GB2457705A

GB2457705A - Signal processing means and a method of signal processing

Info

Publication number: GB2457705A
Application number: GB0803250A
Authority: GB
Inventors: Paul Darlington
Original assignee: APPLE DYNAMICS INTELLECTUAL PR
Current assignee: APPLE DYNAMICS INTELLECTUAL PR
Priority date: 2008-02-22
Filing date: 2008-02-22
Publication date: 2009-08-26
Also published as: GB0803250D0

Abstract

Signal processing means having at least one filter comprising one or more parameters controllable to transform the respective filter from a first state into a second state. The signal processing means further comprises control means operable to provide a series of adjustments to the filter parameters which determine a transformation of the filter from the first state into the second state such that the transformation is at least substantially indiscernible to human perception. The signal processing means may be used, for example, to alter a sound signal generated by a sound masking system used to mask undesirable sound signals.

Description

/ 2457705 Title: Signal processing means and a method of signal processing

DESCRIPTION

The present invention relates to signal processing means and a method of signal processing and particularly to transforming a filter from one state to another state.

Signal processing is the analysis, interpretation, and manipulation of electronic signals. Such signals may, for example, include sound signals, biological signals, radar signals, and many others. Although the specific example of the present invention is directed towards signal processing of a sound signal or sound signals, it will be appreciated that the invention is not in any way limited to sound signals and is equally applicable to other electronic and optical signals. S..

. : Signal processing may be used to alter a sound signal of, for example, sound masking systems, which are used to mask undesirable sound signals. Such masking systems are used, for example, in built spaces such as offices.

A sound masking system operator may wish to make adjustments to the masking sound signal whilst it is being transmitted. Efficacy of the Sound Masking is known to be degraded when recipients or occupants of a space within which Sound Masking is applied are aware of (or reminded of) the presence of the system and are aware of the masking sound. Sudden changes in the level or content of the masking sound signal increases the likelihood of drawing recipients' or occupants' attention to both the system and its sound output. It is, therefore, desirable that a Sound Masking System should incorporate means by which the subjective impact of changes might be minimised. Such changes in system configuration are required during initial S 2 system commissioning and may also be effected when occupancy of the space changes, on a pre-deterrnined time schedule or for other reasons.

It is therefore desirable for there to be signal processing means and a method of signal processing which is able to adjust a signal with minimal or no discemable impact on human perception.

According to the present invention there is provided signal processing means and control means, said signal processing means having at least one filter comprising one or more parameters controllable to transform the respective filter from a first state into a second state, wherein the control means is operable to provide a series of adjustments to the filter parameters which determine a preferred transformation of the filter from the first state into the second state such that the transformation is at least substantially indiscernible to human perception.

The control means is advantageously operable to control the speed of adjustment of each singularity, which collectively define the state of the filter during the process of being transformed.

S S.

The speed of adjustment of each singularity is advantageously a function of the instantaneous radius of each respective singularity.

Additionally, or alternatively, the control means is advantageously operable to determine a preferred path along which the relevant singularity defining the instantaneous state of the filter travels between the first and second filter states.

In a case in which at least one of the first and second state singularities are not disposed on a diameter of the unit circle, the preferred path is advantageously an arc of a circle defined such that extrapolation thereof intersects the unit circle at two points at which the extrapolated paths are normal relative to the unit circle.

In a case in which both the first and second state singularities both lie on a diameter of the unit circle, the preferred path is advantageously defined as a substantially straight line following the diameter.

The signal may be a sound signal and the transformation of the filter from the first state into the second state is such that the transformation is at least substantially indiscernible to human auditory perception.

Also according to the present invention there is provided a method of transforming the state of a signal processing filter from a first state to a second state such that the transformation is as least substantially indiscernible to human perception, S..

comprising: providing signal processing means having a filter, the filter having parameters controllable to transform the respective filter from a first state into a second state, providing control means, using the control means to provide a series of adjustments to the filter parameters thereby determining a preferred transformation of the filter from the first state to the second state such that the transformation is as least substantially indiscernible to human perception.

Determining the preferred transformation advantageously comprises determining the speed of adjustment of each singularity which collectively define the state of the filter during the process of being transformed. The speed of adjustment of each singularity is a function of the instantaneous radius of the respective singularity.

Additionally, or alternatively, the method may further comprise determining a preferred path along which the relevant singularity defining the instantaneous state of S 4 the filter travels between the first and second filter states and adjusting the parameters of the filter accordingly.

In a case in which at least one of the first and second state singularities are not disposed on a diameter of the unit circle, the preferred path is advantageously determined by extrapolating an arc of a circle, passing through the respective singularities, such that it intersects the unit circle at two points at which the extrapolated path is normal relative to the unit circle.

Also according to the present invention there is provided a signal processed by the above-mentioned signal processing means or method. * * I.

S S..

* Also according to the present invention there is provided a carrier medium carrying computer readable code configured to cause a computer to carry out the above-. S mentioned method.

The present invention will now be described in more detail with reference to the following drawings, in which: Figure 1 is a schematic drawing of a sound generating device according to the prior art; Figures 2a to 2f are diagrams representing hypothetical power spectral densities which may elicit human auditory responses; Figures 3a to 3c are diagrams showing specific states of a filter, represented by the roots of hypothetical quadratics, wherein + represents a root of a first state and x represents a root of a second state; Figure 4 is a diagram showing possible paths for the roots during transformation from the first state to the second state; Fi9ure 5 is a diagram showing preferred breakpoints for real roots of a hypothetical quadratic; Figure 6 is a diagram showing transformation between multiple hypothetical quadratic sections; * . S. *5* Figures 7 are schematic diagrams showing the consequences of moving a singularity in particular directions;

S

Figure 8 is a diagram showing randomly selected singularities joined by D-Iine paths 5 according to the present invention; and Figure 9 is a diagram showing two examples of transformation of the state of a filter between a first state and a second state according to the present invention.

Referring to Figure 1, a noise generator 10, according to the prior art, comprises signal generator means 12 and signal processing means 14. The signal generator means 12 may generate the whole of a signal or recall all or part of a signal from storage means, reception from broadcast or narrow cast systems or local generation.

The signal processing means 14 comprises a digital filter 16, for processing the signal generated by the signal generator means 12, and control means 18 for controlling parameters of the filter 16.

The signal output from the filter 16 may be further processed by a sub-system 20.

Such further processing may, for example, involve amplification, distribution or reproduction, which for the purpose of the present invention can be considered as fixed.

The signal output from the sub-system 20 is conveyed to a recipient 22, which in the case of a sound signal is a listener. The signal from the noise generator is detected as a sound at the listener's ears, where it may evoke the responses of auditory perception.

The present invention is particularly concerned with the intentional constraint of a S..

rule-based transformation of the filter 16 from a known first state (Fl), to a second different state (F2) by considerations of psycho-acoustic responses of a listener 22.

Of the many aspects of Sound that might stimulate a response in a listener, certain categories might be associated with the signal generator 12. Such categories are exemplified by temporal patterns in which the sound is either repetitive or has unexpected impulsive content. These are of minimal relevance to the present invention.

Other categories are properly associated with the action of the signal processing means 14. Such other categories include level, rumble, uboominesss, 5hissiness, tonality, and so on, all of which can be explained in terms of the disposition of the signal energy over frequency. This disposition can be altered by the signal S 7 processing means 16. Accordingly, it is these other categories which are of direct relevance to the present invention.

Figure 2 shows a group of hypothetical Power Spectral Densities, which might elicit perception of rumble (Figure 2a), "boominess" (Figure 2b), hissiness" (Figure 2c) and tonality (Figure 2d). The rumble is caused by a rapid roll-off of energy at low frequency, the "boominess" is caused by dominant energy content at low frequency, the "hissiness" by dominant energy at high frequency and the tonality by a sharp peak in the power spectrum.

In addition to the perception of tonality implied by a peak in the signal's power spectrum, shown in Figure 2d, or multiple peaks, shown in Figure 2e a similar percept is evoked if a signal has a power spectral density function with a sharp notch ::: or notches, as shown in Figure 2f.

All of the examples of differing "spectral balance" (disposition of energy across the * audible frequency range) in Figures 2 & 3 can directly be generated by the signal processing means 14, given appropriate input signal from the signal generator 12.

That is assuming the output from the signal generator 12 has energy widely and evenly disposed in frequency.

In addition to prompting subjective descriptions such as "tonality" or "rumble", the spectral examples of Figures 2 and 3 encode features that, when changed, will be additionally audible or distracting to the listener 22. As examples, changes in the frequency of a peak will be particularly audible, even though the level may not change. Sudden onset of rumble, caused by increasing the differential order (and therefore the "slope") of the "roll-on" will be audible, even though the overall low frequency energy might remain constant. It is the change of filter state that is likely to generate a change in the system output that is perceptively undesirable during the morph.

Changes in the configuration of the filter 16 between state Fl and state F2 and instantaneous configurations Fk during the morph may also generate system outputs that evoke undesirable subjective attention.

For the benefit of clarity a brief background in digital filters relevant to the present invention follows.

The controllable parameters of a linear digital filter 16 are the coefficients of the difference equation which describe the filter's operation. The instantaneous values of these parameters (along, formally, with record of previous inputs and outputs stored within the filter's memory) define the filter's state. S.. a

The controlling difference equation has form: $ S..

I

=b,; +b).kxk_) +b2kxk_2 +bN.xkN I.kYk-I -a2kyk_ aN.kyk_N (1) IS * *5 in which x is the filter input, y is the filter output, k is the integer time index and a and b are the controllable parameters.

The difference equation (2) is conventionally re-arranged into a "transfer function" describing the ratio of output to input, using the following notation for the unit time delay operation: 1 9

-

Yk-I -z Yk+I = 2Yk In addition to providing an operator notation for unit delay, z here forms a frequency transform variable (and the process of writing the unit time delay operation in terms S of z is called 2 Transformation", a sub-set of Fourier or Laplace Transformation).

The transfer function associated with the difference equation (1) is: L N i. N-I L y1 U0Z +u1Z **+UNJr

N N-I

x z +a1z...+aN where we assume that the parameters a,b are either fixed in value or vary slowly with k. S... * S*S

The filter's action in the frequency domain is determined by the roots of the . :: numerator and denominator polynomials in z -the numerator roots defining "zeros" * *:.* and the denominator roots defining "poles". The roots being the singularities of the :: 15 filter, the movement of which transforms the filter between the first state Fl and the * *: second state F2 in accordance with the present invention.

In order for the filter to be stable, the poles p must lie within the "unit circle": zJ<1.

For simplicity (and without loss of generality when the filter is implementing a shaping filter) it is a further requirement that all zeros z lie inside or on the unit circle: j z <=1 (this limits the filter to the class of "minimum phase" filters).

In order for the filter to be physically realizable, it is necessary that the coefficients a,b are real. This places a significant further restriction on the location of the poles and zeros. The poles and zeros must either occur in complex conjugate pairs or lie on the real axis. This motivates a factorization of equation (2) into a series of floor(N/2) second order sections (often called "Biquadratic sections): y b01z2 +b1z+b21 b02z2 +b12z+b22 bOfl.,or(yI2)Z2 +bIj,r(N/2)Z+b2J,r(N/2) x + a11z + a21 z2 + a12z + a22 + aI J700,(N12)Z + a2fll,,,(N,2) and an additional bilinear section if N is odd: y = b01z2 + b,1z + b2, b02z2 + b12z + b22 bOfl,,,,(,2)z2 + bj JoorViU2)2 + b2fl,,,,(N,2) b01z + bIN X Z +a,1z+a Z +a,2Z+a22 Z +aI.J,oor(N,2)z+a2Jfr,,(N,2) z+a,N The examples of hypothetical power spectra mentioned above and shown in Figures * :* 2 and 3 are produced when a generated signal having energy uniformly disposed over frequency is passed through a filler with poles or zeros close to the unit circle. * 15

S

With reference to the noise generator of Figure 1, it is desired to transform the state of the filter 16 from the first state Fl to the second state F2. This transformation, applied instantaneously, would be audible to the listener 22 if the difference between Fl and F2 is sufficiently large. In the case of the application in Sound Masking Systems1 an instantaneous change would be distracting and would alert the listener to the presence of the Sound Masking System and its output, which is undesirable.

In an embodiment of the present invention the control means 18 applies a series of adjustments, SF1, to transform the filter 16 by a series of small increments, conveniently (but not necessarily) applied at regular periods of time, kT, where k is a positive integer index and T is a sample period. The filter is thereby transformed from Fl to F2 over a predetermined preferred path defined by: The existence of a finite series of M such adjustments is satisfied when the path converges to the desired final state F2: F2=F1+L,F (3) Auditory perception has just noticeable difference limens (JND's) for any aspect of the sound stimulus (level, pitch, etc), below which changes in that aspect of the * S. ***. stimulus are imperceptible. Thus, increasing the number, M, of increasingly small S...

steps in the trajectory generates an imperceptible transformation between Fl and F2, as the rate of change of the filter and, in consequence, the rate of change of the filter r 15 Output, is such that all changes fall below the JND's. S. * S *S S

The present invention further provides for the determination of paths along which singularities (poles and zeros) may travel, during transformation from Fl to F2, to thereby avoid transformations that might elicit undesirable subjective responses from a listener 22. This is advantageous in that it provides for transformations that are indiscernible to human perception and it results in a speedier process. Generally speaking, singularities (poles or zeros) near the unit circle give rise to frequency selective behaviour, such as that responsible for evoking perceptual judgements such as rumbling or tonal. Conversely, singularities close to the origin are more impotent and less likely to attract the listener's attention.

The preferred path of singularities between Fl and F2 follows. The numerators and denominators of biquadratic factorizations of the transfer functions are quadratic. The two roots of the quadratic can either both be real, or appear as a complex conjugate pair (obeying the requirement for real coefficients of the filter). The total transformation between Fl and F2 is broken down into a set of smaller tasks of transformations between one quadratic factor of (the numerator or denominator of) Fl and one similar factor of F2. The transformation between the linear roots when N is odd follows from the quadratic argument.

Three possible non-trivial combinations are considered: when the quadratic factor of Fl has real roots, whilst that of F2 has conjugate roots, when both quadratics have conjugate roots and when the quadratic factor of Fl has conjugate roots, whilst that of F2 has real roots. These cases are shown in Figures 3a, 3b and 3c, in which Figure 3a shows real to conjugates, Figure 3b shows conjugates to conjugates and Figure 3c shows conjugates to real. The case in which both pairs of roots are real is . discussed later. In Figures 3a, 3b and 3c + represents the root of Fl and UX represents the root of F2. p *. p * * p.. * SI *

When both the pairs of roots are complex conjugates (Figure 3b), any path between the factors of Fl and F2 is feasible provided the roots remain as conjugates throughout the transformation. Several allowed paths are sketched in Figure 4, although, at this stage, there has been no imposition of constraints from psychoacoustic considerations. However, it can be noted that the paths themselves are conjugate reflections of each other.

In the case where one of the root pairs is real (as shown in Figures 3a and 3c) it is necessary to decide upon a "breakpoint" where the two real roots will leave or join the real axis. Any such breakpoint is feasible. However, a method for determining the breakpoint is described below which is useful when both real roots have the same sign. It will be appreciated that the specific method described below is not suitable for the cases shown in Figures 3a and 3c as in both those cases the real roots are of opposite sign.

S

In order to calculate the breakpoint suppose the quadratic has form: s0z2 +sz+s2 The breakpoint may be defined where the quadratic has repeated roots, It is located at: z6 = (4) 2s0 * S. I. * * S* and is achieved when:

S S...

s =J4s0s2 (5) S.. I

S

In other words, given fixed value of s0 and s2, the s, parameter is adjusted until it equals the critical value defined in equation (5), which places the real roots coincident on the real axis. This process draws upon an analogy with the dynamics of second order systems, in which s1 is a damping parameter and the value defined in (5) is called TMcritical damping.

From this coincident root location on the real axis, any pair of conjugate trajectories to/from a conjugate pole pair is realizable, as shown in Figure 5.

The total transformation from a real root pair to a conjugate pair (or vice-versa) involves moving the real roots along the real axis to the breakpoint such as, for example by modifying the damping term s, towards critical value, followed by an arbitrary conjugate trajectory to the complex poles.

In order to transform between real poles (either arising from a bilinear section reflecting odd filter order N, or from quadratic factors of Fl and F2 both having real roots) the roots are moved along the real axis from initial to final value. The transformation must not take them off the real axis (unless they are repeated roots, in which case they may be treated as a conjugate pair).

Having identified physically realizable means to move pairs of singular points from quadratic factors of Fl to similar factors of F2, the task of transforming the total filter from Fl to F2 may now be considered -formed as it is from a set of 2*floor(N/2) quadratic transformations and (when N is odd) two linear transformations. * .* * * * .*

I *1**

It is, of course, possible to transform between any two quadratic factors of (the ** S * numerator or denominator of) Fl and F2. However, the cost of the total S..

transformation is minimised if the factors are grouped according to proximity of the singular points, such that the total distance the singularities are moved is minimized.

* This cost minimization will accrue practically as time saving.

Figures 6 show two pairs of conjugate singularities. Grouping the singularities such that the transformation distance is minimized is shown in the left hand figure. The right hand figure shows the cost of a sub-optimal grouping.

The situation depicted in Figure 6 is simplified relative to more general cases, in which there are more than two pairs of singularities. In such cases, it is beneficial to group quadratics to represent the start points and end points of transformations in order that the total transformation distance is minimized. However, this task is S 15 relatively complex computationally and practically it is usually acceptable to make sub-optimal groupings.

In the case of real to conjugate pair transformations, it is appropriate to assess distance between the conjugate poles and the breakpoint from the real axis.

In the case of real-to-real transformations, the start and end singularities may be grouped according to distance (although, practically, the real singularities may represent a small sub-set of the problem that may be addressed sub-optimally).

Having seen how a general filter 16 may be transformed from one state Fl to another F2, by moving the singular points of Fl along paths satisfying the rules of continued realizability, psycho-acoustic considerations can be taken into account. That is to say S...

how paths might be constrained by issues arising from psycho-acoustic considerations and, subsequently, how the paths themselves might be adapted to be S..

sympathetic to the requirements of psycho-acoustics and the listeners experience of the transformation.

As mentioned above, it has been noted that those singularities close to the unit circle can generate strong frequency selective behaviour capable of evoking strong subjective responses. Changing such singularities, in the course of a transformation between two filter states, will generate an additional stimulus to draw the listener's attention to the spectral feature associated with the singularity.

According to the present invention, singularities are moved slowly when close to the unit circle, to minimize audibiIity5. Conversely, when close to the interior of the unit circle, singularities are moved more quickly, without risk of attracting the listener's attention.

Such scaling of the transformation speed is achieved by scaling the steps along the determined path by a speed which is itself a function of the instantaneous radius of the singularity.

For example, consider, for simplicity, the transformation between the singularities at z, and z2 along a straight line.

The straight line is described by the equation: Ini(z) = mRe(z)+c * ** * * in which the constants rn and c are defined by: *.*.

m = Im(z2) -lm(z1) * .: 15 Re(z2)-Re(z1) c=Im(z1)-mRe(z1)

S * * S. S

The transformation is performed by adding a series of increments to z1, each of form: In which M is a step size, practically derived from (Re(z2)-Re(z,))/M, allowing the transformation from z7 to z2 to be completed in MT seconds.

A transformation speed constraint can be added by scaling the incremental steps along the trajectory: = speed * [ + jmixJ where speed is a speed modifying constant, functionally related to the radius.

Speed constraints of the form: speed = [i -cos(pi* I z) + speed,,.... } have been demonstrated to be useful, in which speed, is the minimum useful speed allowed on the unit circle. It will be appreciated that the speed parameter defined above is analogous to a raised cosine window.

When a singularity is located close to the unit circle, the consequences of a move in a radial direction are different to those of a move normal to the radius. The S...

:*. 15 consequences are illustrated in Figures 7. S..

I

Referring to Figure 7, radial movement of a singularity increases or decreases the :* . aQ of the peak (or notch) in the frequency response. Reduction of the radius reduces the 0, which reduces the perceptual impact of the singularity. Small displacements of a singularity, normal to the radius, shift the frequency of the peak (or notch) in the frequency response, without changing the Such change in frequency is potentially audible, if the change exceeds the JND in pitch, and may cause substantial perceptual impact.

Further from the unit circle, an efficient transformation between two singularities will follow closer to a straight line path: the shortest distance between the two points. The distance from the unit circle will limit the extent to which the frequency response of the filter is influenced and, so, will make such a transformation perceptually impotent.

There is seen to be a change in the preferred paths of transformation between any two singular points as radius changes; near the unit circle, paths should leave and approach singularities on close to radial lines, whereas further from the unit circle, close to the origin of the unit disc, any path is permissible and straight lines are preferred for speed.

In accordance with the present invention perceptually constrained transformations between Fl and F2 are guided along paths determined such that strong singularities are moved away from the unit circle before further modification and only restored to * positions close to the unit circle by a radial movement. Weaker singularities are moved with less consideration of their perceptual impact. I... *. *

* This is achieved using D-Lines" as paths for filter transformations. D-Lines are I. entities of non-Euclidean hyperbolic geometry which are arcs of a circle. The circle of which the D-Line is an arc is formed such that it intersects the unit circle at two points * and is normal to the unit circle at both intersection points. A 0-Line can be constructed to pass through any two points inside (or on) the unit circle, such as the initial and final locations of singularities before and after a transformation. When both singularities lie on a diameter of the unit circle, the circle generating the D-Line has infinite radius and the D-Line becomes a straight line -the diameter of the unit circle.

For all other cases, the D-Line is an arc of a circle.

Figures 8a to 8h illustrate some randomly chosen pairs of singular points and the D-Lines connecting them.

When the singularities lie approximately on a diameter of the unit circle, the D-Lines are approximately straight lines, as seen in Figures 8a and b.

When the singular points move away from a diameter of the unit circle, the curvature of the D-Line increases, as seen in Figures 8c and d.

When one of the singular points is close to the unit circle, the trajectory approaches that point approximately along a radial line, as seen in Figure 8e.

When both initial and final singular points are close to the unit circle, the path approaches each singularity along a radial line and the penetration of the middle of the path into the interior of the unit circle is controlled by the angle between the two singularities (or the circumferential distance between them), as seen in Figures 8f to :::: 8h. This angle represents the frequency difference: singularities to be transformed through a large frequency range are taken on a path closer to the origin than those transformed through a smaller frequency range. 0**

I

: Referring now to Figures 9a and 9b, a group of transformation paths, designed using the combination of D-Lines and real axis breakpoints are shown. The transformation links two randomly chosen states for a 10" order filter (i.e. a filter having 10 poles and zeros). The poles are indicated by a x' and the zeros are indicated by a o'.

Movement of the singularities along the transformation paths can be controlled such that the speed of the transformation is constrained by perceptually inspired considerations, such as the speed= ((radius) example described in previous sections of the present document. In the case of movement along the straight line arcs of the trajectories, such movement follows the example previously presented. In the case of movement along the D-Line, the centre of the circle of which the D-Line is an arc is known, ZX+fy, as is the radius of this circle, r. Movement along this circular path segment conveniently is imparted by incrementing the angle in small steps and scaling these steps by a speed factor.

It will be appreciated that the method of the present invention may be implemented by computer program. * ed * ** **.* *). *4 * S. * S*

S S..

S . .. S * S ** 0 05

Claims

CLAIMS1. Signal processing means comprising control means, said signal processing means having at least one filter comprising one or more parameters controllable to transform the respective filter from a first state into a second state, wherein the control means is operable to provide a series of adjustments to the filter parameters which determine a preferred transformation of the filter from the first state into the second state such that the transformation is at least substantially indiscernible to human perception.
2. Signal processing means as claimed in claim 1, wherein the control means is operable to control the speed of adjustment of each singularity which collectively define the state of the filter during the process of being transformed. * U.:::::: 15
3. Signal processing means as claimed in claim 2, wherein the speed of adjustment of each singularity is a function of the instantaneous radius of that ** .S S

* singularity. S. *
4. Signal processing means as claimed in any preceding claim wherein the * 20 control means is operable to determine a preferred path along which the relevant singularity defining the instantaneous state of the filter travels between the first and second filter states.
5. Signal processing means as claimed in claim 4, wherein, in a case in which at least one of the first and second state singularities are not disposed on a diameter of the unit circle, the preferred path is an arc of a circle defined such that extrapolation thereof intersects the unit circle at two points at which the extrapolated paths are normal relative to the unit circle.
6. Signal processing means as claimed in claim 4, wherein, in a case in which both the first and second state singularities both lie on a diameter of the unit circle, the preferred path is defined as a substantially straight line following the diameter.
7. Signal processing means as claimed in any preceding claim wherein the signal is a sound signal and the transformation of the filter from the first state into the second state is such that the transformation is at least substantially indiscernible to human auditory perception.
8. A method of transforming the state of a signal processing filter from a first state to a second state such that the transformation is as least substantially indiscernible to human perception, comprising: providing signal processing means having a filter, the filter having parameters *:.:: 15 controllable to transform the respective filter from a first state into a second state, *SS.providing control means, S. I S using the control means to provide a series of adjustments to the filter parameters I..thereby determining a preferred transformation of the filter from the first state to the second state such that the transformation is as least substantially indiscernible to * 20 human perception.
9. A method as claimed in claim 8, wherein determining the preferred transformation comprises determining the speed of adjustment of each singularity which collectively define the state of the filter during the process of being transformed.
10. A method as claimed in claim 9, wherein the speed of adjustment of each singularity is a function of the instantaneous radius of that singularity.
11. A method as claimed in any one of claims 8 to 10, further comprising determining a preferred path along which the relevant singularity defining the instantaneous state of the filter travels between the first and second filter states and adjusting the parameters of the filter accordingly.
12. A method as claimed in claim 11, wherein, in a case in which at least one of the first and second state singularities are not disposed on a diameter of the unit circle, the preferred path is an arc of a circle determined by extrapolating the preferred path such that it intersects the unit circle at two points at which the extrapolated path is normal relative to the unit circle.
13. A method as claimed in claim 11, wherein, in a case in which both the first and second state singularities both lie on a diameter of the unit circle, the preferred * I. path is defined as a substantially straight line following the diameter. **S. * *
14. A signal transmitted from an electronic device as claimed in claims ito 7. *** * * *. I* *
15. A signal produced by a method as claimed in claims 8 to 13. * 20
16. A carrier medium carrying computer readable code configured to cause a computer to carry out a method according to any one of claims 8 to 13.