Ideal filter

The ideal filter would be one in which the size of the media particles would decrease uniformly in the direction of flow. The coarsest materials would be at the top the finest at the bottom. Fig. 3 illustrates the ideal arrangement. Materials of different densities and sizes would be required to provide the tapered void... 

Fig. 3—Cross-section through ideal filter, uniformly graded from coarse to fine from top to bottom.

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.

If a beam of polarized radiation is passed through a linear polarizing filter, the intensity transmitted is a function of the angle between the filter polarization axis and the polarization direction of the beam. When the angle is zero, all radiation is transmitted (for an ideal filter there are always losses by reflection, background absorption, etc) when the angle is 90°, all radiation is blocked (absorbed) by the filter. 

A variety of filters with a 0.45 im pore size is available. These filters vary in uniformity of pore size, chemical composition, and flow characteristics. Each of these factors affects the performance of the filter and some filters are better suited for the study of aquatic humic substances than others. The ideal filter would be inert relative to compounds of interest, exhibit good flow characteristics, have a uniform pore size, and be reasonably priced. An evaluation of the suitable filters with respect to pore size, chemical composition, and flow characteristics follows. 

This kind of noise is not very realistic, a true ideal filter is "real-time" impossible. However, such a spectrum can be approximated with a higher order filter with sharp cut-off characteristics. 

Roll-cff Roll-off describes the width of the transition band in a filter design. The ideal filter has a transition band of zero and is thought of as a brick-wall filter. Such ideal filters are not realizable in practice, but as we have seen, real filters have a roll-off that can be improved through increasing the filter order. 

In Eq. (20.3) a is the constant gain or attenuation and z is the time delay in passing through the system. With this definition, H f), the Fourier transforms of the ideal filter impulse response and Y(f), the filter output are given by, respectively. 

Figure 20.42 shows the frequency-domain representation of an ideal and a nonideal filter and the time-domain representation of the input and output signals. Figures 20.42(a), 20.42(b), and 20.42(c) show, respectively, the frequency response of the ideal filter, the input signal waveform, and the output signal waveform, which is a time delayed version of the input waveform. Both the filter response and the input signal are bandlimited to B Hz. 

FIGURE 20.42 (a) Ideal filter frequenq response, (b) waveform of input signal, (c) waveform of output signal from ideal filter, (d) nonideal filter frequenq response with ideal phase but nonideal amplitude response, (e) output waveform of nonideal filter showing its components as time shifted versions of the input signal, (f) output waveform of nonideal filter a dispersed version of the input signal. 

This ideal filter can only be approximated. The frequency response is determined by the dimensions of the resistors and conductivities. Generally, a filter with a linear transmission band has a flat transition band, whereas a filter with a relatively sharp transition band has a wavelike transmission band (Fig. 3-26b)... 

It must be emphasized that none of the existing filters and filter materials meet all requirements (from the analytical point of view) for universal application when seawater samples are to be filtered. As modified from RUey et aL (1975) and Howard and Statham (1993), an ideal filter should ... 

If a system is not causal, then it is noncausal. An ideal filter which will filter in real time aU frequencies present in a signal/(t) requires knowledge of /(t) x > t and is an example of a noncausal system. 

An ideal filter of highest value of filter quality coefficient means that it has the maximum separation capacity with minimum pressure loss, and these two parameters remain constant during the service life of filter. The major criteria of the performance of a filter include filter efficiency, pressure drop, and the filter quality performance. ... 

In real life, the availability of spectral filters would be an important consideration. Costs and delivery times of the ideal filter might convince you to settle for an off-the-shelf filter instead of your first choice. 

---