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InterviewSolution
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A two pole low pass filter has a system function H(z)=\(\frac{b_0}{(1-pz^{-1})^2}\), What is the value of ‘b0‘ such that the frequency response H(ω) satisfies the condition |H(π/4)|^2=1/2 and H(0)=1?(a) 0.36(b) 0.38(c) 0.32(d) 0.46The question was asked in examination.The above asked question is from LTI System as Frequency Selective Filters in section Frequency Analysis of Signals and Systems of Digital Signal Processing |
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Answer» RIGHT OPTION is (d) 0.46 Explanation: Given H(Z)=\(\frac{b_0}{(1-pz^{-1})^2}\) and we know that z=re^jω. Here in this CASE r=1. So z=e^jω. Given at ω=0, H(0)=1=>b0=(1-p)^2 Given at ω=π/4, |H(π/4)|^2=1/2 =>\(\frac{(1-p)^2}{(1-pe^{-jπ/4})^2}\) = 1/2 =>\(\frac{(1-p)^4}{((1-p/\sqrt 2)^2+p^2/2)^2}\) = 1/2 => √2(1-p)^2=1+p^2-√2p Upon solving the above quadratic EQUATION, we get the value of p as 0.32. Already we have b0=(1-p)^2=(1-0.32)^2 =>b0 = 0.46 |
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