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Give complete solution please, with all steps, otherwise thumb will go down. Thank you in advance. Consider a first order low-pass filter given by the following circuit. If

`x(t)`

is a square wave with frequency equal to

`50KHz`

, ranging from 0 to 2 volts, and with the origin being such that the maximum value occurs at the origin and the signal is an even function, determine the Fourier series for

`x(t)`

. a) Give an expression for the output,

`y(t)`

, in the time domain. b) Give an expression for the output,

`y(t)`

, in the frequency domain. c) Consider a

`40dB`

definition of bandwidth, i.e. all out-of-band frequency components are lower than

`-40dB`

relative to the main

`AC`

in-band component, what is the bandwidth of the output signal? d) Determine the average power of the input signal. e) Determine the average power of the output signal.