Which type of property is shown by the following function.

L{K f(t)} = K F(s)

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PGCIL DT Electrical 5 May 2023 Official Paper
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  1. Shifting theorem 
  2. Scaling theorem
  3. Linearity
  4. Distribution theorem

Answer (Detailed Solution Below)

Option 2 : Scaling theorem
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Concept:

Some common Fourier Transform properties are as shown:

If X(ω) is the Fourier transform of x(t) i.e. x(t) ↔ X(ω), then

Time shifting

x(t - t0)  ↔  e-jωto. X(ω)

Frequency shifting

ejωt . x(t) ↔ X (ω - ω0)

Time scaling

\({\bf{x}}\left( {{\bf{at}}} \right)\; \leftrightarrow \;\frac{1}{{\left| {\bf{a}} \right|}} \times \left( {\frac{{\bf{\omega }}}{{\bf{a}}}} \right)\)

Time Reversal

x(-t) ↔ X (-ω)

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