Which of the filter topologies in Figure 1 are not suited for an all-pole filter synthesis? Also, briefly explain why not

In filter design, the term "all-pole filter" refers to filters that have poles but no zeros in their transfer function. Common topologies used for all-pole filters include low-pass, high-pass, band-pass, and band-stop configurations, provided they only feature poles.

Explanation of Unsuitable Filter Topologies

1. Understanding Filter Topologies: Each filter topology has a distinct behavior determined by the location of its poles and zeros.

2. Identification of Unsuitable Filters:

   • Any filter topology that has zeros in its transfer function is not suited for all-pole synthesis.
   • Typical examples would include certain types of band-stop filters (depending on their design).

3. Reason for Unsuitability:

   • Zeros introduce frequency responses that can cancel out certain frequencies, which is contrary to the characteristics of all-pole filters that aim to only attenuate certain frequencies through pole placement without introducing zeros.

Summary

Therefore, any filter topology that includes zeros is not suitable for all-pole filter synthesis. The bandwidth, frequency behavior, and resulting filter quality are fundamentally altered by the presence of zeros, which defeats the purpose of utilizing an all-pole filter approach.