Difference limen for Q-factor depending on frequency

As previously discussed, the difference limen for Q-factor of room modes presented in this thesis is a useful ‘tool’ for room designers to decide on target levels to be achieved in the low frequency range. However, the results have been derived for a generic difference limen where all low frequency modes have been assumed to possess the same Q-factor. This assumption was supported by the measurements on which the room models were based, and also by the expectation that in the most general terms, damping is roughly proportional to frequency. Extrapolations have been derived to indicate difference limen in terms of decay time, but the strong dependence of decay time and centre frequency raised the question of the equivalence of detection in decays across frequency. It is well known that many thresholds in auditory perception vary with frequency and hence it might be expected that other psychoacoustic effects, such as decay detection, might behave similarly.

Recent published work has appeared in this area, concerned with the relative audibility of single resonant artefacts presented individually (Karjalainen et al. 2004), and it may be that there is merit in revisiting these experiments. However, this thesis has pursued ‘room’ simulations as opposed to deconstructing the stimuli into individual modes, and although this deconstruction might be important in gaining a thorough understanding of the mechanics of the percept, the focus on ‘real’ music signals in ‘real’ room conditions is a useful one in obtaining generalisable and applicable data.

To this end, a further experiment may be set-up to extract the difference limen for the Q-factor of room modes, but this time, specific values should be evaluated at different centre frequencies. The same experimental system used in Chapter 8 could be employed, maintaining subjacent experimental principles, such as the use of music samples and representations of real rooms at the ‘high frequencies’. The range of frequencies under test should then be divided into sub- bands. An initial suggestion could be third octave bands in the range 32 Hz to 250 Hz.

The actual construction of the experiment could be achieved in the following way:

• A ‘generic’ small room corresponding to listening standards is used to provide guidance in the density, amplitude and centre frequency of the modes to be used.

• These are divided into third octave band frequency sub-ranges.

• The reductions on the modal Q-factor are exerted at each sub-band keeping all other bands at a fixed reference level.

Chapter 9: Conclusions

There are a number of implications from these experimental conditions. Most obvious is the masking effect that the lower frequency sub-bands wield on the higher frequency ones. More specifically, the difference limen determined for the higher (low) frequency sub-bands would be expected to rise due to the masking effects of the lower (low) frequency sub-bands. However, this may be found to be representative of real room applications, if ‘treatment’ is being applied for control within a limited bandwidth. Indeed, this addresses yet another important link between potential results and real applications, as the perceptual effects of narrow band absorption on the modal sound field could also be evaluated.

On the other hand, and as suggested by Karjalainen et al. (2004), it may be that the auditory sensitive to changes in Q-factor is diminished at the very low frequencies as is common for other percepts (e.g.loudness). Indeed, the results from this experiment would thus further indicate how the detection of changes in the decay time of resonances varies with frequency at the lower frequency range.

9.6.3 Comparison of modal equalisation methods

The subjective experimental methods presented in this thesis convey some advantages to subjective testing, as mentioned before. These are the option of direct comparison between auditory conditions and the possibility of generating sound fields that would be problematic to achieve in real rooms. Given this, these methods are powerful to test the theoretical basis of equalisation methods.

One of the most current, and to some extent, still unanswered questions about modal equalisation is the perceived benefit introduced by magnitude equalisation. Indeed, part of this question has been answered in Chapter 7, where the effects of resonances on single tones were tested but maintaining the amplitude of audition constant. It was shown, as expected, that the effects of resonance are still perceived if wide band transient signals are used. However, it would be expected that in the presence of music signals the percept might be altered. Indeed, determination of results for the perceptual factors using music signals is one of the contributions of the work in this thesis. It follows that a test could be defined to determine the perceptibility of magnitude equalisation under critical listening conditions.

The concept is based on previous work by Karjalainen et al. (2004) that suggests the use of an all pass filter with a determined decay rate to represent a magnitude-equalised system that still maintains decay components. Such a system may be obtained with the use of IIR bi-quad filters where the poles and zeros are placed at the same angles and at the same distances from the unit circle. However, the zeros are placed outside the unit circle giving the system non minimum-

Chapter 9: Conclusions

phase behaviour. The decay characteristics of the resonances may be determined by varying the vector length from pole and zero to unit circle simultaneously.

The experiment could then be set-up in the following way:

• As in previous experiments, a real room is used as a ‘template’ to provide modal density and centre frequencies of the modes.

• These are modelled using a cascade of bi-quad IIR as used in Chapter 8.

• One or more decay settings are chosen as test factors. The previously determined difference limen is used to select decay times that are perceptually significant.

• The two conditions under test are:

o A system representing the full room response where the low frequency

amplitude variation introduced by the resonances is maintained.

o A system modelled with the use of various ‘all-pass’ bi-quad filters where the

decay characteristics are the same as in the ‘template’ room – this corresponds to the magnitude-equalised system.

• Detection of differences between the two systems is determined (with the option of varying parameters such as modal decay and density).

• Audition samples are normalised to be presented at the same A-weighted level

o Another factor that could be introduced is the effect of overall level of

presentation on the detection of differences. This is highly relevant since in practice a control system will address the level of the stimulus.

Such a test could indicate the perceptible benefits of magnitude equalisation; indeed, the previous values determined for the difference limen for Q-factor could be used to inform the selection of systems which benefit magnitude equalisation, as determined by their overall decay response.