dB eff as input parameters and b, a, G as output parameters. (f) Write a MATLAB function HighPassFilter_NU to implement the filter, taking. (e) Determine the normalization gain factor G as function of a and b. (d) Determine the coefficient a as function of. (c) Determine the coefficient b as function of A and a. (b) From H(w), determine the attenuation A as function of a and b. (a) From H(z), determine the frequency response H(w) where. Additionally, a constraint is imposed on the filter speed response1 defined by two parameters: eff n (number of samples to reach the steady state) and (steady state threshold in %). Let’s define the parameter A as the attenuation of the lowest frequency relative to the highest one. The gain G is fixed so as to normalize the filter to unity at the highest frequency. Consider a first-order highpass filter whose the general transfer function is where the coefficients a and b are positive and less than one. Exercise 2.1: Highpass filter Pole/zero placements are useful to design simple filters. Give your comments on the pole/zero pattern and impulse response. To plot the pole/zero pattern, use the following code: (e) Modify your program to set the coefficient a1 value to -1.9 and display the corresponding four quadrant figure. (d) Display your results in a four quadrant figure (see template below) using the subplot function. (c) From the impulse response, complete your program to compute the magnitude (in dB) and phase (in °) spectra of the filter, using the fft, abs and angle functions. (b) From the coefficients of this transfer function (vectors: b = and a = ), write a MATLAB program to compute the first 100 samples of the impulse response, using the filter function. Exercise 1.1: I/O equation Consider a second-order filter with the I/O equation: (a) From the I/O equation, calculate the transfer function H(z).
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