Calculating Bandwidth of AM Signal with Dual Cosine Modulation

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SUMMARY

The bandwidth of an Amplitude Modulated (AM) signal with a modulating signal defined as x(t) = cos(2π70t) + cos(2π90t) and a carrier frequency of 10 kHz is determined by the difference between the highest and lowest frequencies of the modulating components. The bandwidth is calculated as twice the baseband bandwidth, which in this case is 20 Hz (90 Hz - 70 Hz). Therefore, the total bandwidth of the AM signal is 40 Hz, confirming that the carrier frequency does not affect the bandwidth calculation.

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  • Understanding of Amplitude Modulation (AM) principles
  • Knowledge of frequency components in signals
  • Familiarity with cosine functions and their properties
  • Basic grasp of bandwidth calculations in signal processing
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Homework Statement


What is the bandwidth of an AM signal if the modulating signal is
x(t)=cos(2pi70t)+cos(2pi90t) and the carrier frequency is 10kHz?


Homework Equations





The Attempt at a Solution


The carrier frequency is irrelevant because it just means the signal's spectrum is concentrated around it, it has no bearing on bandwidth. I know that bandwidth of an AM signal is two times the baseband bandwidth. However, I am not sure what that would be here because you are summing cosines with different frequencies. If only one cosine was present, the bandwidth would be two times its frequency, but as there are two I don't know what to do. My guess is that the smaller frequency (larger period) prevails as it would dominate the higher frequency component.
 
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there are many ways to define "bandwidth." If it means the highest frequency minus the lowest frequency (that is nonnegative), a cosine alone would have 0 bandwidth. Also, two sinusoids would have a bandwidth equal to the frequency of the faster sinusoid minus the frequency of the slower sinusoid.

90 - 70 = 20
 

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