, a strong pump signal Pp and a much weaker probe signal Pq. The frequency detuning is defined to be the probe frequency minus the pump frequency, i.e., The power Ps of the... 

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