It is possible to derive an almost limitless number of response parameters from an individual room response. However, it is sensible to determine those which are most likely to be perceptually relevant and those which have been suggested in the literature. Throughout this thesis, a number of observations have been made as to the factors most likely to have a significant effect on the overall perceived quality. A selection of response parameters are now described, and metrics derived from them. Once introduced, these metrics are run against each of the fourteen responses to produce an associated score for each room.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0 0.5 1 1.5 2 2.5 3 3.5
Subjective Scores for Modelled Rooms
Room Model
Perceived Quality Rating (z scores)
Figure 9.2: Quality scores for the fourteen room responses
The metrics chosen have been broken down into several classes - decay rate, signal reproduction, frequency deviation and frequency artefacts.
9.6.1 Decay Rate
Results have shown the undesirable characteristics of excessive decay times. Indeed, Chapter 4 determined the optimal spacing of two resonances in order to reduce this decay time and there was a increase in perceived quality for rooms with shorter decays in Chapter 7.
Whilst it is common to consider each resonant mode as having its own individual decay time (Howard and Angus, 2001), wherever there are multiple modes in a small frequency region, it is likely that they will share a similar decay rate. It is therefore suggested that considering the overall decay time at low frequency is a valid metric. This is particularly apparent in cases of high modal density, where the low frequency sound-field may well be considered statistical according to Schroeder’s equation (3.31). In such cases the general decay time across the low frequency region may be perceived as a single entity.
In order to calculate a metric based on the low frequency response, the Schroeder backward integration method is again employed (see Section 6.5.2). The energy de- cay curve is analysed to determine the points at which the energy first drops below -5dB and -35dB. The gradient is then calculated from these points and extrapola- ted to determine the time taken for a drop of 60dB, analogous to the commonly
used acoustical measure of RT60. For this ‘overall low frequency decay time’, the
frequency range for this calculation was between 20 and 250Hz.
In addition to the overall decay across the low frequency range, decay times were calculated for each third octave band. Chapter 4 showed that decays are perceived differently across the frequency range and Chapter 6 revealed the decay time thresholds which are frequency dependent. By analysing the measured decay time at each band, it is possible to investigate whether those at specific frequencies have a higher correlation to perceived quality.
9.6.2 Signal Reproduction
The second class of metrics is referred to as ‘signal reproduction’. These are measures of the ability of the system (in this case the model room) to accurately reproduce the input signal. For this study, the Modulation Transfer Function (MTF) is considered. Initial studies have shown that the MTF is a promising predictor of audio repro- duction quality (Houtgast and Steeneken, 1985; Harris et al., 2006; Fazenda et al., 2006a). The function measures a system’s ability to preserve amplitude modulations of a signal over a set frequency range. The modulation frequencies are defined as re- presentative of audio signals and in particular those found in speech (this technique is applied to define the Speech Transmission Index). Research has been conducted into a set of modulation frequencies more appropriate for music reproduction (Har- ris and Holland, 2008) and as such, the modulation frequencies used in this metric were 0.8, 1, 2, 4, 6 and 8Hz. The algorithm used to calculate the MTF is defined by Schroeder (1978): m(F)¥ N q 0 h 2 f(n)e≠j2 Fn F s N q 0 h 2 f(n) (9.1) where F is the modulation frequency, hf(n) is the discrete impulse response of
the system band-passed with centre frequency f, and fs the sampling frequency of
the impulse.
The function therefore takes the modelled room impulse response and calculates the result for each modulation frequency. These may then be averaged and the result lies between 0 and 1 for each frequency band, where 1 represents the system preserving an an exact copy of the input signal. A further average is taken across each frequency band, which are the third octave bands between 31 and 200Hz, producing the final score.
9.6.3 Deviation from Ideal Response
A number of researchers have proposed metrics based upon the deviation of the frequency response from an ‘ideal’ case. For example, Cox et al. (2004) base a room optimisation algorithm upon the deviation from a straight line through a modelled response.
Another similar metric has been referred to as a ‘figure of demerit’ (Vanderkooy, 2007), which was used in the assessment of active loudspeaker arrangement simu- lations. It considers the frequency range of 20-150Hz, tapered to give precedence to frequencies in the 40-100Hz range. The final score is the deviation of the room response from a one octave smoothed version of itself. Vanderkooy goes on to state that this metric may not have ‘a strong psychoacoustic basis’, but that it may be used nonetheless in the ‘absence of relevant research’. It is hoped that this thesis helps to alleviate this absence.
Within this class of metrics, in addition to the examples shown from the litera- ture, it is suggested that the deviation from a simple 3rd order polynomial curve fit of the response may offer correlation to quality. The rationale behind this is that such a curve should more closely follow the general characteristics of the response. The ‘ideal’ target remains smooth however, and therefore, any response closely ali- gned to this is likely to have a short decay time. A similar deviation from a simple ‘flat’ response case, is also included.
Finally, the deviation is calculated where the ideal response is ‘tilted’ in favour of the lower frequencies. Wankling and Fazenda (2009) suggest that a lack of bass may be perceived as a negative attribute of the room by certain subjects depending on their personal preference, even where the response is otherwise articulate. In larger listening spaces, such as concert halls, Beranek (2003) suggests that a rise in the low frequency energy (bass ratio) is necessary, and that a greater amount of low frequency energy is required to ‘support’ the music. Furthermore, Soulodre and Bradley (1995) observe that the perception of low frequencies is best correlated to the strength of those frequencies. A corresponding metric is therefore determined by defining a weighted line of best fit with a 10dB increase from 200Hz down to 20Hz.
It should be remembered that while the deviation metrics discussed are intui- tively satisfying, they are based upon an average deviation across the frequency range. There is no guarantee that an individual resonance might cause significant audible degradation, and yet as part of the overall response, not decrease the average deviation significantly. It is possible that it is not the ‘average’ smoothness of the response, but the individual elements of it which are perceived. Figure 9.3 shows
0 50 100 150 200 250 60 70 80 90 100 110 120
Pressure Response and 3rd Order Polynomial Line of Best Fit
Linear Frequency (Hz)
RMS Pressure (dB)
Best Fit
Modelled Response
Figure 9.3: A response with a single mode at 100Hz and its associated 3rd order polynomial best fit curve
an example case of a single resonance which is highly likely to cause degradation in the room, and yet scores reasonably highly (0.71) on the polynomial curve metric. Such individual elements are therefore the basis for the final class of metrics.
9.6.4 Frequency Artefacts
The final class of metrics considered are known as ‘frequency artefacts’. These are defined as isolated characteristics of the frequency response which may be signifi- cant in the perceived quality of reproduction. These relate to the general shape of the response which may be observed through a visual inspection. For example, a number of significant peaks may be clear, and acousticians will often flag such fre- quency imperfections for optimisation. By including such metrics in this analysis, it is possible to determine the validity of such a visual approach for calculation of expected perceived quality.
Obvious artefacts such as peaks, troughs and dips of the low frequency room response have been the focus of much research (Bucklein, 1981; Olive et al., 1997; Toole and Olive, 1988). Olive et al. (1997) conclude that resonant peaks are more degrading than comparable dips. Where modal equalisation has been attempted, it has often been the significant peaks which are selected for treatment by the equalisers (Makivirta et al., 2003). Therefore, a ‘number of peaks’ metric is considered. For this study, complex mode parameter detection such as in (Makivirta et al., 2003) has not been undertaken. Rather, the simple metric is determined by taking each frequency response and calculating the number of peaks present in the 20-200Hz
Class Description Short Name Decay RT60 across all frequencies DEC_ALL
RT60 at 32Hz DEC_32 RT60 at 63Hz DEC_63 RT60 at 80Hz DEC_80 RT60 at 100Hz DEC_100 RT60 at 125Hz DEC_125 RT60 at 160Hz DEC_160 RT60 at 200Hz DEC_200
Signal Reproduction Modulation Transfer Function SR_MTF Deviation Vanderkooy Figure of Demerit DEV_VAN
3rd Order Polynomial Best Fit DEV_SMOOTH Flat response DEV_FLAT Bass Tilted response DEV_TILT Frequency Artefacts Significant peaks ART_PEAKS
Significant dips (>6dB) ART_DIPS6 Significant dips (>12dB) ART_DIPS12 Table 9.1: Table showing each metric under test and its associated class range.
In addition to peaks, a metric is proposed based upon the number of significant dips. This is calculated by determining the number of points in the response which are greater than 5dB lower than the previous peak. A second significant dips metric follows the same method, but with significance attributed to a 10dB drop.
Table 9.1 summarises each metric under study along with a short code which is used when presenting the data.