Sampling, discrete frequency

The measurement technique depends upon the determination of the attenuation and phase shift of a microwave signal transmitted through the sample at 22 discrete frequencies. These values are processed via an algorithm to provide an accurate measure of the moisture content. Other types of interrogation schemes are available such as antennas which allow measurements to be made on products on a conveyor system. 

Unfortunately, the result shown in Figure 2 corresponds to time-shared (i.e., essentially simultaneous) excitation/detectlon, so that the (discrete) frequencies sampled by the detector are the same as those initially specified in synthesis of the time-domain transmitter signal. However, FT/ICR is more easily conducted with temporally separated excitation and detection periods. In practical terms, the result is that for FT/ICR, we need to know the excitation magnitude spectrum at all frequencies, not just those (equally-spaced) discrete frequencies that defined the desired excitation spectrum. 

As the interferogram passes through the sample, selective frequencies are absorbed, and the resulting interferogram is transformed into a normal spectrum, by means of a discrete fourier transformation. 

Just as the discrete Fourier transform generates discrete frequencies from sampled data, the discrete wavelet transform (often abbreviated as DWT) uses a discrete sequence of scales aj for j < 0 with a = 21/v, where v is an integer, called the number of voices in the octave. The wavelet support — where the wavelet function is nonzero — is assumed to be -/<72, /<72. For a signal of size N and I < aJ < NIK, a discrete wavelet / is defined by sampling the scale at a] and time (for scale 1) at its integer values, that is... 

For the first problem, we choose a sufficiently large interval L such that the samples outside 0 < n second problem, we will use a similar operation to time domain sampling and sample the spectrum at discrete intervals. Just as w = t.Ts, we define the spacing between each discrete frequency as Fg/N = I/ NTs) where N is the total number of frequency values we want. Each angular frequency therefore lies at... 

Magnetization transfer (MT) or cross-relaxation spectroscopy, also termed Z-spectroscopy by Grad and Bryant (1990), has been extensively used to obtain information on the spectral Uneshape of protons in macromolecules as well as on relaxation in heterogeneous systems (Calucd and Forte 2009). A MT spectrum was obtained by performing saturation transfer (ST) experiments at many discrete frequencies and plotting the ratio of the steady-state water signal with and without RF saturation as a function of the saturation frequency offset. For spatially homogeneous samples,... 

Lasers can also be used as simple excitation sources for optical transitions. Mono or discrete frequency lasers, such as the ruby and argon discharge lasers, were used early on to excite various types of collective excitations through the Raman and Brillouin effects. Information on luminescence processes in a sample... 

Confocal laser raman spectroscopy (LRS). Chemical speciation of elements in soil particles can be analysed by LRS, which yields information on chemical bonding (Banwell McCash 1994). A portion of any light scattered by the specimen has certain discrete frequencies above and below that of the incident radiation, which are characteristic of electrical polarizability of chemical bonds within the specimen. Chemical compounds within soil particles can be identified by comparison of their vibrational spectra with those of reference compounds. Microscope Raman devices can analyse areas of down to 1 m. As water is a weak Raman scatterer (so there is little interference with the signal), LRS can be used with wet samples that are close to their natural state. 

In practical applications, x(t) is not a continuous function, and the data to be transformed are usually discrete values obtained by sampling at intervals. Under such circumstances, I hi discrete Fourier transform (DFT) is used to obtain the frequency function. Let us. suppose that the time-dependent data values are obtained by sampling at regular intervals separated by [Pg.43]

We first discuss signal enhancement in the time domain, which does not require a transform to the frequency domain. It is noted that all discrete signals should be sampled at uniform intervals. 

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