An input signal is defined as such: vin(t) = 7 + 10sin(10πt) + 3sin(20πt) + 2sin(40πt) + 7sin(60πt) + 6sin(80πt) + 10sin(100πt) + 6sin(120πt) + 8sin(140πt) + 3sin(160πt) + 5sin(180πt) + 4sin(200πt) + 7sin(220πt) + 6sin(240πt) + 4sin(260πt) + 5sin(280πt) + 2sin(300πt) + 6sin(320πt) + 8sin(340πt) + 9sin(360πt) It is determined that all frequencies below 30Hz and above 120Hz are not associated with the signal and are hence noise, i.e. it is necessary to pass all frequencies 30-120Hz. Furthermore, there is significant interference from the power supply at 50Hz that must be removed. The band-notch filter that is available for use to remove the 50Hz interference from the power supply has the following function: TFBN ( f ) = 1 f < 30 (50 − f ) 20 30 ≤ f < 50 ( f − 70) 20 +1 50 ≤ f < 70 1 f ≥ 70 $ % & & & ' & & & A filter to remove low frequencies (high-pass filter) is defined as follows where flow is the lowest frequency you need to pass unattenuated (i.e. where the filter has no effect). TFHPF ( f ) = 0 f < f ( low − 20) ( f − flow ) 20 +1 f ( low − 20) ≤ f < flow 1 f ≥ flow $ % & & ' & & A filter to remove high frequencies (low-pass filter) is defined as follows where fhigh is the highest frequency you need to pass unattenuated. TFLPF ( f ) = 1 f < fhigh ( fhigh + 40 − f ) 40 fhigh ≤ f < fhigh + 40 0 f ≥ fhigh + 40 $ % & & ' & & a) Plot vin(t) for time 0 < t < 0.3s 1 Mark Note: remember when plotting the signal that you may have to incorporate the constant 2π in the frequency as ω = 2πf b) Find flow and fhigh and hence define TFHPF(f) and TFLPF(f) 1 Mark c) Plot the frequency domain spectrum of each filter individually and the total filter TF (hint TF is the product of all three filters at each frequency) 1 Mark Note: remember a sine wave has only one frequency component, at the frequency of oscillation d) Plot the signal Vin(f) in the frequency domain, that is the frequency spectrum of vin(t) 1 Mark e) Plot the resulting output signal Vout(f) in the frequency domain 1 Mark Note: Make sure to use the same scale as the input graph in d) in order to make comparison easier f) Comment on the differences between the input and output signals in the frequency domain 1 Mark g) Find the formula for vout(t) 1 Mark h) Plot the resulting output signal vout(t) in the time domain 1 Mark Note: Make sure to use the same scale as the input graph in a) in order to make comparison easier i) Comment on the differences between the input and output signals in the time domain 1 Mark j) What is the highest frequency component of the output signal and what it need to be sampled at to ensure there was no aliasing after analog to digital conversion? 1 Mark