- Matched Z-transform method
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The s-plane poles and zeros of a 5th-order Chebyshev type II lowpass filter to be approximated as a discrete-time filterThe z-plane poles and zeros of the discrete-time Chebyshev filter, as mapped into the z-plane using the matched Z-transform method with T = 0.1 second. The labeled frequency points and band-edge dotted lines have also been mapped through the function exp(sT), to show how frequencies along the iω axis in the s-plane map onto the unit circle in the z-plane.
The matched Z-transform method, also called the pole–zero mapping[1][2] or pole–zero matching method,[3] is a technique for converting a continuous-time filter design to a discrete-time filter (digital filter) design.
The method works by mapping all poles and zeros of the s-plane design to z-plane locations z = exp(sT), for a sample interval T.[4]
Alternative methods include the bilinear transform and impulse invariance methods.
References
- ^ Won Young Yang (2009). Signals and Systems with MATLAB. Springer. p. 292. ISBN 9783540929536. http://books.google.com/books?id=GnfpELDfzmEC&pg=PA292.
- ^ Bong Wie (1998). Space vehicle dynamics and control. AIAA. p. 151. ISBN 9781563472619. http://books.google.com/books?id=n97tEQvNyVgC&pg=PA151.
- ^ Arthur G. O. Mutambara (1999). Design and analysis of control systems. CRC Press. p. 652. ISBN 9780849318986. http://books.google.com/books?id=VSlHxALK6OoC&pg=PA652.
- ^ S. V. Narasimhan and S. Veena (2005). Signal processing: principles and implementation. Alpha Science Int'l Ltd.. p. 260. ISBN 9781842651995. http://books.google.com/books?id=8UbV8vq8uV0C&pg=PA260.
Digital signal processing Theory Sub-fields Techniques Discrete Fourier transform (DFT) · Discrete-time Fourier transform (DTFT) · Impulse invariance · bilinear transform · pole–zero mapping · Z-transform · advanced Z-transformSampling oversampling · undersampling · downsampling · upsampling · aliasing · anti-aliasing filter · sampling rate · Nyquist rate/frequencyCategories:- Control theory
- Digital signal processing
- Filter theory
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