Design a Butterworth low-pass discrete filter that satisfies the following specifications: 0 (e j )

Design a Butterworth low-pass discrete filter that satisfies the following specifications:

0 ≤ α(e^jω) ≤ 3 dB for 0 ≤ f ≤ 25 Hz

α(e^jω) ≥ 38 dB for 50 ≤ f ≤ Fs/2 Hz

and the sampling frequency is F_s = 2000 Hz. Express the transfer function H(z)of the designed filter as a cascade of filters. Use first the design formulas and then use MATLAB to confirm your results. Show that the designed filter satisfies the specifications, plotting the loss function of the designed filter.