Question
A message signal has frequency components at $400 \mathrm{~Hz}$ and $800 \mathrm{~Hz}$. This is used to AM modulate a $30 \mathrm{kHz}$ carrier signal. Plot the frequency spectrum of the AM-modulated signal.
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The message signal has frequency components at \(400 \, \text{Hz}\) and \(800 \, \text{Hz}\). Show more…
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A voice signal occupying the frequency band of 0.4 to $3.5 \mathrm{kHz}$ is used to amplitude-modulate a $10-\mathrm{MHz}$ carrier. Determine the range of frequencies for the lower and upper sidebands.
A periodic modulated (AM) radio signal has the form $$y=(A+B \sin 2 \pi f t) \sin 2 \pi f_{c}\left(t-\frac{x}{v}\right)$$ The factor $\sin 2 \pi f_{c}(t-x / v)$ is called the carrier wave; it has a very high frequency (called radio frequency; $f_{c}$ is of the order of $10^{6}$ cycles per second). The amplitude of the carrier wave is $(A+B \sin 2 \pi f t)$. This amplitude varies with time-hence the term "amplitude modulation" - with the much smaller frequency of the sound being transmitted (called audio frequency; $f$ is of the order of $10^{2}$ cycles per second). In order to see the general appearance of such a wave, use the following simple but unrealistic data to sketch a graph of $y$ as a function of $t$ for $x=0$ over two periods of the amplitude function: $A=3, B=1, f=1, f_{c}=20 .$ Using trigonometric formulas, show that $y$ can be written as a sum of three waves of frequencies $f_{c}$ $f_{c}+f,$ and $f_{c}-f ;$ the first of these is the carrier wave and the other two are called side bands.
Fourier Series and Transform
Applications of Fourier Series
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