Frequency filtering

The phase shift is At fo cp = 45°, at lOfo cp = 5.7°, and at lOOfo cp = 0.57°. The phase shift in a filter is thus substantial even far away from die comer frequency in the passband, and the frequency must be much higher than the corner frequency to ensure negligible phase shift. 

If a repetitive signal is applied to the tissue electrodes via a high-pass filter, no DC polarization is possible. 

The same precaution holds for the phase shift to ensure low phase shift, the frequency must be much lower than the corner frequency. These low-pass filtering effects are an important source of error when reading signals through such high-impedance systems as microelectrodes because of inevitable stray capacitance between the inner conductor and the surrounding tissue. 

Measurement of Immittance with an Endogenic Signal Source 

It is possible to determine the immittance of an electrode system without the use of exogenic signal sources. An endogenic signal is recorded, and the electrode system is loaded with a known admittance in parallel. The reduction in signal amplitude is measured as a function of the admittance load. The source immittance can be then be calculated. 

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Most niobates and tantalates, however, are insoluble and may be regarded as mixed oxides in which the Nb or Ta is octahedrally coordinated and with no discrete anion present. Thus KMO3, known inaccurately (since they have no discrete MO3 anions) as metaniobates and metatantalates, have the perovskite (p. 963) stmcture. Several of these perovskites have been characterized and some have ferroelectric and piezoelectric properties (p. 57). Because of these properties, LiNb03 and LiTa03 have been found to be attractive alternatives to quartz as frequency filters in communications devices. 

A detachable monochromator (19) developed by Spex Industries, was another approach in minimizing stray light. It is a modified Czerny-Turner spectrograph which can be coupled to the exit slit of a double monochromator and function as a variable bandpass, variable frequency filter. This accessory, while providing the versatility of a triple monochromator, does not add much mechanical and optical complexity and can be removed when not wanted. 

Figure 2.9.11 shows schematically the experimental set-up of the ionic current device. The sample is packed between two electrodes that are shaped meander-like in order to avoid eddy currents due to pulsed field gradients. The high frequency filter is essential to prevent an antenna effect of the electrode cables inside the magnet. 

The classical treatment of diffuse SAXS (analysis and elimination) is restricted to isotropic scattering. Separation of its components is frequently impossible or resting on additional assumptions. Anyway, curves have to be manipulated one-by-one in a cumbersome procedure. Discussion of diffuse background can sometimes be avoided if investigations are resorting to time-resolved measurements and subsequent discussion of observed variations of SAXS pattern features. A background elimination procedure that does not require user intervention is based on spatial frequency filtering (cf. p. 140). 

Figure 8.19. Extraction of the scattering of an ideal two-phase structure from the raw scattering data of an isotropic UHMWPE material by means of spatial frequency filtering... 

By means of this procedure our problem is not only reduced from three to two dimensions, but also is the statistical noise in the scattering data considerably reduced. Multiplication by —4ns2 is equivalent to the 2D Laplacian89 in physical space. It is applied for the purpose of edge enhancement. Thereafter the 2D background is eliminated by spatial frequency filtering, and an interference function G(s 2,s ) is finally received. The process is demonstrated in Fig. 8.27. 2D Fourier transform of the interference function... 

The important point is that capacitors will, therefore, allow the flow of AC in preference to DC. Because there is less time for current to decay in a high-frequency AC circuit before the polarity reverses, the mean current flow is greater. The acronym CLiFF may help to remind you that capacitors act as low-frequency filters in that they tend to oppose the flow of low frequency or DC. 

Because the initial emphasis of this study was on extending ACC to liquid-fueled combustors, a simple closed-loop controller, which had been well tested in the previous studies involving gaseous fuel, was utilized. Such a controller, however, may not be effective in a combustor where the oscillation frequencies drift significantly with the control. The main problem was the frequency-dependent phase shift associated with the frequency filter. For such a case, it would be more useful to employ an adaptive controller that can rapidly modify the phase setting depending on the shift in the dominant oscillation frequencies. 

Figure 8. Frequency-filtered Na2+ pump-probe signal in comparison to the averaged signal of Fig, 4. The filtered signal measures by how much the Na2+ signal is modulated with the laser frequency. Such modulations occur when there is interference between excitation by the probe pulse and the wavepackets formed by the pump laser pulse. This interference effect causes both the A EJ and the 2 1 Ilg state wavepacket motion to be observable in the signal.

On the other hand, additional spectroscopic information can be obtained by making use of this technique The Fourier transform of the frequency-filtered transient (inset in Fig. 8) shows that the time-dependent modulations occur with the vibrational frequencies of the A E and the 2 IIg state. In the averaged Na2+ transient there was only a vanishingly small contribution from the 2 IIg state, because in the absence of interference at the inner turning point ionization out of the 2 IIg state is independent of intemuclear distance, and this wavepacket motion was more difficult to detect. In addition, by filtering the Na2+ signal obtained for a slowly varying pump-probe delay with different multiples of the laser frequency, excitation processes of different order may be resolved. This application is, however, outside the scope of this contribution and will be published elsewhere. 

By the use of frequency filters (RG circuits) which cut off the high frequency noise from a low frequency signal. Care must be taken to avoid distortion of the signal. An RC circuit as shown below is a low pass filter of time constant t = RG. This gives a rough value of the cut-off frequency. 

This technique does not present the potential danger of distortion of the signal mentioned above for frequency filters. An example of the improvement of the S/N ratio with averaging is shown in the Figure below. 

H (f) = 0 at high frequencies ( f > fo), where fo is the limiting cut-off frequency of the high-frequency filter, which is chosen according to the noise performance of the measuring instrument and the resolving time of the retrieved signal. 

The transfer characteristics of the high-frequency filter defined by expression (3.9) are ideal. In practice, it is impossible to achieve the ideal filter, so various approximations of the ideal filter must be used. The design of filters approximating the ideal form have been discussed by numerous authors. One simple design uses a filter described by expression (3.9) with the addition of a second-order filter.161... 

Figure 3.7. Unit-step responses of an instrument (a) and of a high-frequency filter (b) in the same frequency range 1 - no filter 2 - with a filter 3 - ideal filter characteristic 4 - approximation by a second order Butterworth filter.

It should be noted that the Lamb equation is appropriate for a low frequency filter rather than a resonant phenomenon such as spectral absorption by the chromophores. Its asymptotic character at short wavelengths leads to a half-amplitude value that is quite different from the similar half-amplitude value for a resonant phenomenon of arbitrary resonance factor, Q. 

Capacitors are used to store electric energy, especially for shorter periods of time, and substitute -> batteries in some cases. They smooth the output of full or half-wave rectifiers in power supplies or are part of electric frequency - filters. 

The discovery by R. M. White of the University of California at Berkeley that surface acoustic waves could be excited and detected by lithographically patterned interdigital electrodes on the surface of piezoelectric crystals [42] has led to widespread use of SAW devices in a number of signal-processing applications. These include frequency filters, resonators, delay lines, convolvers, and correlators [43,44]. 

Thomson AM. Molecular frequency filters at central synapses. Prog. Neurobiol. 2000 62 159-196. 

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