a time-continuous signal is defined as: x(t) = t^(2)/4 − t^(2); t ∈ [- t/2, t/2]; where t > 0 is some constant. calculate the signal energy ex. hint: ex = ex(t) in matlab

To calculate the energy of a time-continuous signal in MATLAB, we need to integrate the squared magnitude of the signal over its defined time interval.

First, let's define the signal x(t) using MATLAB code:

main.m
syms t; % symbolic variable
T = 5; % some positive constant
x_t = t^2/4 - t^2; % define the signal
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Next, we need to calculate the energy of the signal by integrating its squared magnitude over the interval [-T/2, T/2]. The energy can be calculated using the following formula:

main.m
E_x = int(abs(x_t)^2, -T/2, T/2);
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Here, abs(x_t)^2 squares the magnitude of the signal, and int performs the integration over the given interval.

Finally, we can evaluate the energy by substituting the value of T into the equation:

main.m
E_x_value = double(subs(E_x, T));
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The double function will convert the symbolic result into a numeric value, and subs will substitute the value of T into the expression.

Here is the complete code to calculate the signal energy:

main.m
syms t; % symbolic variable
T = 5; % some positive constant
x_t = t^2/4 - t^2; % define the signal
E_x = int(abs(x_t)^2, -T/2, T/2); % calculate energy
E_x_value = double(subs(E_x, T)); % evaluate energy
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The variable E_x_value will contain the energy value of the signal, calculated using the given signal expression and time interval.