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Loudspeaker & Room - case studies  

+++  Acoustic polarity  +++  Phantom center  +++  Room test signal  +++  Room reflections  +++  Driver distortion  +++


Test signals for room reflection
and driver distortion investigations

Acoustic performance data are usually derived from an impulse response measurement. The impulse response itself is derived from a periodic acoustic noise excitation of the system under test, from a rapid frequency sweep or from a maximum length sequence of acoustical ones and zeros. Rarely is the impulse response derived from a popping balloon or a pistol shot. The impulse response is then further analyzed to derive the steady-state frequency response for various lengths of time windows. The impulse response also yields the Energy Time Curve or when integrated the step response of the system in the time domain. Linearity of the system is tested by varying the amplitude of the excitation signal. When measuring in reverberant spaces the steady-state frequency response and its frequency resolution are a function of the time window length and window type. A frequency domain room response can be measured, but it is nearly impossible to say what in the frequency response is due to direct, reflected and reverberant sounds. 

A 3 second sequence, Figure 1, of properly shaped tonebursts of short duration and of different frequencies, going for example from 200 Hz to 12.8 kHz in half-octave steps, and separated by 250 ms in time from each other, can be effectively be used to study a room response both in time and frequency simultaneously.

               Figure 1

Zooming in on the burst sequence we can see a 200 Hz  burst followed by a 280 Hz burst, for example in Figure 2.

              Figure 2

All burts consist of 4 cycles of a sinewave with the amplitude variation of a Blackman window function like for the 200 Hz burst in Figure 3.

               Figure 3

The gradual increase of the signal amplitude from zero to a maximum and its gradual decay to zero assure that both low frequency and high frequency spectral content of the signal are maximally attenuated, Figure 4. The shape of the spectral content is thus uniquely defined by the burst envelope function, Figure 5. A larger number cycles would narrow the spectral envelope and increase the burst energy. A longer burst would also decrease the time resolution and increase the frequency for which a first reflection can be visually differentiated from the direct signal. A direct signal burst at 1600 Hz has a duration of 2.5 ms. A reflection with a delay of 2.5 ms has traveled a distance x = (0.34 m/ms)*(2.5 ms) = 0.85 m and could be from an object at a distance of x/2 = 0.43 m or 17 inch behind the direct signal.  At lower burst frequencies the reflection from the same object will overlap in time with the direct signal and add or subtract from it depending upon their phase relationship. For a 200 Hz burst frequency all first reflections from objects within a 3.4 m (11 ft) radius from the source arrive with some amount of time overlap.

A short burst is also a relatively safe test signal for stressing a driver or clipping an electrical circuit. The onset of distortion is usually audible when the test signal level is increased. The woofer is usually the weakest component because of the large increase of cone excursion with decreasing frequency. The distorted burst waveform and the associated burst spectrum provide pictures for how a particular driver degrades when a large signal is applied. A burst is also more representative of program material than a continuous sinewave. Visually observed distortion correlates strongly with what is heard.


Figure 4





The spectrum of the 200 Hz burst covers a range of frequencies around 200 Hz and overlaps with the spectrum of the 280 Hz burst.

The peak of the spectrum decreases at 6 dB/oct with increasing frequeny. Though the peak amplitude and the rms-value of each burst is the same, its duration changes as 1/f and thus its energy in Ws decreases.


Figure 5


A 4-cycle burst with a Blackman envelope is described in the GoldWave Expression Evaluator by:


A 4-cycle burst with a Cosine envelope is described in the GoldWave Expression Evaluator by:

where x=4

The Blackman burst (red) has higher out-of-band attenuation, which gives useful dynamic range for 2nd and higher harmonic measurements.

The burst response, Figure 1, is captured using the Signal Recording capability of ARTA. In this mode ARTA acts like a digital storage oscilloscope. The burst sequences start with a 100 Hz burst and end with a 400 Hz burst. The record button should be pushed after the 400 Hz burst has been heard to capture the next sequence of the repeated burst file. I use an E-MU Tracker Pre two channel USB Audio Interface unit with my notebook computer. Microphone input and headphone output of the notebook could be used instead, but I get less dynamic range. A modified Panasonic microphone capsule with 9 V battery supply for low distortion picks up the burst signal and any other sounds in the room, which are present during the 5.461 second recording time. Thus the signal to noise ratio of the burst recording and its dynamic ranger are directly affected by how quiet it is in the room and by the volume level of the bursts. I maximize the burst volume to a level below noticing distortion.  

              Figure 6

After the recording has ended push the Zoom Min button to to see the burst response. Using Cursor and Gate markers (left and right mouse buttons) identify the burst to zoom in on by stepping up Zoom Max. The visual dynamic range of the linear amplitude display is not very large and also confused by seeing a positive and negative going signal. Much greater range is obtained by taking the absolute level of the burst wave (= full-wave rectification) and displaying the result on a logarithmic amplitude scale. In ARTA this is accomplished by selecting the ETC mode with a causal window. Again, the Zoom Min button has to be pushed to see the signal as in Figure 7.   

              Figure 7

Stepping up Zoom Max the actual waveform of the rectified burst with its 8 maxima becomes visible. Figure 8.

              Figure 8

Reducing the dB range to 50 dB, going down from the top, gives the window that I use normally for room reflection measurements. Figure 9.

              Figure 9 

The burst sequences were constructed using the Expression Evaluator and Copy and Paste functions in GoldWave. Frequencies in File-01 cover the  reverberant frequency range above the Schroeder frequency of typical listening rooms. It is also the range where maximum volume can be obtained from a typical loudspeaker for higher signal to noise ratio of the test. Table 1.

File-02 and File-03 cover the modal frequency range of typical listening rooms and include low frequencies which tend to be problematic for drivers, thus  requiring lower volume settings for the burst sequence. 

Table 1





Download Burst files:




Play the files in Repeat mode. Push Record in the ARTA Signal Recording window when you hear the 400 Hz burst at the end of a burst sequence.

For practice, download and open with ARTA the "impulse response" file, which was used for the above graphics:


I have used envelope shaped tone-bursts at a time when Fourier Analyzers were not common-place and also to investigate stored energy (resonance) in drivers. ARTA provides this capability in its Burst Decay mode. My paper on "Room Reflections Misunderstood?" was an attempt to correlate visual reflection data with auditory observations. I offer a Toneburst Test Signal CD to investigate the articulation of low frequency sounds and for various loudspeaker and room tests.

With the burst signal sequences of Figure 10 I hope to establish a set of standard test signals for room response measurements that are relatively easy to interpret regarding the physical nature of the response.  Understanding what matters audibly and how it correlates with what is visual in the burst response at different frequencies has still to be learned and confirmed against intuition. Testing rooms with empirically known good or poor stereo performance should serve as guidance. Testing speakers with different radiation patterns and therefore different room interaction should give further insight when comparing test data to perceptual differences. 

I will start this process for the rooms and speaker setups that are available to me. 


155 Hz Highpass Filter

Ambient noise deteriorates the dynamic range of acoustic burst measurements. The time record is broadband and the ETC is not frequency selective. File 01 only consists of burst frequencies above 200 Hz. A 155 Hz 3rd-order Butterworth highpass filter after the microphone is effective in reducing low frequency rumble and 60 Hz hum from various machinery. The following circuitry also provides -9 V bias for the electret microphone capsule and is powered by rechargeable batteries.

  Figure 10

The effectiveness of the filter is visible in the wave form of the burst ETC taken in my small office room. The highpass filter was used in Figure 11, but not in Figure 12. You can compare the two files in more detail using ARTA with office-hpf.pir and office-no-hpf.pir.  

  Figure 11

  Figure 12


Summation of direct signal and delayed reflection

The 4-cycle burst has a duration corresponding to four wavelengths at the chosen frequency. At low frequencies and long wavelengths reflections will overlap in time with the direct signal if the reflecting path is less than four wavelengths longer than the direct signal path. Below are examples of the ETC for a single reflection at 0 dB (not likely) and -6 dB overlapping with the direct signal at different delays. (burst-overlap.xlsx)

From the above pictures it should be apparent that one can say little about the first reflection once it overlaps in time with the direct signal from source to microphone. Ranging and finding the origin of a reflection can only be done with burst frequencies above 1 kHz for typical listening room dimensions and loudspeaker setups.

The boundary between an overlapping and not overlapping reflection is the surface of a spheroid with an axis of rotation of length a = D + 4L and a maximum diameter b = 2sqrt(2LD + (2L)^2) where D is the distance between burst source S and microphone M.

The minimum overlap free distance 2L applies to reflections from directly behind the source or directly behind the microphone. Reflections from objects inside the spheroid overlap the direct signal. The size of the spheroid increases with lower frequencies and longer burst durations.


See also  WATSON loudspeakers outdoors of Sea Pine Cottage as an introductory ping test example








What you hear is not the air pressure variation in itself 
but what has drawn your attention
in the streams of superimposed air pressure variations 
at your eardrums

An acoustic event has dimensions of Time, Tone, Loudness and Space
Have they been recorded and rendered sensibly?

Last revised: 06/17/2022   -  1999-2019 LINKWITZ LAB, All Rights Reserved