The energy of a signal x(t) is denoted by E. If we scale the time variable by a factor of 5, the signal becomes x(5t). The energy of this new signal is not E/5, 5E, E/25, or 25E.

The energy of a signal x(t) is given by the integral over all time of the square of the signal, i.e., E = ∫|x(t)|^2 dt.

When we change the variable from t to 5t, we get a new signal x(5t). The energy of this new signal is given by E' = ∫|x(5t)|^2 dt.

We can change the variable of integration from t to u = 5t. Then du = 5dt, and dt = du/5. The limits of integration change accordingly.

So, E' = ∫|x(u)|^2 du/5 = (1/5) ∫|x(u)|^2 du.

This is the same integral as before, but scaled by a factor of 1/5. Therefore, the energy of the signal x(5t) is E/5.

Question

The energy of a signal x(t) is denoted by E. If we scale the time variable by a factor of 5, the signal becomes x(5t). The energy of this new signal is not E/5, 5E, E/25, or 25E.

The energy of a signal x(t) is given by the integral over all time of the square of the signal, i.e., E = ∫|x(t)|^2 dt.

When we change the variable from t to 5t, we get a new signal x(5t). The energy of this new signal is given by E' = ∫|x(5t)|^2 dt.

We can change the variable of integration from t to u = 5t. Then du = 5dt, and dt = du/5. The limits of integration change accordingly.

So, E' = ∫|x(u)|^2 du/5 = (1/5) ∫|x(u)|^2 du.

This is the same integral as before, but scaled by a factor of 1/5. Therefore, the energy of the signal x(5t) is E/5.

Knowee AI · Accepted Answer

The energy of a signal x(t) is denoted by E. If we scale the time variable by a factor of 5, the signal becomes x(5t). The energy of this new signal is not E/5, 5E, E/25, or 25E.

The energy of a signal x(t) is given by the integral over all time of the square of the signal, i.e., E = ∫|x(t)|^2 dt.

When we change the variable from t to 5t, we get a new signal x(5t). The energy of this new signal is given by E' = ∫|x(5t)|^2 dt.

We can change the variable of integration from t to u = 5t. Then du = 5dt, and dt = du/5. The limits of integration change accordingly.

So, E' = ∫|x(u)|^2 du/5 = (1/5) ∫|x(u)|^2 du.

This is the same integral as before, but scaled by a factor of 1/5. Therefore, the energy of the signal x(5t) is E/5.

If E denotes energy of a signal x(t) then energy of the signal x(5t) is1 pointE/55EE/2525E

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