Find the Convolution Y(t) of X(t) and H(t); That Is $$y ( t ) = h ( t ) ^ { * } x ( t )$$

question 9

Essay

Find the convolution y(t) of x(t) and h(t); that is, find $$y ( t ) = h ( t ) ^ { * } x ( t )$$ $$x ( t ) = 2 \cos ( 3 t ) u ( t ) , \quad h ( t ) = 4 \cos ( 4 t ) u ( t )$$

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Definitions:

Total Cost

The sum of all expenses, both fixed and variable, incurred in producing goods or services.

Purely Competitive Industry

An industry characterized by many sellers offering identical products, where no single seller can influence the market price.

Long-run Equilibrium

A state in which all inputs and outputs in an economy are optimally allocated, and all firms make zero economic profit, reflecting no incentives for market entry or exit.

Consumer Demand

The desire of consumers to purchase goods and services at given prices, which can vary with changes in income, preferences, and prices of related goods.