A Frequency Multiplier Based on Time Recursive Processing

Abstract

This paper describes a digital frequency multiplier for a pulse rate. The multiplier is based on the recursive processing of the input and output periods and their time differences. Special emphasis is devoted to the techniques which provide the development of multipliers based on this principle. The circuit is defined by two system parameters. One is the ratio of two clock frequencies and the other is a division factor of a binary counter. The realization of the circuit is described. The region of the system parameters for the stable circuit is presented. The different aspects of applications and limitations in realization of the circuit are considered. All mathematical analyses are made using a Z transform approach. It is shown that the circuit can be also used in tracking and prediction applications. Computer simulations are performed to prove the correctness of the math and the whole approach.

Frequency Locked Loop Based on the Time Nonrecursive Processing

“…Although digital filters process amplitude samples of the input signal, and TNP FLL uses periods of an input signal, it is very useful to understand the relationship between these two physically different systems in order to utilize, as much as possible, power digital filter theory and software tools in further development and application of TNP FLL. The theory and techniques for developing TNP FLL are basically very similar to the demonstrated ones in [1][2][3][4][5][6][7][8][9][10]. The applicability of this approach is very wide.…”

“…This kind of processing was called "recursive". In [1][2][3][4][5][6][7][8][9][10], to describe different applications, recursive processing was used. This means that the output period is calculated using input and output periods.…”

“…This actually means that all described algorithms in [1][2][3][4][5][6][7][8][9][10] function as feedback systems and they can possess the properties either of phase locked loop (PLL) or FLL. Unlike the described algorithms in [1][2][3][4][5][6][7][8][9][10], this approach of FLL is an open loop system. From the aspect of the algorithm used, it functions similarly to an FIR digital filter.…”

“…The applicability of this approach is very wide. Frequency multiplier is described in [1]. Time shifters are described in [2,3] and time/phase shifting in [4].…”

“…A wide range of tracking and prediction applications is described in [5,6,8]. Most of the algorithms described in [1][2][3][4][5][6][7][8][9][10] are suitable for usage in software form. Such a software predictor is described in [9].…”