Question about single tone signals

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SUMMARY

The bandwidth of single tone signals, such as cosine signals, is effectively zero. The Fourier Transform (F.T.) of a cosine signal results in delta functions at both the positive and negative frequencies, indicating that the signal occupies a single frequency in the frequency domain (FD). Therefore, it is accurate to conclude that an infinite tone has zero bandwidth.

PREREQUISITES
  • Understanding of Fourier Transform (F.T.)
  • Knowledge of frequency domain (FD) analysis
  • Familiarity with cosine signals and their properties
  • Basic concepts of signal bandwidth
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  • Study the properties of Fourier Transforms in depth
  • Explore the implications of bandwidth in signal processing
  • Learn about delta functions and their significance in frequency analysis
  • Investigate the characteristics of different types of signals beyond single tones
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Electrical engineers, signal processing professionals, and students studying communications or waveform analysis will benefit from this discussion.

mazen_zone
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what is the bandwidth of single tone signals?

taking the F.T. for a cosine signal gives a delta at the signal's frequency, so does it mean that its bandwidth is zero since it is occupying only a single freq. in the FD.
 
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mazen_zone said:
what is the bandwidth of single tone signals?

taking the F.T. for a cosine signal gives a delta at the signal's frequency, so does it mean that its bandwidth is zero since it is occupying only a single freq. in the FD.

You get deltas at both the positive and negative frequencies, right? And yes, I believe it would be correct to say that an infinite tone has zero BW.
 

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