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PIN-316 spring 2025
A certain information signal s(t) consisting of two unknown frequencies is buried in the noise n(t) and what is observed is the noisy signal x(t) = s(t) + n(t). The attached
Matlab file ‘project.mat’ contains samples of the noisy signal x(t) sampled at 1 kHz. Download this file and get it into your Matlab workspace with the command:
>> load project.mat
The mat file contains two variables x (vector of sample values) and Fs (sampling frequency). The objective of this project is to determine the unknown frequencies present in the noise and recover the information signal through filtering.
1) Plot the noisy signal x(t) as a function of time (in seconds). Can you recognize the information signal from this plot?
2) Plot the power spectrum and identify the unknown frequencies of the information signal using the “Data Tips” featureof Matlab. What frequencies do you observe? Write both analog and digital/normalized values of frequencies.
3) Based on what you learned from part 2, design a filter that can extract the desired frequencies by suppressing the noise as much as possible. You are free to choose any type of filter you like, but you must show all your work.
4) Give the transfer function of your filter and plot its magnitude response.
5) Convolve your filter with the noisy signal to get the output signal, call it s(t).
6) Plot the power spectrum of s(t). Also, give a time plot of the last 100 samples of s(t).
Your submission should consist of a single PDF containing all calculations, plots, and Matlab code. Please write your observations or comments on each plot.