Consider an LTI system with impulse response $$h\left(t\right)=e^{-5t}u\left(t\right)$$ . If the output of the system is $$y\left(t\right)=e^{-3t}u\left(t\right)-e^{-5t}u\left(t\right)$$ then the input, x(t), is given by

A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output is