Consider the following problems related to the specification of IIR  filters

(a) The magnitude specifications for a low-pass filter are

1 – δ ≤ |H(e^jω)| ≤ 1          0 ≤ ω ≤ 0.5 π

0 < |H(e^jω)| ≤ δ                0.75 π ≤ ω ≤ π

i. Find the value of δthat gives the following equivalent loss  specifications for this filter

α(e^j0) = 0 dB,      α_max = 0.92 dB,                   α_min = 20 dB

ii. What are the values of ω_p and ω_st?

(b) The following are specifications for a low-pass discrete IIR filter  that will be used in processing analog signals

10 ≤ α(e^jω) ≤ 10.1 dBs     0 ≤ f ≤ 2 kHz

         α(e^jω) ≥ 60 dBs                 4 kHz ≤ f ≤ 5 kHz

i. Find the values of α_max, α_min, and the dc loss in dBs.

ii. What is the sampling frequency f_s in kHz in this filter  specifications?

iii. Obtain the equivalent specifications in discrete frequencies  for 0 dB dc loss for this filter.