Sinais e sistemas
\[ E_x = \int_{-\infty}^{\infty} |x(t)|^2 \dif t \qquad P_x = \lim_{\tau \to \infty} \frac{1}{\tau} \int_{-\tau/2}^{\tau/2} |x(t)|^2 \dif t \qquad P_x = \int_{-\infty}^{\infty} S_x(f) \dif f \qquad \] \[ P_x = \frac{1}{T} \int_{-T/2}^{T/2} |x(t)|^2 \dif t \quad \text{(sinal periódico)} \]
Quantização
\[ \SQNR \approx 3 \frac{P_m}{m_p^2}{L^2} \]
Transmissão de pulsos em banda base
\[ \Rs = \frac{1}{\Ts} \qquad B = (1 + \alpha) \frac{\Rs}{2} \qquad P = \Es\Rs \] \[ h_\mathrm{RX}(t) = c \, h_\mathrm{TX}(\Ts-t) \quad \text{(filtro casado)} \] \[ M = 2^k \qquad \Tb = \frac{\Ts}{k} \qquad \Rb = k \Rs \qquad \Eb = \frac{\Es}{k} \qquad \Pb \approx \frac{\Ps}{k} \quad \text{(Gray, alta SNR)} \] \[ \Pb = Q \left( \sqrt{\frac{2 \Eb}{N_0}} \right) \quad \text{(polar)} \qquad \Pb = Q \left( \sqrt{\frac{\Eb}{N_0}} \right) \quad \text{(on-off)} \qquad \Ps = \frac{2(M-1)}{M} Q \left( \sqrt{\frac{6 \Es}{(M^2 - 1) N_0}} \right) \quad \text{(M-PAM)} \]