DocumentCode :
3415506
Title :
Generalising the Polyphase Identity
Author :
Dhuli, Ravindra ; Lall, Brejesh
Author_Institution :
Dept. of Electr. Eng., Indian Inst. of Technol., New Delhi, India
fYear :
2009
fDate :
18-20 Dec. 2009
Firstpage :
1
Lastpage :
4
Abstract :
In this paper, we generalise the well known polyphase identity in multirate signal processing. A cascade of expander, linear system and a decimator is considered for simplification. The nature of the kernel of the linear system resulting in the cascade is studied. The linear system is chosen to be (p, q) shift invariant for further simplification. The different subcases of the problem which are equally important are also highlighted. The properties of cascade of shift invariant systems are derived, simultaneously stressing the important subcases. Interestingly two other problems, decimating a block Toeplitz matrix and a 2-D periodic signal were also addressed in the same framework. As an extension for expanding the kernel, we proposed a new multirate structure.
Keywords :
Toeplitz matrices; linear systems; signal processing; 2D periodic signal; block Toeplitz matrix; decimator; expander cascade; linear system; multirate signal processing; polyphase identity; shift invariant systems; Circuits; Filter bank; Image processing; Kernel; Linear systems; Signal processing; Speech processing; Time domain analysis; Time varying systems;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
India Conference (INDICON), 2009 Annual IEEE
Conference_Location :
Gujarat
Print_ISBN :
978-1-4244-4858-6
Electronic_ISBN :
978-1-4244-4859-3
Type :
conf
DOI :
10.1109/INDCON.2009.5409455
Filename :
5409455
Link To Document :
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