Two new cascade resonator-in-a-loop filter configurationsfortracking multiple sinusoids

A New Adaptive Filter Structure for Tracking Multiple Sinusoids

“…We refer this structure as the "simple cascade" adaptive structure. In papers [2] and [3], an "adaption-intensive" cascade structure with feedback signals was introduced for expanding the "simple cascade" structure to improve performance. This structure is shown in Figure 1.…”

“…A NEW CASCADE STRUCTURE WITH FEEDBACK SIGNALS FOR TTRACKING MULTIPLE SINUSOIDS Arising out of experience of the cascade structure with feedback signals advanced in [2] and [3] (shown in Figure 1), we have devised the modified processing structure shown in Figure 2. The block defined by dashed lines shows the area where our new "streamlined" structure differs from its forebear (which in retrospect we have dubbed our "adaptionintensive" structure shown in Figure 1).…”

“…The adaptive algorithm chosen for use is an approximate Gauss-Newton Gradient algorithm [5], [6]. The update scheme [2]- [6] is:…”

“…where y,,1 (k) is the pseudosensitivity output derived inside the ith adaptive filter [2]- [3], [6], Ye,i(k) is the corresponding error or notch output, emIl is used to preventpf being divided by a very small value or zero, wi (k) is the updated weight coefficient related to a1 by a1 = 1w 2(k) / 2 and the 2 y,,,i(k) term gives the normalized power of yp,i(k) obtained by using a uniform sliding window. Our main interest is in:…”

“…It is then very easy for the adaptive filter a3 to converge to the lone remaining sinusoidal signal at V3. Similar to the "adaption-intensive" cascade structure [2] in Figure 1, the feedback signals (i.e. the enhanced output signals from the adaptive filters a3 and a2) in this new structure are used to purify the input signals to either adaptive filter al or a2.…”