Conditions for Lth-band filters of order 2N as cascades of identical linear-phase FIR spectral factors of order N
2014 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 97, no AprilArticle in journal (Refereed) Published
This paper presents formulas for the number of optimization parameters (degrees of freedom) when designing Type I linear-phase finite-length impulse response (FIR) Lth-band filters of order 2N as cascades of identical linear-phase FIR spectral factors of order N. We deal with two types of degrees of freedom referred to as (i) the total degrees of freedom D-T, and (ii) the remaining degrees of freedom D-R. Due to the symmetries or antisymmetries in the impulse responses of the spectral factors, D-T roughly equals N/2. Some of these parameters are specifically needed to meet the Lth-band conditions because, in an Lth-band filter, every Lth coefficient is zero and the center tap equals 1/L. The remaining D-R parameters can then be used to improve the stopband characteristics of the overall Lth-band filter. We derive general formulas for D-R with given pairs of L and N. It is shown that for a fixed L, the choices of N, in a close neighborhood, may even decrease D-R despite increasing the arithmetic complexity, order, and the delay.
Place, publisher, year, edition, pages
Elsevier , 2014. Vol. 97, no April
Pulse shaping; Lth-band filters; Spectral factors; FIR filters; Linear-phase
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-105405DOI: 10.1016/j.sigpro.2013.10.013ISI: 000331506000001OAI: oai:DiVA.org:liu-105405DiVA: diva2:706693