3. Determine the transfer function for a first order high pass filter with a cut

Question

3. Determine the transfer function for a first order high pass filter with a cutoff frequency of 1000 radians/sec (note radians and not Hertz) and a pass band gain of 1 using the following types. (c) Butterworth type (d) Chebyschev type with 1 db ripple in the pass band In both cases list the TF of the filter below. Then use MATLAB to verify their frequency response (FR) , i.e. to check that they do indeed give the FR you wanted. Attach MATLAB printout at the end. Put your name on the printout. ?

Explanation / Answer

First, calculate the overall mean: Overall Mean = (x¯1 + x¯2 + x¯3) / 3 = (5 + 4 + 6) / 3 = 15 / 3 = 5 Between group sum of squares: SS(between) = n1(x¯1 - x¯)² + n2(x¯2 - x¯)² + n3(x¯3 -x¯)² = 25(5 - 5)² + 25(4 - 5)² + 25(6 - 5)² = 25(0)² + 25(-1)² + 25(1)² = 0 + 25 + 25 = 50 Within group sum of squares: SS(within) = n1·s²1 + n2·s²2 + n3·s²3 = (25 · 2) + (25 · 1.5) + (25 · 1.5) = 50 + 37.5 + 37.5 = 125 Calculate F: F = (SS(between) / (# of groups - 1)) / (SS(within) / (# of groups · ( n - 1))) = (50 / 2) / (125 / (3 · (25 -1))) = 25 / (125 / (3 · 24)) = 25 / (125 / 72) = 25 / 1.736 = 14.4 The critical F needed for a .05 level of significance and a test with 3 groups with 25 cases in each group is 3.12 Since you've gotten an F that is greater than the critical value, you would reject your null hypothesis...............

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