Use MATLAB to solve the following problems. Include only the necessary Plots and check whether the specifications have been met or not. The plots should be neat and meaningful. Labels and titles are necessary. Write a short report $($PDF$)$ describing your findings. The program listing should be included too.

Design a digital low pass filter that meets the following specifications: Pass band ripple: $0\mathrm{.}5dB.$

Pass band edge: $4$ kHz

Stop band attenuation: $30dB.$

Stop band edge: $5$ kHz $.$

Sampling frequency: $F_S=20kHz.$

Determine what order of Butterworth, Chebyshev and Elliptic that must be used to meet the above specifications. Find the transfer function for each of three filters and plot its magnitude and phase. Don't forget to show your work, label the axes and choose proper scale for each figure.

Calculate the output of the Butterworth filter ONLY when the input is a square wave of a fundamental frequency of $3$ kHz $.$ Compute at least $2$ msec $.$ Discuss your answer.MATLAB Part

Use MATLAB to solve the following problems. Include only the necessary Plots and check whether the specifications have been met or not. The plots should be neat and meaningful. Labels and titles are necessary. Write a short report $($PDF$)$ describing your findings. The program listing should be included too.

Design a digital low pass filter that meets the following specifications: Pass band ripple: $0\mathrm{.}5dB.$

Pass band edge: $4$ kHz

Stop band attenuation: $30dB.$

Stop band edge: $5$ kHz $.$

Sampling frequency: $F_S=20kHz.$

Determine what order of Butterworth, Chebyshev and Elliptic that must be used to meet the above specifications. Find the transfer function for each of three filters and plot its magnitude and phase. Don't forget to show your work, label the axes and choose proper scale for each figure.

Calculate the output of the Butterworth filter ONLY when the input is a square wave of a fundamental frequency of $3$ kHz $.$ Compute at least $2$ msec $.$ Discuss your answer.