Receiver and adaptive digital notch filter

A receiver comprising:

• first means producing a digital baseband signal x.sub.1 (n), and second means for (i) filtering out a plurality of at least j of narrowband interferences corrupting x.sub.1 (n) and (ii) producing an output y.sub.j (n),
• said second means comprising a plurality j of adaptive digital notch filters connected in cascade so that the first filter receives x.sub.1 (n) and outputs y.sub.1 (n), and the jth filter receives x.sub.j (n)=y.sub.j-1 (n) and outputs y.sub.j (n), said j filters each having a z-transform transfer function H.sub.i (z), said
• H.sub.i (z)=(1+k.sub.i.sup.* z.sup.-1)/(1+a.sub.i.sup.* z.sup.-1)
• where
• i=1 . . . j
• a.sub.i.sup.* =B.sub.i k.sub.i.sup.*
• .sup.* is the complex conjugate operator
• B.sub.i is a selected multiplier less than 1
• k.sub.i =(k.sub.Ri)/(W.sub.i)
• k.sub.Ri =-C.sub.i (n)/D.sub.i (n)
• C.sub.i (n)=G.sub.i C.sub.i (n-1)+P.sub.i (n-1)P.sub.i.sup.* (n)
• Di(n)=G.sub.i D.sub.i (n-1)+P.sub.i (n-1)P.sub.i.sup.* (n-1) ##EQU3## and G.sub.i is a selected multiplier less than 1 and W.sub.i is a predetermined one of (I) .vertline.k.sub.Ri .vertline. or (II) a predetermined constant q.sub.i
• each said a.sub.i.sup.* and k.sub.i.sup.* being iteratively computed and settling at substantially steady state values when one of the narrowband interferences in y.sub.i (n) is minimized.

An adaptive digital notch filter for use in (i) filtering a digital signal x(n) corrupted with interference, and (ii) providing digital signal output y(n) where the corrupting interference has been reduced, said filter having a z-transform transform function H(z), said

• H(z)=(1+k.sup.* z.sup.-1)/(1+a.sup.* z.sup.-1)
• where
• a.sup.* =Bk.sup.*
• .sup.* is the complex conjugate operator
• B is a selected multiplier less than 1
• k=(k.sub.R)/(W)
• k.sub.R =-C(n)/D(n)
• C(n)=GC(n-1)+P(n-1)P.sup.* (n)
• D(n)=GD(n-1)+P(n-1)P.sup.* (n-1) ##EQU4## and G is a selected multiplier less than 1 and W is a predetermined one of (I) .vertline.k.sub.R .vertline. or (II) a predetermined constant
• said a.sup.* and k.sup.* being iteratively computed at new input samples and settling at substantially steady state values when the interference in y(n) is minimized.