Can two functions have the same frequency domain representation?

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SUMMARY

The discussion centers on the frequency domain representation of two functions: 1/(j.pi.f) and signum(t) = u(t) - u(-t). It is established that both functions can be represented in the frequency domain as 2u(t). The reasoning provided indicates that the equation 2u(t) - 1 equals signum(t), confirming their equivalence in the frequency domain. This highlights the concept of multiple time-domain functions sharing the same frequency representation.

PREREQUISITES
  • Understanding of frequency domain analysis
  • Familiarity with the signum function and unit step function (u(t))
  • Knowledge of complex frequency representations
  • Basic principles of signal processing
NEXT STEPS
  • Study the properties of the Fourier Transform and its applications
  • Learn about the implications of time-domain and frequency-domain equivalence
  • Explore the concept of signal reconstruction from frequency components
  • Investigate the role of the unit step function in signal processing
USEFUL FOR

Signal processing engineers, electrical engineers, and students studying systems and signals who seek to understand the relationship between time-domain functions and their frequency representations.

sanjaysan
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Hi,

I stumbled upon the following two functions which have the same freq domain representation,
1/(j.pi.f)

1.signum(t) = u(t) - u(-t)

2. 2u(t)

what is the reasoning behind them having the same f domain representation?
 
Mathematics news on Phys.org
well
2u(t)-1=signum(t)
 
thanks,that answers my question:)
 

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