WO2011063461A1

WO2011063461A1 - Two degree of freedom anti-aliasing filter

Info

Publication number: WO2011063461A1
Application number: PCT/AU2010/001587
Authority: WO
Inventors: Graham Clifford Goodwin; Juan Carlos Aguero Vasquez; Juan Ignacio Yuz Eissmann
Original assignee: Newcastle Innovation Limited
Priority date: 2009-11-26
Filing date: 2010-11-26
Publication date: 2011-06-03

Abstract

Described herein are anti-aliasing filters (AAFs) having two or more degrees of freedom. In overview, one embodiment provides an AAF including a first input for receiving a primary input signal u(t) indicative of baseline data for a signal path. In some embodiments, this first input corresponds to a continuous-time signal that is provided to a real-world system (for example to control or influence that system). The AAF additionally includes a second input for receiving a secondary input signal y _m(t) measured from an output of the real-world system, the secondary input signal including a signal of interest y(t) and a noise component. Filtering components process the primary and secondary input signals, and an output provides an output signal γ(t) based on that processing. In some cases the filtering components are configured to allow removal of noise without disturbing the overall signal path.

Description

TWO DEGREE OF FREEDOM ANTI-ALIASING FILTER

FIELD OF THE INVENTION

[0001] The present invention relates to signal processing, and more particularly to antialiasing filters. Embodiments of the invention have been developed to provide an antialiasing filter having two degrees of freedom, and methods associated with such filtering approaches, particularly in the context of wide-band control. While some embodiments will be described herein with particular reference to that application, it will be appreciated that the invention is not limited to such a field of use, and is applicable in broader contexts.

BACKGROUND

[0002] Any discussion of the background art throughout the specification should in no way be considered as an admission that such art is widely known or forms part of common general knowledge in the field.

[0003] Anti-aliasing filters (AAFs) are commonly used in the context of analog to digital conversion, primarily to prevent or reduce the impact of noise folding. In broad terms, an AAF is typically provided at the input of a digital signal processing system, upstream of a signal sampler. The intention is to reduce the influence of unwanted noise on signal sampling, for example by reducing the impact of high-frequency signals.

[0004] The present inventors have recognized that known AAFs suffer from a significant deficiency. In particular, by using an AAF to reduce the impact of unwanted noise on a signal of interest, there is a resultant modification of the signal of interest. For example, the application of an anti-aliasing filter can cause phase shift in the signal of interest. This deficiency can lead to significant problems in the context of precision control systems.

SUMMARY OF THE INVENTION

[0005] It is an object of the present invention to overcome or ameliorate at least one of the disadvantages of the prior art, or to provide a useful alternative. [0006] One embodiment provides an anti-aliasing filter (AAF) including:

a first input for receiving a primary input signal u( t) indicative of baseline data for a signal path;

a second input for receiving a secondary input signal y_m(t) measured from a real-world system in the signal path, the secondary input signal including a signal of interest y(t) and a noise component;

filtering components for processing the primary and secondary input signals; and

an output for providing an output signal y(t) based on the processing of the primary and secondary input signals.

[0007] One embodiment provides an anti-aliasing filter wherein u( t) corresponds to a control signal provided to the real- world system

[0008] One embodiment provides an anti-aliasing filter wherein the filtering components include a first filter Fj which acts on the primary input signal u(t) and a second filter F2 which acts on the secondary input signal y_m(t).

[0009] One embodiment provides an anti-aliasing filter wherein the filtering components are configured such that the first and second filters Fj and F2 are interdependent based on a predetermined constraint.

[0010] One embodiment provides an anti-aliasing filter wherein the predetermined constraint is for zero phase shift between y_m(t) and y(t).

[0011] One embodiment provides an anti-aliasing filter wherein the predetermined constraint is for the transfer function from u(t) to y(t) is the same as from u(t) to y(t).

[0012] One embodiment provides an anti-aliasing filter wherein the predetermined constraint is for the signal path from y_m( t) to y( t) to have a value of "1".

[0013] One embodiment provides an anti-aliasing filter wherein the predetermined constraint is for reduced disturbance in the signal path due to reduction or removal of the noise component. [0014] One embodiment provides an anti-aliasing filter wherein the predetermined constraint is for zero disturbance in the signal path due to reduction or removal of the noise component.

[0015] One embodiment provides an anti-aliasing filter wherein the filtering components are configured such that the first and second filters Fj and F2 are independently controllable.

[0016] One embodiment provides an anti-aliasing filter wherein the filtering components include analogue electronics.

[0017] One embodiment provides an anti-aliasing filter wherein the filtering components include a computer.

[0018] One embodiment provides an anti-aliasing filter wherein the computer samples the primary and secondary input signals at a high rate.

[0019] One embodiment provides an anti-aliasing filter wherein the primary input signal u(t) is influenced by the output signal y(t) subject to a feedback loop.

[0020] One embodiment provides an analogue to digital converter including an AAF as described herein.

[0021] One embodiment provides a control system including an AAF as described herein.

[0022] One embodiment provides a digital feedback loop including an AAF as described herein.

[0023] One embodiment provides a method of processing a measured analogue signal y_m( t) including the use of an AAF as described herein.

[0024] One embodiment provides a method for processing an analogue signal measured from a real-world system, the method including the steps of:

receiving a primary input signal u( t) ) indicative of baseline data for a signal path; receiving a secondary input signal y_m( t) measured from a real- world system in the signal path, the secondary input signal including a signal of interest y(t) and a noise component; processing the primary and secondary input signals; and

providing an output signal y(t) based on the processing of the primary and secondary input signals.

[0025] One embodiment provides a method wherein u(t) corresponds to a control signal provided to the real- world system

[0026] One embodiment provides a method wherein processing includes applying a first filter Fj which acts on the primary input signal u(t) and a second filter F2 which acts on the secondary input signal y_m(t).

[0027] One embodiment provides a method wherein the first and second filters Fj and F2 are interdependent based on a predetermined constraint.

[0028] One embodiment provides a method wherein the predetermined constraint is for zero phase shift between y_m(t) and y(t).

[0029] One embodiment provides a method wherein the predetermined constraint is for the transfer function from u(t) to y(t) is the same as from u(t) to y(t).

[0030] One embodiment provides a method wherein the predetermined constraint is for the signal path from y_m( t) to y( t) to have a value of "1".

[0031 ] One embodiment provides a method wherein the predetermined constraint is for reduced disturbance in the signal path due to reduction or removal of the noise component.

[0032] One embodiment provides a method the predetermined constraint is for zero disturbance in the signal path due to reduction or removal of the noise component.

[0033] One embodiment provides a method wherein the first and second filters Fj and F2 are independently controllable.

[0034] One embodiment provides a computer program product configured to perform a method as described herein.

[0035] One embodiment provides a method readable medium carrying a set of instructions that when executed by one or more processors cause the one or more processors to perform a method as described herein. [0036] One embodiment provides a computer system including a processor configured to perform a method as described herein.

[0037] One embodiment provides a system including:

a digital controller for providing a digital signal uu

a first component responsive to discrete-time signal uu for providing a continuous-time signal u( t) to a real- world system;

a second component for measuring a value from the real world system and in response providing an analogue measured value signal y_m(t), which includes a signal of interest y(t) and a noise component;

an AAF coupled to the first and second components for processing u(t) and y_m(t), thereby to provide an analogue output signal y(t);

a sampling component for sampling the analogue output signal y(t) thereby allow the generation of a corresponding digital signal y .

[0038] One embodiment provides a system wherein y influences uu in a feedback loop.

[0039] Reference throughout this specification to the term "degrees of freedom" refer to the inputs, variables or parameters that define an output or state of a system. For example, a ball that can move horizontally or vertically has two degrees of freedom. Similarly, a filter having two variable input signals has two degrees of freedom.

[0040] Reference throughout this specification to the term "aliasing" refers to the signal artifact that occurs when a continuous time signal is sampled (converted to a digital signal) or a digital signal is resampled at a lower sample rate. Specifically, aliasing occurs when a signal is sampled at a rate lower than twice the maximum frequency contained in that signal. If this condition is not satisfied, higher frequency signals are folded back or "aliased" as undesired lower frequency signals.

[0041 ] Reference throughout this specification to "one embodiment", "some embodiments" or "an embodiment" means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases "in one embodiment", "in some embodiments" or "in an embodiment" in various places throughout this specification are not necessarily all referring to the same embodiment, but may. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.

[0042] As used herein, unless otherwise specified the use of the ordinal adjectives "first", "second", "third", etc., to describe a common object, merely indicate that different instances of like objects are being referred to, and are not intended to imply that the objects so described must be in a given sequence, either temporally, spatially, in ranking, or in any other manner.

[0043] In the claims below and the description herein, any one of the terms comprising, comprised of or which comprises is an open term that means including at least the elements/features that follow, but not excluding others. Thus, the term comprising, when used in the claims, should not be interpreted as being limitative to the means or elements or steps listed thereafter. For example, the scope of the expression a device comprising A and B should not be limited to devices consisting only of elements A and B. Any one of the terms including or which includes or that includes as used herein is also an open term that also means including at least the elements/features that follow the term, but not excluding others. Thus, including is synonymous with and means comprising.

BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Preferred embodiments of the invention will now be described, by way of example only, with reference to the accompanying drawings in which:

[0045] FIG. 1 is a schematic representation of a control architecture according to one embodiment.

[0046] FIG. 2 is a schematic representation of an anti-aliasing filter (AAF) according to one embodiment.

[0047] FIG. 3 is a schematic representation of a control architecture according to one embodiment.

[0048] FIG. 4A is a graph of simulated output disturbance sensitivity for a prior art AAF. [0049] FIG. 4B is a graph of simulated measurement noise sensitivity for a prior art AAF.

[0050] FIG. 5A is a graph of simulated output disturbance sensitivity for an AAF according to one embodiment.

[0051 ] FIG. 5B is a graph of simulated measurement noise sensitivity for an AAF according to one embodiment

DETAILED DESCRIPTION

[0052] Described herein are anti-aliasing filters (AAFs) having two or more degrees of freedom. In overview, one embodiment provides an AAF including a first input for receiving a primary input signal u(t) indicative of baseline data for a signal path. In some embodiments, this first input corresponds to a continuous-time signal that is provided to a real- world system (for example to control or influence that system). The AAF additionally includes a second input for receiving a secondary input signal y_m( t) measured from an output of the real- world system, the secondary input signal including a signal of interest y(t) and a noise component. Filtering components process the primary and secondary input signals, and an output provides an output signal y(t) based on that processing. In some cases the filtering components are configured to allow removal of noise without disturbing the overall signal path.

[0053] For the sake of understanding the invention, the operation of the anti aliasing filter will be described in relation to continuous time signals. However, it will be appreciated that in some embodiments, the invention is used to perform filtering on discrete time signals. For example, when downsampling a discrete time signal to a lower sample rate. In other embodiments, the invention finds applications in spatial filtering, such as anti-aliasing of optical signals to reduce aliasing when downsampling a high resolution image. While spatial filtering often involves filtering in two or three dimensions, essentially the same mathematics as described below can be utilized (albeit with the time variable substituted for a spatial variable).

[0054] It will be appreciated that, while the invention is described in the form of an analog filter, implemented using of a number of electronic components to operate on continuous signals, the invention can also be implemented as a digital filter, implemented using software to operate on digitized data.

BASIC CONTROL ARCHITECTURE EXAMPLE

[0055] FIG. 1 illustrates a digital control architecture 101 according to one embodiment. In overview, architecture 101 operates in relation to a real- world system referred to as Plant 102. The nature of Plant 102 is ignored for the present purposes, and it will be appreciated that a substantially unlimited number of examples could be realised. Considered at a relatively theoretical level, Plant 102 modifies a continuous- time signal u(t) by applying a plant transfer function G(s) to the signal u(t) to provide an output y(t) (here upper case letters are used to represent Laplace Transforms of signals i.e. G(s) = -C{g t)}). From a practical perspective, this plant transfer function describes (or estimates) a range of real-world phenomena or operations that can be imparted onto a signal by a system. Examples of such operations include the addition of noise, convolution of signals, attenuation or amplification of signals, filtering, dispersion and time shifting. In practice, Plant 102 could describe substantially any real world system, based on definitions for u(t) and y(t), and the nature of G(s).

[0056] So as to provide a relatively straightforward example, in one embodiment architecture 101 is implemented in the context of an ABS (anti-lock braking) system for a motor vehicle, and Plant 102 describes the motor vehicle. In this regard, u(t) determines the braking force applied to wheels in the vehicle as function of time. From a practical perspective, there is a desire to measure differential wheel speed (for example to influence subsequent braking force characteristics in a control feedback loop). As such, the considered output of Plant 102, y(t), describes the differential wheel speed. However, measurements y(t) are affected by noise, and so what is measured is actually something slightly different, referred to herein as y_m(t). In broad terms, an AAF is required to remove noise from y_m(t) to yield values more closely resembling the true output y(t). This might be achieved by way of gain adjustments, and so on. In this case, G(s) is likely to be complicated indeed. However, based on experimentation and modeling, and appropriate mathematical model G(s) can be defined to describe (by way of estimation) the operation of Plant 102. The accuracy of such a model will be reliant on the degree of sophistication in modeling. [0057] It will be appreciated that the above example is provided for the sake of explanation only, and the present inventive concepts are by no means intended to be limited to such an example. Embodiments of the present invention are applicable to control systems in a broader context, independent of physical application.

[0058] In overview, a discrete-time control signal Uk is provided to a control component 103. Component 103 converts the discrete-time signal to a continuous-time control signal u(t), which is provided to Plant 102 thereby to influence plant 102. Control component 103 is provided with the descriptor "Hold", reflecting the effect of converting a discrete-time signal to a continuous-time signal by holding each sample value for one sample interval (based on the sample interval of an upstream analogue- to-digital converter). In some cases component 103 is a Zero Order Hold (ZOH). In an alternative embodiment, a continuous time signal u(t) is provided directly to Plant 102.

[0059] Plant 102 modifies the input signal u(t) according to its transfer function G(s) and provides an interest y(t), which in the present case in an analogue continuous-time signal. Measuring equipment is provided for observing this signal. For example, in one embodiment the signal of interest is a temperature, and this is measured by a thermometer.

[0060] In practice, the signal of interest y(t) is polluted by noise, such as unwanted high frequency signals. This effect is presently illustrated by way of a noise signal v(t). This noise signal can cause undesired effects, such as "noise folding" in a sampled output based on the measurements. In the illustrated example, a measurement is made at point 104. Accordingly, rather than measuring y(t), what is measured is y_m(t), a signal that includes the signal of interest y(t) and the noise component v(t).

[0061 ] An anti-aliasing filter, in the form of AAF 105, is provided downstream in the signal path from point 104. In overview, much like a traditional AAF, AAF 105 is configured to reduce/eliminate noise in y_m(t), thereby to alleviate noise folding concerns during sampling. However, AAF 105 is additionally configured to reduce/eliminate distortions in the signal path, such as phase shift, that otherwise might ensue due to noise canceling. To this end, AAF 105 includes two inputs: • A first input for receiving a primary input signal u( t) that is indicative of baseline data for the signal path. In the present example, u(t) is provided from component 103 (i.e. AAF 105 is coupled to component 103), and therefore reprints a continuous-time signal that is provided to a real- world system defined by Plant 102. That is, a signal without noise introduced by the system.

• A second input for receiving a secondary input signal y_m(t) measured from the real- world system defined by Plant 102. That is, a signal that has been modified by Plant 102 and includes noise v(t).

[0062] AAF 105 is illustrated in more detail in FIG. 2, showing the first input 201, a second input 202, and an output 203. In further embodiments additional inputs supplement inputs 201 and 202 providing additional degrees of freedom, and in some embodiments the present input 201 is substituted for or supplemented with alternate inputs for receiving "baseline" information about the signal path, thereby to assist in understanding the effect of filtering on the signal path.

[0063] AAF 105 provides an output signal y(t) based on the processing of u(t) and y_m(t). In broad terms, this output signal ideally corresponds to the signal of interest y(t), although the degree of similarity will be reliant on the operation of AAF 105. Typically, the primary concern is the extent to which AAF 105 is able to filter out noise (i.e. v(t)). However, the present inventors have also appreciated that filtering of noise can cause phase shift and/or other undesired effects in the signal path, causing further distinction between y(t) and y(t). That is, there is an inevitable coupling between the (desirable) impact of the filter on noise and the (undesirable) impact on the signal path. As discussed further below, by also receiving and processing u(t), AAF 105 is configured to reduce or eliminate the impact of such undesirable impacts on the signal path. For the present purposes, AAF 105 is described as a "two degree of freedom" (2-DOF) AAF, on the basis that there are two filtering functions that are able to be selectively controlled.

[0064] In some embodiments, the filtering components within AAF 105 are based on analogue electronics. However, as is common in the field of AAF technology, in other embodiments AAF 105 includes or is used in conjunction with a computer or processor. For example, analogue signals are sampled at a high rate such that computer processing is effectively able to mimic the functionality of analogue electronics. There are significant advantages associated with the use of a computer, including the ability to implement more complex/more flexible functionalities.

[0065] In the context of AAF 105, the filtering components include a first filter Fj which acts on the primary input signal u(t) and a second filter F₂ which acts on the secondary input signal y_m(t). That is, the following equation applies:

Y(s) = Fis)U(s) + F2(s)Y s) _{( 1)}

[0066] That is, Y(s) is the result of applying Fi to \J(s) and F₂ to Y_m(s), In the above equation, and in other equations provided herein, uppercase letters are used to represent Laplace transforms (i.e. U(s) = L{ u(t) }).

[0067] It will be noted that the above equation can be used to describe a traditional AAF, if Fi is set to zero (necessary in traditional AAFs as there is no input for receiving u(t) or a corresponding signal, and only y_m(t) is received as input).

[0068] In some embodiments Fj and F₂ are independently controllable, effectively providing two "knobs" with which to adjust filtering. However, embodiments described below are predominately focused on a scenario where Fj and F₂ are interdependent based on a predetermined constraint. As a particular example, a predetermining constraint is considered whereby signal path disturbances (such as phase shift) between y_m(t) and y(t) are eliminated (i.e. the signal path from y_m(t) to y(t) is 1). This allows for the reduction/elimination of undesirable impacts on the signal path that might be caused by the filtering of noise out of y_m( t).

[0069] Moving into the underlying theory, there is a general class of filters that yields the key property whereby the transfer function from u(t) to y(t) is the same as from u(t) to y(t). That is, the signal path from y_m(t) to y(t) is 1. In the context of FIG. 1, Plant 102 is associated with a plant transfer function G(s), being the transfer function from u(t) to y(t), and assumed to be the same as from u(t) to y_m(t) (that is, no change in transfer function is brought about by noise). Therefore, the transfer function from u(t) to y(t) is given by the following equation: = F₁ (_S) + F₂ (s)G(s) (2)

U(s)

[0070] Now, the transfer function from U(s) to Y_m(s) should ideally be the same as the transfer function from U(s) to Y(s), providing a condition for unbiasedness in filter estimates. This leads to the following equation:

F^ + F^Gis)

(3)

[0071] That is, any effects resulting from applying F₂ to the plant transfer function are cancelled by application of Fj . As such, this equation provides a predetermined constraint for zero phase shift in AAF 105. This is a particularly useful result, and various embodiments of the present invention take the form of (or make use of) an AAF that satisfies equation 3.

[0072] As noted above, G(s) is not inherently known for a real- world system, and analysis based on modeling of Plant 102 is required to estimate G(s). In this regard, the effectiveness of AAF 105 will be related to the level of accuracy/sophistication in the modeling of G(s).

CONTROL LOOP EXAMPLE

[0073] A more complex architecture is illustrated in FIG. 3, taking the form of a control loop 301. In particular, this figure illustrates a computer controlled feedback loop making use of a 2-DOF AAF such as AAF 105 described above. Various components correspond to those shown in FIG. 1, and similar reference numerals are used. This example is used for the purpose of a mathematical simulation further below.

[0074] Control loop 301 relates to a continuous-time system that is controlled by a discrete time controller, in the form of digital controller 302. As in the case of FIG. 1, a 2-DOF AAF 105 is provided for anti-aliasing. AAF 105 is configured such that it satisfies equation 3 above. That is, Fj and F2 are selected to reduce/eliminate phase shift in AAF 105, such that the transfer function from u(t) to y(t) is the same as from u( t) to y( t). That is, the signal path from y_m( t) to y( t) is 1. [0075] A primary objective of control loop 301 is to keep the "true" output y(t) as close as possible to a reference /¾, in the presence of output disturbances such as d₀(t). However, the discrete-time measurements available for controller 302 are samples of the AAF output (i.e. = y(kA)). Although a traditional AAF is designed to simply avoid/reduce the effect of noise v(t), following on from the discussion above, AAF 105 is intended to achieve this task without introducing distortion into the signal path from u(t) to y(t).

[0076] In analyzing control loop 301, the following transfer functions are of interest:

• Tj, being the open loop transfer function from u(t) to y(t). This is denoted as T₁ = F₁ + F₂G.

• T₂, being the open loop transfer function from v(t) to y(t). This is denoted as T2 = F2.

[0077] There are two different output responses to be considered in the closed loop:

• The Fourier transform of the output response Y^jw) due to the disturbance d₀(t).

This is given by the following formula:

G(jw)H (jw)C_q (e^]wA )[T₂ (jw)D(jw)]_q

Y_l {j ) = D{jw) -

Where D(jw) is the Fourier transform of the disturbance and where the square brackets represent the folding effect produced by sampling the signals (i.e. the aliasing of the spectrum of the signals):

[S (jw)] _q = ∑ SO + j¾)

• The Fourier transform of the output response due to the output response Y₂ (jw) due to the measurement noise v(t):

G(jw)H(jw)C (e^JW& )[T₂ (jw)V(jw)]_a

Y₂ (jw) = - Where V(jw) is the Fourier transform of the measurement noise.

[0078] The usual goal of a control system is, firstly, to keep Y^jw) small at low frequencies so as to minimize the impact of disturbances; and secondly, to keep Y₂ ( jw) small at high frequencies to minimize the impact of high frequency measurement noise. Additionally, it is undesirable to have high peaks for Y^jw) or Y₂ ( jw) at any frequencies.

SIMULATION EXAMPLE

[0079] So as to better illustrate the concepts outlined above, a specific example is provided below based on control loop 301. This example assumes the following Plant transfer function:

[0080] It will be appreciated that, in practical examples, the plant transfer function would be derived from modeling of a real world system, and a more complex function is likely.

[0081 ] For the present example, it is assumed that control component 103 is a zero order hold (ZOH). That is, it represents a mathematical model of the practical signal reconstruction performed by a conventional digital-to-analog converter (DAC), describing the effect of converting a discrete-time signal to a continuous-time signal by holding each sample value for one sample interval (in this case being the sample interval at the output of AAF 105).

[0082] For the purposes of a comparative simulation, AAF 105 is compared with a hypothetical standard AAF. By way of clarification:

• AAF 105 is a 2-DOF AAF, receiving inputs u(t) and y_m(t), and apply Fj(s) and F2(s) such that Y(s) = F i(s)U (s) + F 2(s)Y_m (s) . Furthermore, AAF 105 is configured such that Fj(s) and F2(s) satisfy ( F₁ (s) + F₂ (s)G(s) = G(s) ). That is, the transfer function from u(t) to y(t) is the same as from u(t) to y(t). • The hypothetical standard AAF receives only y_m( t) as input, and is configured simply to deal with noise signal v(t) to avoid the folding of noise during sampling.

[0083] For the sake of this simulation, a sampling frequency of 20 rad/s is considered (i.e. w_s = 20). Furthermore, the controller assumes a nominal closed loop bandwidth of 2 rad/s. As is standard industrial practice, this ignores the presence of an AAF.

[0084] It is assumed that the output disturbance d₀(t) has flat spectrum up to the Nyquist frequency (10 rad/s in this case), such that:

[F₂ (jw)D(jw)]_q = \F₂

o) e [0,10]

[0085] On the other hand, it is assumed that the measurement of noise v( t) is present with uniform energy distributed up to at least 20 rad/s. As such, when sampling the output signal, a second component has to be included in the spectrum in the output response, being:

[0086] The results of a simulation based on these criteria are illustrated in FIG. 4A to FIG. 5B. Specifically, four different models for ^fsj are considered, being second order Butterworth filters with cut off frequencies of 20 rad/s, 10 rad/s, 7 rad/s and 5 rad/s respectively. For AAF 105, Fj(s) is determined by the defined relationship between F₂(s) and G(s).

[0087] FIG. 4A and FIG. 4B simulate the use of a standard (one degree of freedom) AAF, and respectively show output disturbance sensitivity and output measurement noise sensitivity. Large peaks 401 are immediately apparent in the sensitivity functions; these increasing as the cutoff frequency of the Butterworth filters are reduced. These are an artifact of distortions in the signal path (such as phase shift), and will ultimately lead to an unstable control loop.

[0088] FIG. 5A and FIG. 5B are directed towards the use of a 2-DOF AAF as presently proposed, and also respectively show output disturbance sensitivity and output measurement noise sensitivity. It is observed that reduction of the cutoff frequency has almost no effect on sensitivities. This confirms that the feedback path in the control loop has not been distorted, and thus that the effect of AAF 105 does not have a significant impact on the true output of the feedback loop. This presents a significant advantage over known AAFs.

CONCLUSIONS

[0089] It will be appreciated that the disclosure above provides various significant improvements in AAF technology and in the field of systems control generally. In particular, the present disclosure allows for an AAF that achieves noise reduction objectives without causing signal path disturbances.

[0090] It should be appreciated that in the above description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together in a single embodiment, FIG., or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various inventive aspects. This method of disclosure, however, is not to be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the Detailed Description are hereby expressly incorporated into this Detailed Description, with each claim standing on its own as a separate embodiment of this invention.

[0091] Furthermore, while some embodiments described herein include some but not other features included in other embodiments, combinations of features of different embodiments are meant to be within the scope of the invention, and form different embodiments, as would be understood by those skilled in the art. For example, in the following claims, any of the claimed embodiments can be used in any combination.

[0092] Furthermore, some of the embodiments are described herein as a method or combination of elements of a method that can be implemented by a processor of a computer system or by other means of carrying out the function. Thus, a processor with the necessary instructions for carrying out such a method or element of a method forms a means for carrying out the method or element of a method. Furthermore, an element described herein of an apparatus embodiment is an example of a means for carrying out the function performed by the element for the purpose of carrying out the invention.

[0093] In the description provided herein, numerous specific details are set forth.

However, it is understood that embodiments of the invention may be practiced without these specific details. In other instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description.

[0094] Similarly, it is to be noticed that the term coupled, when used in the claims, should not be interpreted as being limited to direct connections only. The terms "coupled" and "connected," along with their derivatives, may be used. It should be understood that these terms are not intended as synonyms for each other. Thus, the scope of the expression a device A coupled to a device B should not be limited to devices or systems wherein an output of device A is directly connected to an input of device B. It means that there exists a path between an output of A and an input of B which may be a path including other devices or means. "Coupled" may mean that two or more elements are either in direct physical or electrical contact, or that two or more elements are not in direct contact with each other but yet still co-operate or interact with each other.

[0095] Thus, while there has been described what are believed to be the preferred embodiments of the invention, those skilled in the art will recognize that other and further modifications may be made thereto without departing from the spirit of the invention, and it is intended to claim all such changes and modifications as fall within the scope of the invention. For example, any formulas given above are merely representative of procedures that may be used. Functionality may be added or deleted from the block diagrams and operations may be interchanged among functional blocks. Steps may be added or deleted to methods described within the scope of the present invention.

Claims

THE CLAIMS DEFINING THE INVENTION ARE AS FOLLOWS:

1. An anti-aliasing filter (AAF) including:

2. An AAF according to claim 1 wherein u(t) corresponds to a control signal provided to the real-world system

3. An AAF according to claim 1 wherein the filtering components include a first filter Fj which acts on the primary input signal u(t) and a second filter F2 which acts on the secondary input signal y_m( t).

4. An AAF according to claim 3 wherein the filtering components are configured such that the first and second filters Fj and F2 are interdependent based on a predetermined constraint.

5. An AAF according to claim 4 wherein the predetermined constraint is for zero phase shift between y_m(t) and y(t).

6. An AAF according to claim 4 wherein the predetermined constraint is for the transfer function from u(t) to y(t) is the same as from u(t) to y(t).

7. An AAF according to claim 4 wherein the predetermined constraint is for the signal path from y_m( t) to y( t) to have a value of "1".

8. An AAF according to claim 4 wherein the predetermined constraint is for reduced disturbance in the signal path due to reduction or removal of the noise component.

9. An AAF according to claim 4 wherein the predetermined constraint is for zero disturbance in the signal path due to reduction or removal of the noise component.

10. An AAF according to claim 3 wherein the filtering components are configured such that the first and second filters Fj and F2 are independently controllable.

11. An AAF according to any preceding claim wherein the filtering components include analogue electronics.

12. An AAF according to any preceding claim wherein the filtering components include a computer.

13. An AAF according to claim 12 wherein the computer samples the primary and secondary input signals at a high rate.

14. An AAF according to any preceding claim wherein the primary input signal u(t) is influenced by the output signal y(t) subject to a feedback loop.

15. An analogue to digital converter including an AAF according to any preceding claim.

16. A control system including an AAF according to any preceding claim.

17. A digital feedback loop including an AAF according to any preceding claim.

18. A method of processing a measured analogue signal y_m(t) including the use of an AAF according to any preceding claim.

19. A method for processing an analogue signal measured from a real-world system, the method including the steps of:

receiving a primary input signal u(t) ) indicative of baseline data for a signal path;

receiving a secondary input signal y_m( t) measured from a real- world system in the signal path, the secondary input signal including a signal of interest y(t) and a noise component;

processing the primary and secondary input signals; and providing an output signal y(t) based on the processing of the primary and secondary input signals.

20. A method according to claim 19 wherein u(t) corresponds to a control signal provided to the real- world system

21. A method according to claim 19 wherein processing includes applying a first filter Fj which acts on the primary input signal u(t) and a second filter F₂ which acts on the secondary input signal y_m( t).

22. A method according to claim 21 wherein the first and second filters Fj and F₂ are interdependent based on a predetermined constraint.

23. A method according to claim 22 wherein the predetermined constraint is for zero phase shift between y_m(t) and y(t).

24. A method according to claim 22 wherein the predetermined constraint is for the transfer function from u(t) to y(t) is the same as from u(t) to y(t).

25. A method according to claim 22 wherein the predetermined constraint is for the signal path from y_m( t) to y( t) to have a value of "1".

26. A method according to claim 22 wherein the predetermined constraint is for reduced disturbance in the signal path due to reduction or removal of the noise component.

27. A method according to claim 22 the predetermined constraint is for zero disturbance in the signal path due to reduction or removal of the noise component.

28. A method according to claim 21 wherein the first and second filters Fj and F₂ are independently controllable.

29. A computer program product configured to perform a method according to any one of claims 19 to 28.

30. A computer readable medium carrying a set of instructions that when executed by one or more processors cause the one or more processors to perform a method according to any one of claims 19 to 28.

31. A computer system including a processor configured to perform a method according to any one of claims 19 to 28.

32. A system including:

a digital controller for providing a digital signal uu

33. A system according to claim 32 wherein y influences uu in a feedback loop.

34. An AAF substantially as herein described with reference to any one of the embodiments of the invention illustrated in the accompanying drawings and/or examples.

35. A method substantially as herein described with reference to any one of the embodiments of the invention illustrated in the accompanying drawings and/or examples.

36. A system substantially as herein described with reference to any one of the embodiments of the invention illustrated in the accompanying drawings and/or examples.