4. a) Find the coefficients of the trigonometric Fourier series expansion of the following waveform, x(t): xt) Input 0 2 Then use your answer to the above question to find a compact trigonometric Fourier series expansion and sketch its magnitude response function. [Note: Useful integral formulas: St cos(at)dt = cos(at) sin(at), t sin(at)dt = sin(at) - cos(at)] tsin a2 a 2 b) Suppose the above waveform is fed to the following filter circuit, where x(t) and y(t) denote the input and output voltages, respectively. What kind of filter is it and why? Using its filtering characteristics into consideration, what is the approximate steady state output? Door suth