Question

PROBLEM 8.1 Consider a bandpass filter specified by the system function 2Swns H (s) = Note that the half-power bandwidth of (1) is 2Çwn (a) Figure 1 shows the magnitude squared frequency response for a particular instance of (1) (b) In part (a), you looked at the "horizontal ct of 0.5 on the magnitude squared graph. Let's Find wn and C from the graph look at another cut. Measure the two frequencies on the graph for which the magnitude squared is 0.2, and confirm that the peak frequency is the square root of the product of the frequencies that yield a magnitude squared response of 0.2. (Note that this property holds for any horizontal cut.) (c) The constant in the numerator of (1) was a chosen so that the filter had a gain of 1 at its peak frequency. Many physical implementations of bandpass filters with adjustable bandwidth are better modeled using this system function: wnS Halt (s) = 82+2(ar,s + wn What is the magnitude squared of the peak frequency response of this alternative system function (You should be able to answer this question without having to do a lot of work Frequency Response (magnitude squared 1.1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 10 12 14 16 18 20 Frequency in kHz Figure 1: Frequency response for Problem 1

Answer 1

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