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Question

A CT signal x(t) can be depicted as follows. It is a periodic function with T0 = 1 microsecond, and amplitude A = 1. The second signal y(t) is a sinusoidal function with the fundamental frequency of 900 MHz, i.e., y(t) = cos(2pifc*t), fc = 900 MHz. Please use MATLAB to plot these two signals' waveforms separately, then plot the waveform of the product z(t) = x(t)y(t). Use MATLAB to plot the Fourier transform (frequency representation) of the above-mentioned signals, i.e., X(f), Y(f), and Z(f). Design a 4th order lowpass Butterworth filter with the corner frequency of 1 MHz. Then send the above signal x(t) to this filter, and find out the output in both time and frequency domains (plot the signal waveform and frequency spectra). If the signal z(t) is sent to an ideal bandpass filter with the center frequency of fc (900 MHz), and bandwidth of 1 MHz, 2 MHz, or 5 MHz, respectively, what is the output signal from this bandpass filter? Plot the output signal in both time domain and frequency domain.

          A CT signal x(t) can be depicted as follows. It is a periodic function with T0 = 1 microsecond, and amplitude A = 1. The second signal y(t) is a sinusoidal function with the fundamental frequency of 900 MHz, i.e., y(t) = cos(2*pi*fc*t), fc = 900 MHz. Please use MATLAB to plot these two signals' waveforms separately, then plot the waveform of the product z(t) = x(t)y(t).

Use MATLAB to plot the Fourier transform (frequency representation) of the above-mentioned signals, i.e., X(f), Y(f), and Z(f).

Design a 4th order lowpass Butterworth filter with the corner frequency of 1 MHz. Then send the above signal x(t) to this filter, and find out the output in both time and frequency domains (plot the signal waveform and frequency spectra).

If the signal z(t) is sent to an ideal bandpass filter with the center frequency of fc (900 MHz), and bandwidth of 1 MHz, 2 MHz, or 5 MHz, respectively, what is the output signal from this bandpass filter? Plot the output signal in both time domain and frequency domain.

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