ECE :: Signals and Systems
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If a complex voltage wave is applied to a pure inductance, the resulting current wave is much smoother than the voltage wave.
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If a function f(t) is Laplace transformable, then
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In the given figure shows a periodic triangular wave. The Fourier series will have
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A discrete LTI system is non-casual if its impulse response is
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consider the following as regards cumulative disribution function F(x)
- 0 ≤ F(x) ≤ 1
- F(- ∞) = 0
- F(∞) = 1
- F(x1) ≤ F(x2) If x1 < x2
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Assertion (A): Fourier series can also be written in exponential form.
Reason (R): sin (n ωt) and cos (n ωt) can be expressed as sum or difference of exponentials.
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In a complex wave, the negative half of the wave is a reproduction of the positive half wave. Then
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|f(t)| e-σ1t dt < ∞ for a real positive σ1 
|f(t)| e-σ1t dt < 0 for a real positive σ1 
|f(t)| e-σ1t dt < 0 for a real positive σ1 
|f(t)| e-σ1t dt < ∞ for a real positive σ1 
and k > 0