## How to read an audio waterfall chart?

The cumulative spectral decay plot offers useful information about the performance of the drivers, or the system as a whole. It’s basically a frequency response chart, but with the added time element. It shows how the frequency response develops, after the input signal has stopped.

Normally, after the input signal has ended, the speaker should stop as well. However, some frequencies will decay slowly, and will show up on the graph as sustained frequencies in time. This will be an indicative of speaker ringing or panel resonances. Since there is an extra axis, the plot will be 3D (waterfall graph).

This article presumes that you already know what an impulse response is, and how to make a quasi anechoic frequency response measurement.

### Cumulative spectral decay plot

Here is an example of a CSD plot, for a M-Audio BX5 speaker :

Now let’s try to decipher the graph :

• The X-axis describes frequency, like in a normal frequency response chart.
• The Y-axis describes magnitude in dB, also like in normal frequency response chart. In addition, you have color coding. As you will move along the Z-axis, it will be hard to tell where you are at on the Y-axis. Colors help.
• The extra Z-axis describes time. At the rear, you have the 0 ms mark, which corresponds to the point in time when the input signal has stopped. The first frequency response curve (at o ms), indicates the actual anechoic frequency response of the speaker. As you move along the Z-axis, towards the front, you will see different frequency response curves that depict the response of the speaker after the input signal has stopped, at various points in time.
• The yellow circle shows missing data for the low frequencies, because it is a gated frequency response measurement.

### How to design loudspeakers - video courses

Regarding the performance of the M-audio BX5, what does this particular graph tells us? It shows us that there is a sustained frequency at around 500 Hz and 1200 Hz. Also if we look at the magnitude, we can see that this happens at the -15 dB mark. These frequencies decay slowly, but the output is quite low. If you want perfection, you could say that this is an issue. However, I’d say this is a well mannered speaker. The frequencies above 2 kHz have no sustain whatsoever.

### How to measure cumulative spectral decay using ARTA

The process is quite simple. You just have to make an impulse response measurement, like you would do if you were measuring frequency response.

Place the marker correctly on the impulse response, to mark the gate window, like you would on a gated frequency response measurement. Instead of clicking the FR button, click the CS button, as shown above.

You can leave everything as is. However, I like to use smoothing of 1/6 octave. Click OK, and there you have it, Cumulative spectral decay plot. If you find this process confusing make sure you have read the articles linked in the beginning.

### Other CSD plots examples

Let’s look at other CSD plots examples and see how we can interpret the data. The gated far-field measurements were made on the following speakers :

##### Tweeter CSD plot

As you can see there is little to complain about this tweeter. You can see a slight decay tail at 700 Hz. That is to be expected because that’s the resonant frequency of the driver. Another tail at 2.2 kHz. Similar to the one at 700 Hz, very low in magnitude, nothing to worry about.

##### Mid-bass CSD plot

Judging by this cumulative spectral decay plot, there are some issues. Low frequencies exhibit some amount of sustain. But that’s -15 db below the original signal. At 1 kHz, the output is a bit higher, closer to -10 dB, so that might be something to worry about. Couple of spikes at 4 kHz  and 6 kHz.

##### 2 way system

As you can see, some of the individual problems of the drivers are solved when they are crossed over. Since the crossover point is at 2600 Hz, the two spikes at 4 and 6 kHz are gone.

### Conclusion

The cumulative spectral decay tells us if there are any problems with resonances. If the driver is ringing because of inadequate damping / cone break-up / high impedance spikes at resonance, or some enclosure panels are resonating, it should appear on the CSD plot. In all of the examples above, not one had any severe problems. However, if you see a decay tail which has the same magnitude as the original signal (o ms), that clearly indicates an issue which needs attention.

#### References

1. Testing Loudspeakers by Joseph D’Appolito (Audio Amateur Pubns,1998)