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drkidd22
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Homework Statement
Sketch the signal:
x(t) = 2^(-t*u(t)) over (-1 < t < 1)
The Attempt at a Solution
Attached is an excel fine with my work out. I want to know is it is correct.
The "u(t)" in the function represents the unit step function, which is equal to 0 for all negative values of t and equal to 1 for all positive values of t. It essentially serves as a switch to turn the function on at t = 0.
The base of the function can be any positive number, but 2 is often used because it is a convenient and commonly used number in signal processing.
The graph of the function will be a decaying exponential with a steep initial drop at t = 0, gradually approaching 0 as t increases.
This function can be used to model the decay of certain physical systems, such as radioactive decay or the discharge of a capacitor in an electrical circuit.
Yes, the function can be modified by changing the base or adding other terms to the exponent. This can alter the rate of decay or create different shapes of decay curves.