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193   filter, pi-[section] cavity                                                           filter, ripple



           duction of wideband p-cavity filters in comparison with other  most general form of digital filter. Its transfer function has
           types of filters. IAM                                both zeroes and poles (see filter characteristics), as opposed
           Ref.: Veselov (1988), p. 95; Isipov, L.S., and Balandinskiy, B.B. Antenny 29,   to a nonrecursive filter, which  has  only zeroes  (because  it
              p. 160, in Russian.                               uses only feedforward weightings). When implemented with
           A presumming filter is a bandpass filter  used in synthetic  a tapped delay line, the recursive filter theoretically has infi-
           aperture radar processing to reduce the number of samples  nite memory and is termed an infinite impulse response (IIR)
           that must be processed in the final processing.      filter, as opposed to the nonrecursive type, which is a finite
                                                                impulse response (FIR). A comparison of the main features of
           .Ref.: Brookner (1977), p. 257.
                                                                the two types is given in Table F5.
           pulse-compression filter (see PULSE COMPRESSION).        The nonrecursive filter  is more complicated  and  less
           The filter Q-factor is equal to the ratio of the average elec-  flexible, and so to obtain a specified frequency response it
           tromagnetic energy stored in it to the energy lost in the period  requires more components than the recursive filter, but it is
           of oscillations at the resonance frequency. One distinguishes  always stable and has no transient period. This is especially
           between the external Q-factor, Q  and the unloaded (internal)  important in  radar applications,  where strong interference
                                     e
           Q-factor Q . In determining the former, one allows for losses  (clutter or jamming) can cause prolonged ringing in the recur-
                    i
           only in external active loads, and in determining the unloaded  sive filter, masking targets until the ringing damps out. In sur-
           Q-factor, only for ohmic losses due to the nonideal nature of  veillance radars, the number of pulses is restricted, so
           the conductors  and dielectrics inside the resonance system.  operation  of processors  such as the moving target detector
           The full (loaded) Q-factor of a filter Q is found by the for-  will take place during the transient period if a recursive filter
           mula                                                 is used. On the other hand, the recursive filter is much more
                                                                flexible because poles and zeroes are available for shaping
                               1   1   1
                               ---- =  ------ +  -----          the frequency response, offering practically any desired fre-
                               Q   Q   Q
                                    e   i                       quency response even without use of staggered PRF. SAL
           IAM                                                  Ref.: Skolnik (1980), pp. 110–114; Cowan (1988), p. 17.
           Ref.:Gardiol (1984); p. 138; Sazonov (1981), p. 170.
                                                                                     Table F5
           A quasioptimum filter is a mismatched filter that introduces  Comparison of Recursive and Nonrecursive Filters
           minimum losses relative to the optimum filter. Most radar sig-
           nal-processing filters fall into this class (e.g., doppler filters  Feature  Nonrecursive  Recursive
           operating in a background of nonwhite noise). IAM
           Ref.: Sloka (1970), p. 19; Barton (1988), p. 268.      Absolutely linear phase   Yes    No
                                                                  response
           A range-gated filter is an MTI or doppler filter operating on
           range-sampled signals. The range gating has the effect of pro-  Internal noise power  Much less  Much greater
           ducing a comb filter with repeated responses at intervals of
                                                                  Complexity of calculat-  Simpler  More compli-
           the pulse repetition frequency, thereby matching the spectrum
                                                                  ing coefficients                 cated
           of the coherent pulse train. All signals are reduced in band-
           width to lie within the pulse repetition frequency, but the total  Transient period  No  Yes
           system bandwidth remains matched to the pulse bandwidth if
                                                                  Number of operations  Much greater  Much less
           multiple range-gated channels cover the entire pulse repeti-
           tion interval.                                         Design flexibility  Less         Greater
               Range-gated MTI filters can readily be implemented
           with either broad or narrow rejection notches of arbitrary  A ripple filter is a device accomplishing data smoothing by
           depth and with steep transitions from stopband to passband.  linear  combination of data based on a given criterion. The
           DKB                                                  least squares method usually is used as the criterion. Ripple
           Ref.: Skolnik (1980), pp. 117–119.                   filters are differentiated by the shape of the curve used for
                                                                smoothing (smoothing with a straight line, with parabolas of
           The rectangular filter has an idealized bandpass frequency
                                                                the second, fourth degree, etc.), as well as by the number of
           response:
                                                                data added with certain weights defining filter length. Filter
                           H( f ) = 1, | f-f | £ B/2,
                                       0
                           H( f ) = 0, | f-f | > B/2            coefficients are numerically equal to the weights of the added
                                       0
           where f  is the center frequency and B is the bandwidth. This  data and are defined by filter type.
                 0
           response is approximated by a multiple-stage, stagger-tuned  The transfer function  of a ripple filter has maximum
                                                                value at zero frequency and drops with increasing frequency.
           receiver. DKB
                                                                The frequency response drops more quickly as filter length is
           A recursive filter is a digital filter including multipliers that  increased, while the magnitude of the subsequent oscillations
           provide feedforward (weighting coefficients a) and feedback  drops slightly.
           (weighting coefficients b) (see filter characteristics). It is the
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