Given the recurrence relation: $y[n] = x[n] + 0.5y[n-1]$ I want to determine the filter type (i.e. LPF, HPF etc.)

I try to use Z transform, and get that the the transfer function is $H(z) = \frac{2z}{2z-1}$ So I derive that the filter is HPF (High pass). Is it correct?

  • $\begingroup$ Hint : what is the gain at z = 1? I.e. DC. Is it 0? If it's not 0, it's not a high-pass filter. $\endgroup$ – Ben Feb 4 '19 at 16:34
  • $\begingroup$ H(1) = 2 and H(infinity) = 1, so it means it is LPF? $\endgroup$ – ron653 Feb 4 '19 at 16:47
  • $\begingroup$ Evaluating at z = infinity makes no sense. The frequency response is evaluated over the unit circle, with DC at z = 1, and freq pi at z = -1 $\endgroup$ – Juancho Feb 4 '19 at 17:14
  • $\begingroup$ So how I determine the type of the filter? $\endgroup$ – ron653 Feb 4 '19 at 17:43
  • 1
    $\begingroup$ Most filters don't fit an easy category like high/low pass. Why do you need to know the filter type and what is the range of "allowed" answers ? $\endgroup$ – Hilmar Feb 4 '19 at 18:18

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