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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