The relation between the input samples, {x[n]}, and the output samples, {y[n]} f

Question

The relation between the input samples, {x[n]}, and the output samples, {y[n]} for a digital filter is given by where a is a real number and M is an even positive integer. the transfer function for this filter is given by The sampling frequency for this filter is set to be equal to 300 Hz. This filter is to be used to enhance a signal above noise. The signal has a non-zero amplitude spectrum for spectral frequencies Hz. This signal is also contaminated by mains Interference at 50 Hz and harmonics at 100 Hz and 150 Hz. Determine M such that the designed filter eliminates the mains interference and Its two harmonics. Determine an appropriate value for a. Sketch the unit circle in the z-plane marking clearly the zeros and poles of your designed filter and also the point on the unit circle corresponding to a frequency of 50 Hz.

Explanation / Answer

a) A synthetic atmosphere is created by blending 2 mol percent CO2, 20 mol percent O2 and 78 mol percent N2. If the total pressure is 750 torr, calculate the partial pressure of the oxygen component. Mole fraction of oxygen is (20/100) = 0.2 Therefore, partial pressure of oxygen = (0.2)(750 torr) = 150 torr b) If 25 liters of this atmosphere, at 37°C, have to be produced, how many moles of O2 are needed? PO2 = 150 torr (1 atm/760 torr) = 0.197 atm V = 25 L T = (273+37K)=310K R=0.0821 L atm/mol K PV = nRT n = (PV)/(RT) = (0.197 atm * 25 L)/(0.0821 L atm/mol K * 310K) n = 0.194 mol

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