Question

Delta-pulse and its time scale property

We know that the specially important unit-impulse signal δ(t) can be understood through its limiting approximation, δ(t)=lim ε-> ₀ 1/ε rect(t/ε)

Find the convolution results of δ(10(t-1))* e⁻¹⁰ᵗ = ?

Answer 1

The convolution of δ(10(t-1)) * e⁻¹⁰ᵗ can be found by integrating the product of the two functions. The delta pulse function consists of a single spike at t = 1 with magnitude 10. The exponential function decays exponentially as time increases.

Step-by-step explanation:

The convolution of δ(10(t-1)) * e⁻¹⁰ᵗ can be found by integrating the product of the two functions. The delta pulse function δ(10(t-1)) consists of a single spike at t = 1 with magnitude 10. The exponential function e⁻¹⁰ᵗ decays exponentially as time increases. When convolving these two functions, the exponential function will have a larger effect on the signal near t = 1 due to the spike in the delta pulse function.