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4. Let $m(t) = 2cos(200\pi t)$ be a message signal which is multiplied by a carrier $cos(2400\pi t)$ to produce a DSB-SC signal $\phi(t) = m(t)cos(2400\pi t)$. a) Sketch the spectrum of $\phi(t)$ and identify the lower and upper sidebands. b) What is the bandwidth of $\phi(t)$? c) Suppose we want to generate a single sideband signal with upper sidebands of $\phi(t)$. Let us call it $\phi_{USB}(t)$. What is $\phi_{USB}(t)$? (You can take the inverse Fourier transform of the upper sidebands you identified in part a)

          4. Let $m(t) = 2cos(200\pi t)$ be a message signal which is multiplied by a carrier
$cos(2400\pi t)$
to produce a DSB-SC signal $\phi(t) = m(t)cos(2400\pi t)$.
a) Sketch the spectrum of $\phi(t)$ and identify the lower and upper sidebands.
b) What is the bandwidth of $\phi(t)$?
c) Suppose we want to generate a single sideband signal with upper sidebands of $\phi(t)$.
Let us call it $\phi_{USB}(t)$. What is $\phi_{USB}(t)$? (You can take the inverse Fourier transform
of the upper sidebands you identified in part a)

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4. Let m(t) = 2cos(200π t) be a message signal which is multiplied by a carrier
cos(2400π t)
to produce a DSB-SC signal ϕ(t) = m(t)cos(2400π t).
a) Sketch the spectrum of ϕ(t) and identify the lower and upper sidebands.
b) What is the bandwidth of ϕ(t)?
c) Suppose we want to generate a single sideband signal with upper sidebands of ϕ(t).
Let us call it ϕUSB(t). What is ϕUSB(t)? (You can take the inverse Fourier transform
of the upper sidebands you identified in part a)

Added by Brenda C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Sam Stansfield

Step 1

The Fourier transform of a signal is given by: F(ω) = ∫[ϕ(t)e^(-jωt)]dt In this case, ϕ(t) = m(t)cos(2400t), so we can rewrite it as: ϕ(t) = 2cos(200t)cos(2400t) Using the trigonometric identity cos(A)cos(B) = (1/2)[cos(A+B) + cos(A-B)], we can rewrite ϕ(t) Show more…

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Let m(t) = 2cos(200Ï€t) be a message signal which is multiplied by a carrier cos(2400Ï€t) to produce a DSB-SC signal Ï†(t) = m(t)cos(2400Ï€t). 4. Let m(t) = 2cos(200t) be a message signal which is multiplied by a carrier cos(2400t) to produce a DSB-SC signal Ï†(t) = m(t)cos(2400t). a) Sketch the spectrum of Ï†(t) and identify the lower and upper sidebands. b) What is the bandwidth of Ï†(t)? c) Suppose we want to generate a single sideband signal with upper sidebands of Ï†(t). Let us call it uss(t). What is uss(t)? (You can take the inverse Fourier transform of the upper sidebands you identified in part a)

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