Adaptive tracking notch filter system

An automatic tracking notch filter system tracks a large-magnitude narrow band signal through frequency effectively eliminating it. A frequency variable notch filter is responsive to a control input at which is applied a small amplitude AC dither signal. The resulting fluctuation in frequency of the notch filter causes corresponding fluctuations in the magnitude of the notch filter output. The output signal is rectified and band pass filtered around the dither frequency before being demodulated with the dither signal to provide a DC error signal indicating the magnitude and direction in frequency of the filter misalignment. The error signal is integrated and input to the control input of the notch filter with the dither signal such that the notch filter tracks the narrow band signal in response to the feedback signal provided at its control input.

BACKGROUND OF THE INVENTION 
In many systems utilizing electronic signals, an unwanted resonant spike or 
other large-magnitude narrow band signal is present in an otherwise useful 
signal due to physical properties of the system. One example of such a 
system is a control system for adjusting the mirror segments of a 
segmented mirror, such as is used in astronomy or light beam steering 
applications. These mirror segments often have a resonant frequency which 
typically introduces a large phase shift in the control system feedback 
loop which can destabilize the system. Unless the system bandwidth is much 
lower than the mirror resonant frequency, an appropriate phase margin 
required for system stability is difficult to achieve. 
The traditional method of removing or suppressing such a narrow band signal 
is through the use of a narrow band stop or notch filter centered around 
the center frequency of the narrow band signal. However, the center 
frequency of the narrow band signal may often vary in both frequency and 
amplitude as a function of temperature, loop band-width, or other system 
parameters. Such variation imposes a severe restriction on a fixed 
frequency notch filter. Obtaining sufficient attenuation over the 
variation in the narrow band center frequency has required the use of a 
low Q filter or multiple filters. In addition to being less efficient, 
each of the low Q filter and the multiple filter approaches, when used in 
a feedback amplifier, can add a significant phase lag at the unity gain 
crossover frequency of the system. The corresponding reduction in phase 
margin results in a reduced bandwidth or lower relative stability. More 
desirable would be a high Q notch filter with automatic frequency tracking 
to suppress a narrow band signal while tracking it through frequency 
variations. 
SUMMARY OF THE INVENTION 
A tracking notch filter system automatically tracks and suppresses a narrow 
band portion of a signal input to the filter. The notch filter system 
includes a variable notch filter, the notch center frequency of which 
moves in response to a signal applied to a control input of the notch 
filter. To determine the optimum notch center frequency, a dither signal 
generator also applies an AC dither signal to the control input. This 
causes the notch center frequency to fluctuate at the frequency of the 
dither signal. Center frequency adjustment is made as a function of the 
filter output response to the dither signal. 
In a specific embodiment a feedback loop feeds back and modifies an output 
signal of the notch filter. Within the feedback loop the output signal is 
converted to a signal having a dither frequency component. A band pass 
filter passes the component at the dither frequency. That component has 
amplitude corresponding to the offset of the notch center frequency from 
the input signal frequency and a phase corresponding to the direction of 
offset. To extract both amplitude and direction information, the component 
is input to a synchronous demodulator to be demodulated by a dither drive 
signal. The demodulated signal is then integrated with an integrator and 
used to modify the dither drive signal applied to the notch filter control 
input. 
Further included with the suppression filter may be a feed-forward circuit 
which generates a DC scaling signal proportional to the magnitude of the 
input. The scaling signal is used in the feedback loop to control the 
magnitude of the feedback signal prior to its being applied at the notch 
filter control input.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT 
FIG. 1 shows a system block diagram of a preferred embodiment of a tracking 
notch filter system. Bridged-T notch filter 10 has an input V.sub.I and an 
output V.sub.O. The notch filter 10 is variable in frequency such that its 
center frequency may be shifted up or down in frequency in response to a 
control input 12. Prior to application of input signal V.sub.I, the notch 
filter 10 is manually adjusted using filter adjustor 14. To perform this 
adjustment, filter input switch 15 is switched to provide electrical 
contact between the filter control input 12 and filter adjustor 14. Filter 
adjustor 14 is then used to adjust the notch filter so that the notch 
center frequency f.sub.n is located at the expected center frequency of a 
narrow band portion of V.sub.I that is to be suppressed. At this time, the 
quality factor (Q) of the filter is also manually adjusted using Q adjustor 
16 such that the notch filter frequency response best fits the response of 
the narrow band signal portion. Once the adjustments are complete, filter 
input switch 15 is switched to enable the feedback control of the notch 
filter system by providing electrical contact between filter input 12 and 
summing node 41. 
A positive control voltage applied through control input 12 causes the 
notch center frequency to increase while a negative voltage causes the 
notch center frequency to decrease. A dither signal from a dither 
generator 18 is applied to the control input 12 in combination with an 
error signal f.sub.E. The dither signal is an AC signal and in the present 
embodiment is a sinusoid. The application of the AC signal to the control 
input 12 causes the center frequency of the notch filter 10 to fluctuate 
at the frequency .omega..sub.d of the dither signal. The amplitude of the 
dither signal is typically small relative to the amplitude and bandwidth 
of the input signal V.sub.I. 
FIG. 2 shows the frequency response of an input signal V.sub.I having a 
narrow band signal component centered at frequency f.sub.c. The frequency 
response of a notch filter system for suppressing the narrow band portion 
of V.sub.I is also shown in FIG. 2 relative to the frequency scale of 
V.sub.I. The notch filter has a notch center frequency f.sub.n. The goal 
of the notch filter system is to keep the notch center frequency f.sub.n 
as close as possible to the narrow band center frequency f.sub.c of 
V.sub.I. In FIG. 2 f.sub.n is slightly higher in frequency than narrow 
band center frequency f.sub.c. Thus an error in the alignment of the notch 
center frequency exists which must be corrected. 
As demonstrated by the arrows adjacent the notch filter frequency response 
of FIG. 2, the center of the notch filter is varying in frequency with the 
control input signal .DELTA.f.sub.n. .DELTA.f.sub.n =f.sub.E 
+Asin(.omega..sub.d t) and causes a sinusoidal fluctuation of the notch 
center frequency f.sub.n at the dither frequency .omega..sub.d. FIG. 3A 
shows the control input signal .DELTA.f.sub.n. FIG. 3B illustrates the 
output of the notch filter with a high frequency input and dither of the 
notch frequency with the control signal .DELTA.f.sub.n. The fluctuation of 
the notch filter frequency response causes a fluctuation in the magnitude 
of V.sub.O. The signal of FIG. 3B corresponds to a situation in which the 
notch filter is offset higher in frequency than the narrowband signal 
portion, such as in FIG. 2. Since the notch filter center frequency 
increases with positive increases in voltage at the .DELTA.f.sub.n input 
the sinusoidal fluctuation in the envelope of the output signal V.sub.O 
shown in FIG. 3B is in phase with the dither signal. 
To demonstrate the system performance of the present embodiment a sinusoid 
at frequency .omega..sub.c is input as signal V.sub.I where .omega..sub.c 
=2.pi.f.sub.c. It is assumed that .omega..sub.c &gt;&gt;.omega..sub.d. As the 
signal passes through the notch filter system, it is attenuated by the 
notch filter 10 which is fluctuating in frequency around f.sub.n. With the 
notch filter center frequency f.sub.n offset slightly higher in frequency 
than f.sub.c, as in FIG. 2, the shifting of the notch filter upwards in 
frequency causes the attenuation of a signal at f.sub.c to decrease. This 
corresponds to a magnitude increase in the .omega..sub.c frequency 
component of V.sub.O. Similarly, the shifting downward in frequency of the 
notch filter causes the attenuation at f.sub.c to increase, and the 
magnitude of V.sub.O to correspondingly decrease. Therefore, when the 
filter is offset as in FIG. 2, the application of the dither signal to the 
notch filter causes a dither frequency sinusoidal fluctuation in the 
envelope of V.sub.O which is in phase with the dither signal. This is 
demonstrated in the sketch of V.sub.O shown in FIG. 3B. As shown, the 
result is that V.sub.O appears as the amplitude modulated signal 
(sin.omega..sub.c t)(sin.omega..sub.d t), the modulating frequency being 
the dither frequency .omega..sub.d. 
The notch filter output signal V.sub.O is input to the band pass filter 20 
of the feedback loop, as shown in FIG. 1. Band pass filter 20 passes only 
frequencies in the range of the narrow band signal portion of V.sub.I, 
removing high frequency and low frequency signal components which are 
outside the frequency range of interest. For the pure .omega..sub.c input 
signal of the present example, signal V.sub.OBPF is identical to V.sub.O, 
since V.sub.O has no very high or very low frequency components to be 
removed by filter 20. V.sub.OBPF, like V.sub.O, therefore consists of a 
sin.omega..sub.c t carrier modulated by a sin.omega..sub.d t envelope. 
However, if V.sub.O were to contain any frequency components outside the 
range of filter 20, these components would not be present in V.sub.OBPF. 
This filtering increases the signal-to-noise ratio of the feedback signal 
by removing the signal power outside of the frequency range of interest. 
After filtering, the signal V.sub.OBPF is input to full wave rectifier 22. 
Rectifier 22 is a non-linear element of the feedback loop which forces the 
signal V.sub.OBPF to be all positive. The resulting signal V.sub.OF is 
shown in FIG. 3D. As demonstrated by V.sub.OF, all the negative signal 
portions of V.sub.OBPF become inverted by the rectifier. However, the 
signal V.sub.OF is still modulated by the .omega..sub.d frequency 
component. The rectification of signal V.sub.OBPF adds some harmonics to 
the signal, as well as adding a DC component. 
Once rectified, signal V.sub.OF is input to band pass filter 24. Band pass 
filter 24 is a narrow response filter centered around the dither frequency 
.omega..sub.d. The output of filter 24 is signal V.sub.OBF which is the 
dither frequency component of V.sub.OF. Signal V.sub.OBF is shown in FIG. 
3E. Contained in V.sub.OBF is information sufficient to determine the 
frequency error of the notch filter center frequency so that a correcting 
error signal may be generated. However, prior to demodulating signal 
V.sub.OBF, the signal is normalized to the input signal to conform the 
magnitude of the error signal to any changes in the magnitude of input 
signal V.sub.I. 
Referring to FIG. 1, the signal V.sub.OBF is input to AGC divider 26. The 
AGC divider 26 isolates the feedback signal from amplitude variations in 
input signal V.sub.I by normalizing V.sub.OBF to the input signal. This is 
accomplished by dividing V.sub.OBF by DC scalar signal V.sub.AGC which has 
a magnitude proportional to the magnitude of V.sub.I. To obtain the AGC 
divider signal, input signal V.sub.I is fed into a band pass filter 28 
similar to the band pass filter 20 of the feedback circuit. The band pass 
filter 28 is the first stage in an automatic gain control feed-forward 
circuit, and filters out a band of frequencies encompassing the range of 
the narrow band signal. The output of band pass filter 28 is then fed into 
rectifier 30 which separates the filtered signal into a series of harmonic 
components including a DC RMS signal. The output of the rectifier 30 is 
then passed through low pass filter 32 to remove any high frequency 
components leaving just the DC component. To manually adjust the scaling 
of the feedback signal by the AGC feed-forward circuit, an AGC bias 
voltage from AGC bias input 34 may be added to the output of low pass 
filter 32 (V.sub.IA). V.sub.AGC is then used to scale V.sub.OBF in divider 
26 by dividing V.sub.OBF by V.sub.AGC. Thus the feedback signal is 
normalized to the system input and divider output V.sub.EAC is generated. 
After being normalized, the divider output signal V.sub.EAC is input to 
synchronous demodulator 38. During calibration 18 of the notch filter 
system, one output of the dither signal generator 18 is input to phase 
adjustor 36 where the phase of V.sub.d is manually adjusted. The phase 
adjustment compensates for any phase shift in the feedback signal 
introduced by feedback components 20, 22, 24, 26. This assures that 
relative phase shift between the feedback signal and the phase-adjusted 
dither signal is due to the positioning of the notch filter 10 in 
frequency, and not to inherent reactances of the feedback components. The 
output of the phase adjustor V.sub.da and the divider 26 are fed into 
synchronous demodulator 38. The demodulator 38 is a multiplier which 
outputs a DC component V.sub.EDC having a magnitude proportional to the 
magnitude of V.sub.EAC and a polarity corresponding to the relative phase 
relationship between V.sub.da and V.sub.EAC. If the notch filter center 
frequency is higher in frequency than the narrow band center frequency, as 
in FIG. 2, V.sub.EAC is in phase with V.sub.d and the multiplication of 
V.sub.EAC with V.sub.d causes V.sub.EDC to have a positive DC component. 
FIG. 3F shows V.sub.EDC for the previous example of the single frequency 
(.omega..sub.c) input signal. 
The output of demodulator, V.sub.EDC, is input to integrator 40. The 
integrator circuit averages the V.sub.EDC input signal over time. This 
provides a DC signal, f.sub.E, which goes to zero when the DC component of 
V.sub.EDC becomes zero. The integrator 40 also inverts V.sub.EDC so that 
f.sub.E has a polarity opposite to that of the DC component of V.sub.EDC. 
The error signal f.sub.E is combined with the dither signal at summing node 
41. From summing node 41, the combined signals are applied to the notch 
filter input 12 through filter input switch 15. Prior to applying the 
feedback signal, the notch filter center frequency f.sub.n is slightly 
higher than the narrow band signal portion center frequency f.sub.c, as 
shown in FIG. 2. Therefore, V.sub.da and V.sub.EDC are in phase, and 
V.sub.EDC is positive. Since this makes f.sub.E negative, the application 
of the signal at the dither input of notch filter 10 causes the center 
frequency f.sub.n of the notch filter to decrease in frequency. Thus, the 
filter center frequency gets closer to frequency f.sub.c to more 
efficiently attenuate the narrow band signal portion. The more efficient 
attenuation correspondingly reduces the error signal by reducing the 
magnitude of the dither frequency component of V.sub.O. This feedback 
control of the notch center frequency f.sub.n continues to shift f.sub.n 
in frequency until f.sub.n =f.sub.c. Thus, the notch filter "tracks" the 
narrow band signal portion. 
In contrast to FIG. 2, the possibility of the notch filter being offset 
lower in frequency than the narrow band signal portion of V.sub.I is 
demonstrated in FIG. 4. The sinusoidal dither signal input to the filter 
in FIG. 4 still causes the notch filter center frequency to fluctuate in 
frequency sinusoidally, as in FIG. 2. However, when the filter notch moves 
upward in frequency in response to the positive half cycle of the dither 
signal, the attenuation of the narrow band signal increases, causing a 
corresponding decrease in the magnitude of V.sub.O. Similarly, the 
negative half cycle of the dither signal causes an increase in the 
magnitude of V.sub.O. Therefore, when the filter is positioned lower in 
frequency than the narrow band signal, the dither frequency component 
.omega..sub.d of V.sub.O is 180.degree. out of phase with the dither 
signal. The dither frequency component is extracted and demodulated, Just 
as with the feedback signal for the filter positioning of FIG. 2. However 
since this .omega..sub.d component is 180.degree. out of phase with the 
dither signal, the demodulation of this signal with the adjusted dither 
signal V.sub.da generates a demodulator output V.sub.EDC which has a 
negative DC component. 
When a negative DC signal component is input to integrator 40, the 
inverting nature of the integrator causes the circuit to generate an 
output, f.sub.E, with a positive DC component. This positive f.sub.E is 
then combined with the dither signal and input to the notch filter 10 
through switch 15. The positive DG error signal causes the position of the 
notch filter center frequency to increase in frequency. Since the original 
position as shown in FIG. 4 was lower than the narrow band signal center 
frequency, this moves the filter into better alignment with the narrow 
band signal. The filter notch therefore continues to move upward in 
frequency until f.sub.n =f.sub.c and the DC error signal is minimized. 
Thus the narrow band signal portion is "tracked" and the efficiency of the 
filter is maximized. 
By comparing the example of FIG. 2 and that of FIG. 4, it will be apparent 
that whichever way the center frequency of the tracking notch filter may 
drift relative to the portion of the input signal to be suppressed, the 
filter system shifts the notch center frequency to compensate for the 
drift. Thus, the notch filter system tracks the signal portion to provide 
the most effective attenuation. 
While the invention has been particularly shown and described with 
reference to a preferred embodiment thereof, it will be understood by 
those skilled in the art that various changes in form and details may be 
made therein without departing from the spirit and scope of the invention 
as defined by the appended claims. In particular, the above method of 
dithering a variable notch filter to get usable output fluctuations can be 
applied to types of filters other than notch filters. Band pass filters 
could easily use the method of the present invention. In addition, low 
pass or high pass filters, having a center frequency at the filter 3 dB 
point, could also be adapted to use dithering for tracking an input 
signal. By matching the characteristic of a variable filter to the signal 
portion being tracked, a system can be arranged which forces the filter to 
seek a frequency band which allows the lowest (or highest) output 
fluctuation. If more than one signal portion needs to be tracked and 
filtered, more than one filter may be used in series, each tracking a 
different signal portion. 
Implementation of the tracking notch filter concept shown in FIG. 1 can be 
accomplished either with analog circuit components or with digital 
techniques such as digital signal processors, computers or discrete logic 
components.