Hand Analysis 1. Perform a theoretical analysis by hand on the modulation / demodulation scheme shown below. Sketch time-domain waveforms and spectra (magnitude and phase) at each point in the system. The signal gt  is a lowpass filtered 725 Hz square wave with an amplitude of 2 V p-p and 50% duty cycle. Assume ideal lowpass filter in the analysis. The modulator's and demodulator's local oscillators l1 t  and l2 t  are 10.5 kHz sinusoid, with an amplitude of 2 V . Note that the multiplier has a gain of –6 dB. Determine the magnitude response of the reconstruction filter to achieve ideal demodulation of the original signal. 725 Hz LPF g t  3 kHz Cutoff Gain = 0dB l1 t   cos 2 f ct  Modulator Modulation and coherent g AM t cos 2 f ct  demodulation g AM t  scheme g t  Reconstruction Transmission filter Medium l2 t   cos 2 f ct  Demodulator All multipliers have a gain of –6dBMATLAB® Simulation 2. Perform a MATLAB® simulation of the modulation / demodulation scheme, showing ALL signals as both a time-domain waveform and a magnitude spectrum:  Choose a MATLAB® "sample rate" of fs=100e3 and choose N=1024 samples.  The signal gt  is a 725 Hz square wave (ranging from -1 to +1) with 50% duty cycle.  The lowpass filter is an Elliptic filter with a cutoff frequency of 3 kHz. It can be created with the following MATLAB® ellip function: [b,a]=ellip(5,0.1,50,3000/(fs/2)); The vectors b and a can be used with the MATLAB® filter function. You may need to adjust the magnitude of the filter response to achieve the correct amplitude in the reconstruction of the signal.  The local oscillators l1 t  and l2 t  are sinusoids with frequency f c 10.5 kHz and amplitude of 2 V .  The reconstruction filter is an Elliptic filter with a cutoff frequency of 5 kHz. It can be created with the following MATLAB® ellip function: [b,a]=ellip(5,0.1,50,5000/(fs/2));  All time-domain waveforms should extend from 0 to 10 milliseconds, with a range of –4 to 4.   All magnitude spectra should extend from 0 to 25 kHz, with a range of –80 dB to 0 dB.