Discrete time adaptive notch filter

A method of removing N narrowband signal components from a signal, the method comprising:

• processing a digital representation of the signal with a filter having a transfer function of
• H
• (
• z
• -
• 1
• )
• =
• 1
• +
• a
• 1
• ⁢
• z
• -
• 1
• +
• a
• 2
• ⁢
• z
• -
• 2
• +
• …
• +
• a
• N
• ⁢
• z
• -
• N
• 1
• +
• ρ
• ⁢
• a
• 1
• ⁢
• z
• -
• 1
• +
• ρ
• 2
• ⁢
• a
• 2
• ⁢
• z
• -
• 2
• +
• …
• +
• ρ
• N
• ⁢
• a
• N
• ⁢
• z
• -
• N
• where z is a complex-frequency variable, the coefficients a1 . . . aN define the location of zeros of the transfer function, and the coefficients a . . . ay multiplied by a factor ρ (where ρ<1) define the location of poles of the transfer function, to remove the N components from the signal.

A discrete-time, digital filter for notch filtering a complex digital signal, the filter having a transfer function of

• H
• ⁡
• (
• z
• -
• 1
• )
• =
• 1
• +
• a
• 1
• ⁢
• z
• -
• 1
• +
• a
• 2
• ⁢
• z
• -
• 2
• +
• …
• +
• a
• N
• ⁢
• z
• -
• N
• 1
• +
• ρ
• ⁢
• a
• 1
• ⁢
• z
• -
• 1
• +
• ρ
• 2
• ⁢
• a
• 2
• ⁢
• z
• -
• 2
• +
• …
• +
• ρ
• N
• ⁢
• a
• N
• ⁢
• z
• -
• N
• where z is a complex-frequency variable, the coefficients a1 . . . . aN define the location of zeros of the transfer function, and the coefficients a1 . . . . aN multiplied by a factor ρ (where ρ<1) define the location of poles of the transfer function.