Ideal Differentiator Frequency Response

• Discontinuity at $z = -1$ ensures no exact finite-order solution
• Need oversampling factor, as in interpolator design
  (e.g., $20$ kHz to $22.05$ kHz)
  Response is unconstrained between bandlimit and $f_s/2$
• As before, a small increment in oversampling factor yields a much larger decrease in required filter order to meet a given spec