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filter, microwave                                                           filter, pi-[section] cavity  192



           belong to the  class of reciprocal multiports.  Ferrite filters,  Multistage filters are used, for example, for matched fil-
           which can be retuned within a frequency band, possess nonre-  tering of pulse-compression waveforms  through cascaded
           ciprocal properties.                                 connection of delay lines. IAM
               Design of microwave filters is quite complex and is done
                                                                A nonlinear filter is one whose input and output signals are
           in several stages, beginning with a simplified circuit, the pro-
                                                                related through nonlinear differential equations. This is typi-
           totype circuit, and ending  with parameter adjustments from
                                                                cal when signals or interference have non-Gaussian distribu-
           the results of experiments.
                                                                tion or when interference  is  not  additive.  In practice,
               Microwave filters are used in microwave circuits and
                                                                quasilinear filtering methods are often used. SAL
           also to form inter-stage connections in receiving and trans-
                                                                Ref.: Korostelev (1987), p. 260; Fal’kovich (1981), p. 203.
           mitting devices. They are also called RF filters. IAM
                                                                nonrecursive filter (see recursive filter).
           Ref.: Saad (1971), p. 153; ITT (1975), Ch. 7–9; Sazonov (1988), p. 122; Gas-
              sanov (1988), p. 51.
                                                                An optical filter is a filter based on the phenomenon of varia-
           A mismatched filter is one that fails to meet the specification  tion of light amplitude and phase when it passes through an
           of a  matched filter and hence  provides an output  signal-to-  optically inhomogeneous medium.  It has broad bandwidth
           noise ratio less than the ratio of input signal energy to noise  and makes it easy to implement multichannel and multifunc-
           spectral density. It thus has a mismatch loss, relative to that  tional signal processing. Practically any frequency and phase
           optimum performance. It is often used in radars to simplify  response can be  synthesized in  the  optical filter. The basic
           the filter design, to reduce time sidelobes in a pulse-compres-  components of the optical filter are the optical system, units
           sion system, or to compensate for expected presence of non-  storing input signal and filter frequency response that are
           white (colored) noise. IAM                           light modulators, and the units of photoelectron registration at
           Ref.: Barton (1964), p. 20, (1969), p. 84; Sloka (1970), pp. 19, 64.  the output. The advantages of optical filters are very suitable
                                                                for analog filtering of pulse-compression waveforms. IAM
           A moving-target-indicator (MTI) filter is a filter intended
           to reject clutter components at and near zero frequency, or  Ref.: Sloka (1970), p. 221; Zmuda (1994), p. 408.
           near the center frequency of the clutter spectrum, while pass-  An optimum filter provides the maximum attainable perfor-
           ing as much as possible of the target signal spectrum. The fre-  mance for a  specified optimization criterion. Two  typical
           quency responses of  the  single-  and double-delay line  examples are filters that provide maximum output signal-to-
           cancelers, often used in MTI systems, are given by   noise ratio or minimum rms error in signal fidelity. In radar
                                                                applications, the term optimum filter is usually applied to a
                                       æ  f ö
                            H f () 2 sin=  p ---                linear filter providing the maximum possible signal-to-inter-
                              1        è  f ø
                                          r                     ference ratio. In this case the filter does not retain the shape of
                                                                the input signal but deliberately distorts  it so  that  spectral
                                          2
                                    æ   f ö
                            H f () 4 sin=  è  p--- r            components of the signal are superimposed to maximize the
                                        f ø
                              2
                                                                signal-to-interference ratio. The useful by-effect of optimum
                                                                filtering in this case is a pulse compression phenomenon,
           where H(f) is the frequency response and f  is the pulse repeti-
                                             r                  widely exploited in modern radar.
           tion frequency. More complicated response is available when
                                                                    In general, when the interference consists of white noise
           feedback is used around the cancelers, or when range-gated
                                                                of spectral density  N ,  and clutter has an energy spectrum
                                                                                  0
           channels are filtered in low-pass digital or analog filters (see  2
                                                                |S(f)| , the square of the signal spectrum, the optimum filter
           also CANCELER). DKB
                                                                transfer function is
           Ref.: Barton (1988), pp. 236–238.
                                                                                          S * f ()
           Multidimensional filtering is the filtering of a multidimen-          Hf () --------------------------------
                                                                                     =
           sional signal (a signal that depends on a set of parameters),               N +  kS f () 2
                                                                                        0
           typically during integration, for the purpose of more precise
                                                                where  k is a constant  related to the  clutter-to-noise  ratio.
           estimation of signal parameters. In the simplest case, a scalar
                                                                When the interference  is  random white noise, the optimum
           parameter linearly dependent on the multidimensional signal
                                                                filter is called a matched filter, and its transfer function from
           is evaluated; for example, when evaluating generally grouped
                                                                the equation above is simply the complex conjugate of the
           coordinates of complex targets and when integrating uniform
                                                                signal spectrum. DKB, SAL
           measurements in radio navigation. Similar problems are
                                                                Ref.: Nathanson (1969), pp. 301–306; Leonov (1988), p. 61.
           solved using linear filters. In the general case, nonlinear fil-
           ters are used to evaluate multidimensional parameters. IAM  A  pi-[section] cavity filter is a microwave  bandpass  filter
           Ref.: Fal'kovich (1981), p. 237.                     with pi-shaped bent cavity. It uses striplines and has smaller
                                                                dimensions compared with other types of bandpass filters and
           A multistage filter consists of a cascade of similar stages.
                                                                also uses a simple  production technology. It is used  in  the
           The frequency response of a multistage filter is the product of
                                                                low-frequency microwave range as well as for relative bands
           frequency characteristics of the stages.
                                                                of more than 20% through the use of its advantages in pro-
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