The filters mentioned here are the most frequently used. When such sharp rolloffs are desirable and group-delay linearity is a concern, the designer can alleviate the problem by cascading the filter with delay equalizers. The group delay of elliptic filters is the most nonlinear, especially near the passband edge. In contrast, a Chebyshev filter of order 10 and a 25th-order Butterworth filter would have to be specified to meet or exceed the given specifications. For example, for k = 0.75, A p = 2 dB, and A r = 60 dB, a sixth-order elliptic filter is required. The magnitude response of elliptic filters is equiripple in the passband and the stopband and is characterized by the steepest rolloff for a given order n. Inverse Chebyshev filters have sharper rolloffs than standard Chebyshev filters and have group-delay characteristics more nonlinear than Butterworth filters but less so than standard Chebyshev filters. Flatness is achieved by including the stopband zeros (loss poles) in the transfer function. Inverse Chebyshev filters exhibit a flatter passband magnitude response than does a Butterworth filter of the same order. The inverse Chebyshev (Chebyshev type 2) filters have a maximally flat magnitude response in the passband and an equiripple characteristic in the stopband. The design tradeoff is between achieving magnitude response specifications with the lowest filter order n and the increased group-delay nonlinearity for the sharper rolloff filter types. We can make similar observation between Chebyshev and Butterworth filters. For a given order n a Butterworth filter has a higher attenuation in the stopband and steeper rolloff in the transition band than does a Bessel filter. Chebyshev filters, on the other hand, have an equiripple magnitude response characteristic in the passband. Butterworth filters have a maximally flat magnitude response characteristic. Bessel filters are characterized by a maximally flat group-delay characteristic. The magnitude responses of all-pole filters such as Bessel, Butterworth, and Chebyshev (type 1) are monotonically decreasing functions of frequency in the stopband. Section VI discussed design methods for some popular normalized analog filters. NAZIR A PASHTOON, in Handbook of Digital Signal Processing, 1987 F Analog Filters in Retrospect This can lead to a considerable simplification of the costly microelectronic lithographic processes required for gigahertz device fabrication. In another significant contrast with passive LC circuitry, SAW filters can also be designed to operate very efficiently in harmonic modes up to about the ninth harmonic frequency. As these advanced design concepts require application of digital sampling techniques as well as the Remez exchange algorithm, their examination will be deferred to a later chapter. This type of filter finds application in equalizer circuitry in transmission channels. Moreover, and again in contrast to LC or other conventional analog filters, the amplitude response of a linear-phase SAW filter can be shaped to be nonsymmetric about center frequency. A single linear-phase SAW filter can be designed to have up to about 10 bandpass or bandstop responses, in contrast to the single resonance provided by one LC-tuned circuit. In their bandpass operation, however, they have much more design versatility than LC filters. They can not be implemented as lowpass filters, but only as bandpass (or bandstop) ones. The alternating polarities of fingers in a SAW IDT restrict their signal processing capabilities to AC signals. (Courtesy of SAWTEK Incorporated, Orlando, Florida.) Illustrating the compact sizes of various SAW bandpass filters and resonators.