Alias-Component Matrices of Multirate Systems

• Published in: IEEE transactions on circuits and systems. II, Express briefs Vol. 56; no. 6; pp. 489 - 493
• Main Author: Mehr, A.S.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2009; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Alias-components; Circuits; Councils; Delay; Delay effects; Design methodology; Filter bank; Frequency; Frequency bands; Interpolation; Invariants; Kernel; Kernels; Linear systems; Mathematical analysis; Matrices; Matrix methods; multirate systems; Sampling methods; Time varying systems
• ISSN: 1549-7747; 1558-3791
• DOI: 10.1109/TCSII.2009.2020927

We consider a multirate system, which is a generalization of linear time-invariant systems. Such a system is invariant to a certain shift in the input sequence. In particular, assume that p and q are coprime. A multirate system with the property that a delay of mq samples in its input sequence results in a delay of mp samples in its output sequence is called an ( mp , mq )-periodic system. This multirate system can be obtained by cascading an upsampler, followed by a linear periodically time-varying (LPTV) kernel system, then followed by a downsampler. Here, we study the alias-component matrices of multirate systems. We show that they can be obtained from the alias-component matrices of their LPTV kernels by some row and column additions. An example shows the use of the method to design rate changers for a specified frequency band swap.