Question 24.11: Apply the t-ω duality principle to the previous result. Inte......
Apply the t-ω duality principle to the previous result. Interpret the result physically.
Step-by-Step
We have f(t) = δ(t) and F(ω) = 1. The duality principle tells us that
f (−ω) = δ(−ω) which equals {\frac{1}{2 \pi}}{\mathcal{F}}\{1\}
that is,
{\mathcal{F}}\{1\}=2\pi\delta(\omega)
(since δ(−ω) = δ(ω)). This is illustrated in Figure 24.10. Physically F(t ) = 1 can be regarded as a d.c.waveform. This result confirms that a d.c. signal has only one frequency component, namely zero.
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