8.6. Design a first-order digital lowpass Butterworth filter with a cutoff frequency of 1.5 kHz and a passband ripple of 3 dB at a sampling frequency of 8,000 Hz. a. Determine the transfer function and difference equation. b. Use MATLAB to plot the magnitude and phase frequency responses.

The question is in the picture below.

4. Consider the series RLC circuit in Homework 7, Question 2. The component values are R = 1 ohms, inductance = 0.3 henries, and capacitance C = 0.6 farads. Enter w (double-u) for w (omega). x(t) L C (a) Find the frequency response function H(w) Y(w) = X(w) H(w) = (b) Find the positive linear frequency fo = wo in Hz at which |H(w) = 1. This is the resonant frequency or the center frequency of the bandpass filter. fo = (c) Find the two positive frequencies f₁₁ = 1 and (fcı < fœ₂) in Hz, at which |H(w)| = fc2 = These are the half-power frequencies of the bandpass filter. fc₁ = fc₂ = R www y(t)

Q3: (a) An instrument is calibrated in an environment at a temperature of 20°C and the following output readings y are obtained for various input values x: y 13.1 26.2 39.3 52.4 65.5 78.6 x 5 10 15 20 25 30