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 mean value ¯x. hint: x¯ = ¯x(t). in matlab

To calculate the mean value of the given time-continuous signal in MATLAB, you can evaluate the integral of the signal over its defined time interval and then divide by the length of the interval. Here's the MATLAB code to calculate the mean value of the signal:

main.m
syms t; % Define t as a symbolic variable

x_t = t^2/4 - t^2; % Define the signal x(t)

t_max = t/2; % Upper bound of the time interval
t_min = -t/2; % Lower bound of the time interval

x_mean = int(x_t, t_min, t_max) / (t_max - t_min); % Calculate the mean value

% Substitute t with a specific value to calculate the mean value numerically
t_value = 2; % Replace 2 with your desired value for t
mean_value = subs(x_mean, t, t_value);

% Display the mean value of the signal
mean_value
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Make sure you have the Symbolic Math Toolbox installed in MATLAB to perform the symbolic integration. By substituting the value of t with your desired constant, mean_value will give you the mean value of the signal.

Please note that the provided signal is not properly defined. The expression x(t) = t^2/4 - t^2 is the same as x(t) = -t^2/4. Also, the interval t ∈ [-t/2, t/2] does not allow for a meaningful calculation of the mean value.