Crest Factor of Musical Signals (abstract)

 

 

... the result of ASDA (Statistical Analysis of the Amplitude Distribution) is summarized in a series of numerical quantity (average, peak, RMS etc.) and a bar chart that represents the normalized distribution for the amplitude of the signal. For example we can know how many times the signal takes values close to maximum value (in the track) or for how long is situated above or below the 50% of maximum… and so forth. The ASDA "counts" how many times the signal crosses a number of fixed thresholds. For musical signals  thresholds were established as shown in Table 1.3.

 

 

 

 

Modulation %

Modulation dB

1

 0 to 3.125%

Till -24dB

2

6.25% to 12.5%

-24dB to -18dB

3

12.5% to 25%

-18dB to -12dB

4

 25% to 50%

-12dB to -6dB

5

 50% to 70%

-6dB to -3dB

6

 70% to 85%

-3dB to –1.5dB

7

 85% to 100%

-1.5dB to 0dB

 

 Tabella: 1.3 ASDA thresholds



Figure 1.4 Analysis of Distribution of the Amplitude: in this example the signal crosses 4 times the threshold.
 
The thresholds are set as percentages of the peak amplitude of the signal in the track (Maximum  Relative Modulation or MMR) in order to compare different distributions. Since the signal is regularly sampled "the number of times" is also "how long" the amplitude of the signal falls within a certain range.
As the audio CD contains a stereo signal we can use the figures of Lissajous that allow us to view the spatial distribution and to detect the presence of any restrictions imposed on the amplitude of the signal (signal modulation too high).

 Let us see two examples concerning a very good record and a poor quality one.
See Figure 1.5. The first figure shows the ASDA  of track #2 ripped from the CD "Beethoven - Sonaten" performed by Emil Giles for Deutsche Grammophon (track "classical"). The quality of this track should be classified as "very good" or “excellent”. The red and green bars rapresent the two channels (left and right). The numbers over the bars indicate how many samples of the signal has been detected inside a particular range. For example, in this track, 11/15 of the total time are below the 3% of Maximum Relative Modulation (MMR) and only two samples from the left channel and 19 from the right channel  are between 85 and 100% of MMR for a total time of less than half millisecond (Figure 1.7).

The second track comes from the CD of Celine Dion (One Heart). In this second case, the crest factor is decidedly low. In this track ( "pop") the largest number of occurrences is concentrated between 12 and 50% of MMR which in this case is very close to Absolute Maximum of Modulation (MMA). Signals over time are represented with the same amplitude scale and, by comparison, the signal appears much more intense for the “pop” track . In the "classical" track, due to low graphic resolution, peaks (very short) are not visible: a significant segment time is given in figure 1.7 where you see the peak highlighted by a circle.

 

 



 

Figura 1.5 ASDA di Beethoven (up) e Celine Dion (down)

 

 

The figures of Lissajous of the two tracks (Figure 1.6) show the tendency of the “pop” track  (right) to overcome the limits of the graph. A more accurate analysis of the “pop” track  (Figure 1.8) shows many  "clipped" segments. These saturations are recorded on the CD and they do no coincide with the MMA (equivalent to 32767) but they are at a slightly lower level (32432). That means that  the clipping was imposed before the A/D section by a limiter or a compressor.


The quality of a record depends on many factors starting from the expertise of the performers, the number and arrangement of microphones, the background noise, the mixing, equalization, compression, until the last step: the recording into two stereo tracks. The ASDA analysis contains information on the dynamics (through the crest-factor) and (if any) saturation (or sovramodulation). The highest value for the crest factor was found equal to 28 (The rite of Spring – Stravinsky – Telarc). Higher values are found in sample recordings (instruments in anecoic room).

 


 

Figure 1.6: Lissajous figures of the two tracks ( "classical" on the left that appears correct, "pop" right  highly clippled). The red rectangle represents the limit of Absolute Maximum Modulation, the diagonal is the virtual central channel. The sound quality is very different. The “pop” track has an high RMS value anl will sound louder whem palyed with an MP3 portable reader.

 

 

 

 Figura 1.7: Beethoven – Traccia 2 – the signal rich is maximum in a single isolated peak.

 

 

Figura 1.8: the  "pop" track :  DX e SX, 512  samples segment with clipping. Anyway it sounds (!)