Filter second-order

The flame-photometric detector (FPD) is selective for organic compounds containing phosphoms and sulfur, detecting chemiluminescent species formed ia a flame from these materials. The chemiluminescence is detected through a filter by a photomultipher. The photometric response is linear ia concentration for phosphoms, but it is second order ia concentration for sulfur. The minimum detectable level for phosphoms is about 10 g/s for sulfur it is about 5 x 10 g/s. 

I will use a second-order, common-mode filter. The frequency of operation is 100 KHz. A good starting point is to assume the need for 24dB of attenuation at 100 KHz. That make the corner frequency of the common-mode filter... 

The first major pole is contributed by the output L-C filter. It represents a second order pole which exhibits a Q phenomenon, which is typically ignored, and a -40dB/decade rolloff above its corner frequency. The phase plot will quickly begin to lag starting at a frequency of 1/lOth the corner frequency, and will reach the full 180 degrees of lag at 10 times the corner frequency. The location of this double pole is found from... 

Figure E-5 Frequency response of a second-order common-mode filter L = 1 mhl).

Figure 3.11. Smoothing a noisy signal. The synthetic, noise-free signal is given at the top. After the addition of noise by means of the Monte Carlo technique, the panels in the second row are obtained (little noise, left, five times as much noise, right). A seven-point Savitzky-Golay filter of order 2 (third row) and a seven-point moving average (bottom row) filter are...

Scale-space filtering provides a multiscale description of a signal s trends in terms of its inflexion points (second-order zero crossings). The only legal sequences of triangles between two adjacent inflexion points are (in terms of triangular episodes) ... 

Hirose et al. [26] proposed a homodyne scheme to achieve the background-free detection of the fourth-order field. With pump irradiation in a transient grating configuration, the fourth-order field propagates in a direction different from that of the second-order field because of different phase match conditions. The fourth-order field is homodyned to make ffourth(td. 2 D) and spatially filtered from the second-order response hecond td, 2 D). 

This process, according to the manufacturer,54 has been developed in such a way that space requirements are kept to a minimum. A BIOPAQ IC reactor is used as the initial step in the treatment process. The name of this anaerobic reactor is derived from the gas-lift driven internal circulation that is generated within a tall, cylindrical vessel. These reactors have been operational in the paper industry since 1996. The second step in the purification process is a mechanically mixed and aerated tank. The aerating injectors can be cleaned in a simple way without the need to empty the aeration tank. Potential scaling materials are combined into removable fine particles. At the same time, the materials that may cause an odor nuisance are oxidized into odorless components. The process can be completed by a third and a fourth step. The third step focuses on suspended solids recovery and removal. The fourth step is an additional water-softening step with lamella separation and continuous sand filters in order to produce fresh water substitute. The benefits claimed by the manufacturer are as follows54 ... 

Figure 13 Timing diagram for the clean HMBC experiment with an initial second-order and terminal adiabatic low-pass 7-filter.42,43 The recommended delays for the filters are the same than for a third-order low-pass J filter. <5 and 8 are gradient delays, where 8 — <5 + accounts for the delay of the first point in the 13C dimension. The integral over each gradient pulse G, is H/2yc times the integral over gradient G2 in order to achieve coherence selection. The recommended phase cycle is c/)n = x, x, x, x 3 — 4(x), 4(y), 4( x), 4(—y) with the receiver phase c/)REC = x, x.

Little, B. E. Chu, T. Haus, H. A., Second order filtering and sensing with partially coupled traveling waves in a single resonator, Opt. Lett. 1998, 23, 1570 1572... 

Gratings also diffract light in the second, third and higher orders. If a grating reinforces light at 600 nm in the first order, it will also reinforce fight at 300 nm in the second order and 200 nm in the third order. Gratings are usually paired with simple optical filters to remove unwanted... 

Savchenkov, A.A., Ilchenko, V.S., Elandley, T., and Maleki, L., 2003, Second-order filter response with series-coupled silica microresonators, IEEE Photon. Technol. Lett. 15(4) 543-544. 

The use of a sharp cutoff filter is recommended to avoid second-order interference from the Ne 335.5 nm line emitted by the lamp. 

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.

The modulus of the gain factor of such a filter (Butterworth) is shown in Fig. 3.7 b (curve 4). The total unit-step response of a measuring instrument equipped with a filter determined by the second-order expression (3.12) is presented in Fig. 3.7a (curve 2). Verification tests of the method have given good agreement between theory and experiment. 

HR filters can be implemented in any number of different ways, including direct form, parallel form, cascaded second order sections and lattices. 

A very fast CPU customized for the calculation of second order sections was used by Neve [Lidbetter, 1983] (in collaboration with the BBC) in 1979. They used a Time Division Multiplex (TDM) parallel data bus with 16 time slots. At each time slot, the channel processor executed 14 microinstructions (at a rate of 100 ns) of a filter... 

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