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A filter described by the equation: y(n) = x(n) + x(n-1) + 0.9 y(n-1) - 0.81 y(n-2)
(a) Find the transfer function H(z) for the filter and find the poles and zeros of the filter.
(b) Plot the poles and zeros of the filter using zplane(b,a) and tell whether or not this filter is stable.
(c) Plot the magnitude and phase of the frequency response of the filter. Annotate the plots to indicate the magnitude and phase response at points ω=0.33π and ω=π.
(d) Generate 200 samples of the signal x(n) = sin(0.33π n) + 5 cos(nπ) and process them through the filter. Plot both the filter's input x(n) and output y(n) on the same graph.
(e) How are the amplitudes of the two sinusoids affected by the filter?
(f) Determine the equation for the steady-state output yss(n) of the filter whose input is x(n).
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An FIR filter has coefficients b = [ 1.0000 -0.6387 1.0214 0.8210 -0.7470 1.0920 ] (a) Find H(z) for the filter and plot its frequency response (magnitude and phase
Create a text file with simulated data. Calculate an experimental y using the first function and some reasonable values for the parameters Add noise Save the x values and ca
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Adaptive filters can also be used in other applications. Speech recognition, for example, is performed in a non-stationary environment, and therefore may require adaptive filtering
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