ANC because the step size must be reduced to ensure stability. Furthermore, it is not
always feasible to place the reference sensor far away from the signal source. The second
method for reducing crosstalk is to place an acoustic barrier (an oxygen mask in an
aircraft cockpit, for example) between the primaryand reference sensors. However,
manyapplications do not allow an acoustic barrier between sensors, and a barrier may
reduce the correlation of the noise component in the primaryand reference signals. The
third technique involves allowing the adaptive algorithm to update filter coefficients
during silent intervals in the speech. Unfortunately, this method depends on a reliable
speech detector that is veryapplication dependent. This technique also fails to track the
environment changes during the speech periods.
8.5.4 Adaptive Notch Filters
In certain situations, the primaryinput is a broadband signal with an undesired
narrowband (sinusoidal) interference. The conventional method of eliminating
such sinusoidal interference is byusing a notch filter tuned to the frequencyof
the interference. To design the filter, we need to estimate the precise frequencyof the
interference. A verynarrow notch is usuallydesired in order to filter out the inter-
ference without seriouslydistorting the signal of interest. The advantages of the
adaptive notch filter are that it offers an infinite null, and the capabilityto adaptively
track the frequencyof the interference. The adaptive notch filter is especiallyuseful
when the interfering sinusoid drifts slowlyin frequency. In this section, we will present
two adaptive notch filters.
The adaptive structure shown in Figure 8.7 can be applied to enhance the broadband
signal, which is corrupted bymultiple narrowband components. For example, the input
signal expressed in (8.5.5) consists of a broadband signal v(n), which is music. In this
application, e(n) is the desired output that consists of enhanced broadband music
signals since the narrowband components are readjusted by W(z) so that theycan
cancel correlated components in d(n). The adaptive system between the input x(n) and
the output e(n) is an adaptive notch filter, which forms several notch filters centered at
the frequencyof the sinusoidal components.
A sinusoid can be used as a reference signal for canceling each component of
narrowband noise. When a sinewave is employed as the reference input, the LMS
algorithm becomes an adaptive notch filter, which removes the primaryspectral com-
ponents within a narrowband centered about the reference frequency. Furthermore,
multiple harmonic disturbances can be handled if the reference signal is composed of a
number of sinusoids.
A single-frequencyadaptive notch filter with two adaptive weights is illustrated in
Figure 8.10. The reference input is a cosine signal
n A cos!
A 908 phase shifter is used to produce the quadrature reference signal
n A sin!