1. Engineering
  2. Electrical Engineering
  3. please answer both parts and show all work...

Question: please answer both parts and show all work...

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Please answer both parts and show all work.

4. (25 points) Assume that we have designed a lowpass filter following a certain set of design specifications. If the specifications change, we can rely on the already designed filter and map it to another filter via so-called frequency transformation mapping. Frequency transformation of a lowpass digital filter to another lowpass digital filter can be achieved by the following mapping (1) 1- az-i where Z is the complex variable associated with the transfer function of the first (old) filter, and z is the complex variable associated with the transfer function of the transformed (new) filter. If a lowpass digital filter with a passband cutoff frequency 6 0.4T and a stopband cutoff frequency 0.6T is to be transformed to a lowpass digital filter with a passband cutoff frequency wi 0.2T. (a) (10 points) determine the parameter a (b) (15 points) determine the stopband cutoff frequency of the new filter ws. Hint: To answer a (b), start by substituting Z ei and 2 eju in (1)

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