V_{out}(t) = H(\omega) A\text{sin}(\omega t + \theta(\omega) )+ H(2\omega) B \text{cos}(2\omega t + \theta(2\omega)) given that H(\omega)e^{j\theta(\omega)} = \frac{R_2}{R_1(1 + j\omega C_1R_2)}

V_{out}(t) = H(\omega) A\text{sin}(\omega t + \theta(\omega) )+ H(\omega) B \text{cos}(2\omega t + \theta(\omega)) given that H(\omega)e^{j\theta(\omega)} = \frac{R_2}{R_1(1 + j\omega C_1R_2)}

V_{out}(t) = H(\omega) A\text{sin}(\omega t + \theta(\omega) ) - H(\omega) B \text{cos}(2\omega t + \theta(\omega)) given that H(\omega)e^{j\theta(\omega)} = \frac{R_1R_2}{(1 + j\omega C_1R_1)}

V_{out}(t) = H(\omega) A\text{sin}(\omega t + \theta(\omega) )+ H(2\omega) B \text{cos}(2\omega t + \theta(2\omega)) given that H(\omega)e^{j\theta(\omega)} = \frac{R_1}{R_2(1 + j\omega C_1R_1)}

V_{out}(t) = H(\omega) A\text{sin}(\omega t + \theta(\omega) )+ H(\omega) B \text{cos}(2\omega t + \theta(\omega)) given that H(\omega)e^{j\theta(\omega)} = \frac{R_1}{R_2(1 + j\omega C_1R_1)}