Exercises

1. A recirculating elementary filter has a pole at $i/2$. At what angular frequency is its gain greatest, and what is the gain there? At what angular frequency is the gain least, and what is the gain there?
2. A shelving filter has a pole at 0.9 and a zero at 0.8. What are: the DC gain; the gain at Nyquist; the approximate transition frequency?
3. Suppose a complex recirculating filter has a pole at $P$. Suppose further that you want to combine its real and imaginary output to make a single, real-valued signal equivalent to a two-pole filter with poles at $P$ and $\overline{P}$. How would you weight the two outputs?