How to generate a DSB-SC signal?

How to generate a DSB-SC signal for t Є (-0.05,0.05), the carrier frequency is 500 Hz and Plot the waveform and spectrum of the information, carrier and modulated signals.

Answer 1

[LO]

To generate a DSB-SC signal for t∈(−0.05,0.05)t \in (-0.05, 0.05)t∈(−0.05,0.05) with a carrier frequency of 500 Hz and plot the waveform and spectrum of the information, carrier, and modulated signals, follow these steps:Step 1: Generate the Modulating Signal (m(t))

For simplicity, let the modulating signal be a sine wave:

m(t)=Am⋅sin⁡(2πfmt)m(t) = A_m \cdot \sin(2 \pi f_m t)m(t)=Am​⋅sin(2πfm​t)

Where:

• AmA_mAm​ is the amplitude of the modulating signal,
• fmf_mfm​ is the frequency of the modulating signal (choose a lower frequency, for example, 50 Hz).

Step 2: Generate the Carrier Signal (c(t))

The carrier signal is:

c(t)=Ac⋅cos⁡(2πfct)c(t) = A_c \cdot \cos(2 \pi f_c t)c(t)=Ac​⋅cos(2πfc​t)

Where:

• fc=500 Hzf_c = 500 \, \text{Hz}fc​=500Hz (the given carrier frequency).

Step 3: Generate the DSB-SC Modulated Signal (s(t))

The DSB-SC modulated signal is the product of the carrier and modulating signal:

s(t)=Ac⋅m(t)⋅cos⁡(2πfct)s(t) = A_c \cdot m(t) \cdot \cos(2 \pi f_c t)s(t)=Ac​⋅m(t)⋅cos(2πfc​t)Step 4: Plot the Signals

• Plot the modulating signal, carrier signal, and the modulated signal over time for t∈(−0.05,0.05)t \in (-0.05, 0.05)t∈(−0.05,0.05).
• Use Fourier transform to plot the frequency spectrum of the modulated signal.

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