Filter comer frequency

Figure 7. Bilayer conductance induced by affinity-purified connexin-32. A, Sucrose-permeable liposomes formed with affinity-purified connexin-32 were fused with planar phospholipid bilayers as described. Highly filtered (5-Hz comer frequency) currents show unstable conductances, but large, rapid fluctuations that cluster around multiples of about 125 pS may be discerned (arrowheads). The bilayer voltage was 50 mV. B, Higher resolution recording of channels from affinity-purified connexin-32. Records show discrete gating conductance transitions, but with a high rate and amplitude of current fluctuations through the open channels. Unitary conductance is difficult to determine, but is near 200 pS. The bilayer voltage was 100 mV.

If an adjustable-gain high-pass filter has been used to eliminate the low-frequency contamination, the resulting spectrum would look like a band-pass filter spectrum. But, such a filter introduces a limit in the low range of the meter, and a nonlinearity at the lower end of the meter range. The comer frequencies or 3-dB points of such a filter will yield a frequency at the high end that can be related to the lowest possible measurable flow. 

To eliminate DC from an AC signal, a blocking capacitor is inserted. Together with a resistor they form a high-pass filter. Figure 8.10(a). The time constant is RC, and the so called 3 dB comer frequency fo is 1/2tcRC. At that frequency, the phase shift is 45°, and the amplitude has dropped to 63%. This is clear from the transfer function ... 

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. 

The ECG amplifier can readily be designed using the instrumentation amplifier as the principal building block. Active filters with a lower-comer frequency of 0.05 Hz and an upper-corner frequency of 100 Hz are also typically added [8]. 

Differently from PGA, PGV and PGD can be read only after processing the accelerometric record, and their values are strictly related to the band-pass filtering, especially in case of PGD, which strongly depends on the low-cut comer frequency. 

For a sinusoidal motion of arbitrary frequency / = ojI2ti, the modulus of this complex function represents the amplitude relation between the mass relative motion z t) and the ground acceleration u t), and its phase is the relative phase between them. Both are plotted in Fig. 3 as functions of frequency. The amplitude response is flat for acceleration up to the comer frequency/o and decays at higher frequencies as/ The frequencies of interest are usually in the flat zone, so the instmmental correction for amplitude is simply a constant factor. Observe, nevertheless, that the phase response deviates from flatness even for frequencies well under the natural frequency. This response function is formally like the response of a second-order low-pass filter with cutoff frequency/o = (0(J2n. 

Seismic Instrument Response, Correction for. Fig. 4 Amplitude and phase response of an RC filter with a comer frequency of 1 Hz. The phase response (or phase shift) is given in degrees... 

A filter with the desired characteristics (6 dB/octave roll-off on either side of a given frequency) is not difficult to implement - it is basically a combination of a first-order high-pass and a first-order low-pass filter, with both comer frequencies being set to the desired new fo and of course an amplification stage. 

This section illustrates the inversion of three-component waveform data for the seismic moment tensor. A full moment tensor is solved for an earthquake located on the Ha3rward Fault in California. The broadband velocity data were instmment corrected, integrated to displacement, and filtered with an acausal, bandpass, Butterworth filter with comers set at 0.02 and 0.05 Hz. Green s functions were computed for an appropriate layered velocity stracture using a frequency-wavenumber integration method and were bandpass filtered with the same filter applied to the data. Figure 7 shows the fit to the data, the P-wave radiation pattern, and pertinent source information. This earthquake is a tectonic earthquake and the solution is predominantly double couple. The small CLVD and volume increase components are due to noise and episte-mic uncertainty. 

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