A car was ignited & a signal from the engine i.e a(z) was passed through a cascade of 2 passive RC lowpass filters to generate an output signal, b(z). a.Show a differential equation derivation to describe the system b.Make a sketch utilizing circuit diagram c.Mention if the RC system in question above is i.Time in-variant / Time variant ii.Non linear / linear iii.Non-invertible / Invertible iv. Non-causal / Causal v. Have no memory / Have memory sytems. d. d2b(z)/dz2 + 3(db(z)/dz) +2b(z) = 3(da(z)/dz) +2a(z) Let's assume that the d.e(differential equation) above is that which is characterised by the RC system in the main question above. Where a(z) & b(z) is the input & output of the RC system respectively.
A car was ignited & a signal from the engine i.e a(z) was passed through a cascade of 2 passive RC lowpass filters to generate an output signal, b(z).
a.Show a differential equation derivation to describe the system
b.Make a sketch utilizing circuit diagram
c.Mention if the RC system in question above is
i.Time in-variant / Time variant
ii.Non linear / linear
iii.Non-invertible / Invertible
iv. Non-causal / Causal
v. Have no memory / Have memory
sytems.
d. d2b(z)/dz2 + 3(db(z)/dz) +2b(z) = 3(da(z)/dz) +2a(z)
Let's assume that the d.e(differential equation) above is that which is characterised by the RC system in the main question above.
Where a(z) & b(z) is the input & output of the RC system respectively.
Considering an impulse of a(z)=δ(z) is applied to the system, determine the output b(z) of the system
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