Name
Abstract | ||
|---|---|---|
By interpreting the Green-function reproduction property of exponential splines in signal processing terms, we uncover a fundamental relation that connects the impulse responses of allpole analog filters to their discrete counterparts. The link is that the latter are the B-spline coefficients of the former (which happen to be exponential splines). Motivated by this observation, we introduce an extended family of cardinal splines-the generalized E-splines-to generalize the concept for all convolution operators with rational transfer functions. We construct the corresponding compactly supported B-spline basis functions, which are characterized by their poles and zeros, thereby establishing an interesting connection with analog filter design techniques. We investigate the properties of these new B-splines and present the corresponding signal processing calculus, which allows us to perform continuous-time operations, such as convolution, differential operators, and modulation, by simple application of the discrete version of these operators in the B-spline domain. In particular, we show how the formalism can be used to obtain exact, discrete implementations of analog filters. Finally, we apply our results to the design of hybrid signal processing systems that rely on digital filtering to compensate for the nonideal characteristics of real-world analog-to-digital (A-to-D) and D-to-A conversion systems. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1109/TSP.2005.843699 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
analog filter design technique,b-spline domain,part ii,corresponding signal processing calculus,b-spline basis function,cardinal exponential spline,b-spline coefficient,discrete implementation,discrete counterpart,analog filter,allpole analog filter,exponential spline,poles and zeros,spline,transfer function,transfer functions,convolution,modulation,digital filtering,green function,sampling,splines,digital filter,signal processing,calculus,filtering,convolution operator,filter design,green s function,impulse response,analog signal processing,differential operators,digital signal processing,digital filters,transient response | Signal processing,Digital filter,Convolution,Control theory,Operator (computer programming),Analog signal,Rational function,Analog signal processing,Mathematics,Filter design | Journal |
Volume | Issue | ISSN |
53 | 4 | 1053-587X |
Citations | PageRank | References |
27 | 3.19 | 16 |
Authors | ||
1 | ||