a method of estimating a period and a time delay , or phase , of an input signal . a plurality of transition times } i are received , each transition time } i having a weight α } i comprising a forgetting factor α and a weighting factor } i . upon receiving an n th transition time to and determining an n th weighting factor γ 0 , maximum likelihood estimates } and } φ of the period and the time delay , respectively , are calculated . the estimates are computed recursively , with } depending upon α , γ 0 , t 0 , and a preceding maximum likelihood estimate } of the period . the value of } φ depends upon α , γ 0 , and t 0 . the estimates } and } φ also depend on sums s n − 1 = σ i =− 0 i n α − i } i . after the estimates } and } φ are computed , the sums are updated in anticipation of the next transition time . the method is preferably implemented electronically , resulting in a digital phase locked loop . the weighting factors allow the digital phase locked loop to lock onto a signal having absent transitions .