On the correction of linear time-varying systems by means of time-varying FIR filters

Abstract

In this paper, methods for the design of time-varying finite impulse response (FIR) filters which facilitate the correction of time-varying systems are presented. The two possible cases where an undesired time-varying system requires either prepro cessing or postprocessing are considered. In particular, we show how the methods from [1], [2] can be used for the precorrection of time-varying systems. Though, these presented methods allow for the correction of systems exhibiting periodically recurring time varying behavior, these techniques can also be applied to the non periodic case. A mixed-signal application is presented to verify the viability of the presented precorrection case. To this end, a system model for non-uniform zero-order-hold (ZOH) signals in a digital-to-analog converter (DAC) is introduced. Finally, numerical simulations are performed to illustrate the increase of performance when the proposed precorrection is employed.

Correction Structures for Linear Weakly Time-Varying Systems

“…In order to assess the correction performance, the SNR was calculated as (27) where represents the overall delay of the system, cf. (14), and specifies the number of considered samples. The output spectrum of the nonuniform ZOH signals is shown in Fig.…”

“…As presented in [28], the output of a nonuniform ZOH including an ideal low-pass filter may be described as [14] ( 30) where the CTFT of is defined as for for .…”

“…Changing the indices of the discrete-time model of the time-varying ZOH in (32) to (34) and comparing it to the time-varying system in (7), which has been used to derive our precorrection structure, reveals that the filter is given by [14] (35)…”

“…Various methods exist to compensate the effect of -periodically time-varying systems, for example by means of a subsequent -periodically time-varying reconstruction filter [13], synthesis filters in a filter bank [17] or by utilizing a multichannel bank of filters employing multirate theory [18]. These techniques offer great flexibility to correct for general frequency characteristics, however, the design complexity of these reconstruction filters is challenging as matrix inversions have to be performed or optimization problems need to be solved [6], [14], [19]. The resulting computational load is especially a disadvantage if the characteristics of the time-varying system change during operation, and the correction system has to be redesigned to meet the desired compensation performance.…”

“…Thanks to this significant observation, structures to compensate linear weakly time-varying systems can be seen in a completely different context. The structures proposed in [9], [21], [22], [24], [25] can be redesigned by updating a few time-varying multipliers only which offers a significantly reduced design complexity compared to the filter design based approaches in [6], [14], [19].…”