Question

Q2) By using the properties of the impulse function \(\delta(t)\), find the equivalent of the following expressions. The symbol ' * ' denotes the convolution operation and \(\delta'(t)\) is the derivative of the impulse function. a) \(x_1(t) = sinc(t)\delta(t)\) b) \(x_2(t) = sinc(t)\delta(t - 5)\) c) \(x_3(t) = \Pi(t) * \sum_{n=-\infty}^{\infty} \delta(t - n)\) d) \(x_4(t) = \Lambda(t) * \delta'(t)\) e) \(x_5(t) = \int_{-\infty}^{\infty} cos(t)\delta(t)dt\) f) \(x_6(t) = \delta(3t)\delta(5t)\)

          Q2) By using the properties of the impulse function \(\delta(t)\), find the equivalent of the
following expressions. The symbol ' * ' denotes the convolution operation and \(\delta'(t)\) is the
derivative of the impulse function.
a) \(x_1(t) = sinc(t)\delta(t)\)
b) \(x_2(t) = sinc(t)\delta(t - 5)\)
c) \(x_3(t) = \Pi(t) * \sum_{n=-\infty}^{\infty} \delta(t - n)\)
d) \(x_4(t) = \Lambda(t) * \delta'(t)\)
e) \(x_5(t) = \int_{-\infty}^{\infty} cos(t)\delta(t)dt\)
f) \(x_6(t) = \delta(3t)\delta(5t)\)

Q2) By using the properties of the impulse function δ(t), find the equivalent of the
following expressions. The symbol ' * ' denotes the convolution operation and δ'(t) is the
derivative of the impulse function.
a) x1(t) = sinc(t)δ(t)
b) x2(t) = sinc(t)δ(t - 5)
c) x3(t) = Π(t) * ∑n=-∞^∞δ(t - n)
d) x4(t) = Λ(t) * δ'(t)
e) x5(t) = ∫-∞^∞ cos(t)δ(t)dt
f) x6(t) = δ(3t)δ(5t)

Added by Alexis C.

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