A recursive filter is defined: y[n] = (1 - α)x[n] + αy[n-1], 0 < α < 1 Use algebra to obtain the impulse and step responses of the given recursive filter.
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Step 1
Impulse response: The impulse response of a filter is the output when the input is a single impulse (i.e., a single sample with value 1 and all other samples with value 0). Therefore, we can set x[n] = δ[n], where δ[n] is the Kronecker delta function: y[n] = Show more…
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