Can two functions have the same frequency domain representation?

AI Thread Summary
Two functions can indeed have the same frequency domain representation, as demonstrated by the functions 1/(j.pi.f) and signum(t) = u(t) - u(-t). The relationship between these functions is clarified by the equation 2u(t) - 1 = signum(t). This indicates that both functions represent the same signal in the frequency domain despite their different forms in the time domain. Understanding this concept is crucial for analyzing signals in various applications. The discussion effectively highlights the equivalence of these functions in terms of their frequency domain characteristics.
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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