The u(a) is a unit step function that is zero for all negative values and 1 for all values greater than or equal to 0. So the integral is zero for all values from negative infinity to zero, so we can change the limit of the integral to 0 (or rewrite it as 2 integrals, one from -infinity to 0 and one from 0 to infinity, and the first one will be zero).
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Great, can't tell you how much I needed this.
I'm glad it was helpful
good job
would changing the domain from time to frequency for both the input and impulse allow us just to multiply them instead of convolution?
Yes, we could multiply the spectra of the 2 signals
nice👌👌
What if x(t) given is equal to 1?
thanks a ton
Why we replaced minus infinity with zero
The u(a) is a unit step function that is zero for all negative values and 1 for all values greater than or equal to 0. So the integral is zero for all values from negative infinity to zero, so we can change the limit of the integral to 0 (or rewrite it as 2 integrals, one from -infinity to 0 and one from 0 to infinity, and the first one will be zero).