Other simple non-recursive filters

• Test the following filter at DC and $f_s/2$:
  $$y(n) = x(n) - x(n-1).$$
  What type of filter is this?

• Verify that the following filter passes both DC and the Nyquist limit (1/2 the sampling rate):
  $$y(n) = x(n) + x(n-2).$$
  • what about at a frequency in between, $f = fs/4$?
    $$x(n) = [A, 0, -A, 0, A, 0, -A, \ldots],$$

  • at this frequency the filter produces no output; assume therefore a band-reject (notch) filter, with a notch at $f_s/4$.

• Verify that the following filter rejects both DC and the Nyquist limit, yes boosts a frequency at $f_s/4$.
  $$y(n) = x(n) - x(n-2).$$
  • what kind of filter is it?