The objective of this last computer exercise is to use MATLAB to convert a continuous time second order band pass filter to a discrete time band pass filter using:
The objective of this last computer exercise is to use MATLAB to convert a continuous time second order band pass filter to a discrete time band pass filter using:
- the bilinear transformation.
- the impulse invariance method
That is, starting with an H(s), convert to H[z] using the two above techniques. Compare the two results for H[z].
Start with:
where bandwidth 𝜷is set to 2𝝅50 rad/sec and 𝜔o is set to 2𝝅300 rad/sec. Assume an actual sampling interval ∆t = 0.0005 sec. For the bilinear transformation, adjust the actual sampling interval to∆t’ by pre-warping to match discrete time center frequency to continuous time center frequency 𝜔o. (Do this pre-warping by hand calculation.)
Use MATLAB to do the actual conversions from H(s) to H[z]. The “MATLAB Examples” file posted on Canvas shows ways of doing the conversions.
Submit plots showing magnitude and angle of H[z] for the bilinear transformation.
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