04-01-2013, 02:15 PM
An FPGA Architecture Design of a High Performance Adaptive
Notch Filter
[attachment=46481]
Abstract
The occurrence of narrowband interference near frequencies carrying information is a common
problem in modern control and signal processing applications. A very narrow notch
filter is required in order to remove the unwanted signal while not compromising the integrity
of the carrier signal. In many practical situations, the interference may wander
within a frequency band, in which case a wider notch filter would be needed to guarantee
its removal, which may also allow for the degradation of information being carried in
nearby frequencies. If the interference frequency could be autonomously tracked, a narrow
bandwidth notch filter could be successfully implemented for the particular frequency.
Adaptive signal processing is a powerful technique that can be used in the tracking and
elimination of such a signal.
An application where an adaptive notch filter becomes necessary is in biomedical instrumentation,
such as the electrocardiogram recorder. The recordings can become useless
when in the presence of electromagnetic fields generated by power lines. Research was
conducted to fully characterize the interference.
Research on notch filter structures and adaptive filter algorithms has been carried out.
The lattice form filter structure was chosen for its inherent stability and performance benefits.
A new adaptive filter algorithm was developed targeting a hardware implementation.
The algorithm used techniques from several other algorithms that were found to be beneficial.
Introduction
Adaptive filtering is a powerful technique for signal processing and control systems [1–
4]. It allows a filter to adjust its weights according to the signals it encounters. Figure 1.1
displays common block diagram representations of adaptive filter systems. The output of
the programmable filter ˆy[n], is subtracted from a reference sequence y[n], which produces
an error sequence "[n]. The error sequence and the input sequence x[n] provide information
to properly update the filter’s weights. For this application, the weights will determine the
notch center frequency and the notch bandwidth. The depth of the null in the adaptive notch
filter is superior to that of the fixed filter because the adaptive process maintains the correct
phase relationships for canceling the undesired signal contents [1].
Design Considerations
Adaptive filtering consists of a programmable filter and an update algorithm. Both of these
components allow for optimizations. The update algorithm consists of minimizing a cost
function, typically denoted as J(n). Minimization of the cost function implies that the result
of the error sequence will be closer to converging to zero after each iteration, resulting
in continuously improved approximations fˆy[n]g of y[n]. The update algorithm for the filter
weights has experienced a significant degree of research. Numerous theoretical derivations
have been presented, some of which are based on the least mean squares (LMS) [5–9],
the normalized least mean squares (NLMS) [10–15], and the Steiglitz-McBride methods
(SMM) [16, 17]. Some algorithms use the gradient of the error sequence, some utilize
phase, some techniques have constrained weight vectors and others have variable weighting
factors. The Pilot Notch technique can be added to any existing algorithm in an attempt
to improve performance [18]. The algorithms need to consider stability [19], correlation
between random variables, and signal to noise ratios. It is important to know the various
qualities and trade-o s between di erent algorithms, because the operation and performance
is closely related to the statistical parameters of the signal environment.
ElectromagneticWaves
As explained by Maxwell’s equations, a time-varying electric field induces a magnetic field
and vice versa. The electric and magnetic fields oscillate in phase and are perpendicular
to each other and the direction of propagation, as depicted by Figure 1.3. This second
property is characteristic of transverse waves, thus an electromagnetic wave is a transverse
wave. Therefore particles do not move along with the electromagnetic wave, they will
simply oscillate about their individual positions as the wave front passes by at the speed of
light (c 3 108 m/s).
Notch Filter
[attachment=46481]
Abstract
The occurrence of narrowband interference near frequencies carrying information is a common
problem in modern control and signal processing applications. A very narrow notch
filter is required in order to remove the unwanted signal while not compromising the integrity
of the carrier signal. In many practical situations, the interference may wander
within a frequency band, in which case a wider notch filter would be needed to guarantee
its removal, which may also allow for the degradation of information being carried in
nearby frequencies. If the interference frequency could be autonomously tracked, a narrow
bandwidth notch filter could be successfully implemented for the particular frequency.
Adaptive signal processing is a powerful technique that can be used in the tracking and
elimination of such a signal.
An application where an adaptive notch filter becomes necessary is in biomedical instrumentation,
such as the electrocardiogram recorder. The recordings can become useless
when in the presence of electromagnetic fields generated by power lines. Research was
conducted to fully characterize the interference.
Research on notch filter structures and adaptive filter algorithms has been carried out.
The lattice form filter structure was chosen for its inherent stability and performance benefits.
A new adaptive filter algorithm was developed targeting a hardware implementation.
The algorithm used techniques from several other algorithms that were found to be beneficial.
Introduction
Adaptive filtering is a powerful technique for signal processing and control systems [1–
4]. It allows a filter to adjust its weights according to the signals it encounters. Figure 1.1
displays common block diagram representations of adaptive filter systems. The output of
the programmable filter ˆy[n], is subtracted from a reference sequence y[n], which produces
an error sequence "[n]. The error sequence and the input sequence x[n] provide information
to properly update the filter’s weights. For this application, the weights will determine the
notch center frequency and the notch bandwidth. The depth of the null in the adaptive notch
filter is superior to that of the fixed filter because the adaptive process maintains the correct
phase relationships for canceling the undesired signal contents [1].
Design Considerations
Adaptive filtering consists of a programmable filter and an update algorithm. Both of these
components allow for optimizations. The update algorithm consists of minimizing a cost
function, typically denoted as J(n). Minimization of the cost function implies that the result
of the error sequence will be closer to converging to zero after each iteration, resulting
in continuously improved approximations fˆy[n]g of y[n]. The update algorithm for the filter
weights has experienced a significant degree of research. Numerous theoretical derivations
have been presented, some of which are based on the least mean squares (LMS) [5–9],
the normalized least mean squares (NLMS) [10–15], and the Steiglitz-McBride methods
(SMM) [16, 17]. Some algorithms use the gradient of the error sequence, some utilize
phase, some techniques have constrained weight vectors and others have variable weighting
factors. The Pilot Notch technique can be added to any existing algorithm in an attempt
to improve performance [18]. The algorithms need to consider stability [19], correlation
between random variables, and signal to noise ratios. It is important to know the various
qualities and trade-o s between di erent algorithms, because the operation and performance
is closely related to the statistical parameters of the signal environment.
ElectromagneticWaves
As explained by Maxwell’s equations, a time-varying electric field induces a magnetic field
and vice versa. The electric and magnetic fields oscillate in phase and are perpendicular
to each other and the direction of propagation, as depicted by Figure 1.3. This second
property is characteristic of transverse waves, thus an electromagnetic wave is a transverse
wave. Therefore particles do not move along with the electromagnetic wave, they will
simply oscillate about their individual positions as the wave front passes by at the speed of
light (c 3 108 m/s).