Comb Filtering Perception
Analysis in modulation domain of perception of comb filtering caused by a room reflection
Method
Using a psychoacoustic model based on ERB (Equivalent Rectangular Bandwidth) wavelet and amplitude modulation (AM), a signal representaion is made in the AM modulation domain. This AM modulation domain shows the level of modulation transfer at each center and modulation frequencies.
Reference is the ideal system characterised by the ideal impulse response.
WAV file of ideal impulse response:
Ideal impulse response in AM modulation domain:
FFT frequency response of the corresponding impulse response will also be shown for comparison of the psychoacoustic model and the raw mathematical comb filtering.
Analysis of One Equal Amplitude Reflection
One ideal 0 dB reflection at 0.2 ms
WAV file of ideal reflection:
Response in AM modulation domain:
FFT frequency response:
Comment: There is one dominant notch at 2.5 kHz. In the modulation domain the area below center freq of 1 kHz and below modulation freq of 10 Hz is clean.
One ideal 0 dB reflection at 0.5 ms
WAV file of ideal reflection:
Response in AM modulation domain:
FFT frequency response:
Comment: The dominant notch is at 1kHz, and above this center freq the modulation domain is affected by comb filtering.
One ideal 0 dB reflection at 1 ms
WAV file of ideal reflection:
Response in AM modulation domain:
FFT frequency response:
Comment: Dominant notch at 500 Hz. The clean areas in the modulation domain are below center freq of 200 Hz and below modulation freq of 20 Hz. Also above center freq of about 5 kHz is clean up to the modulation freq of 200 Hz.
One ideal 0 dB reflection at 2 ms
WAV file of ideal reflection:
Response in AM modulation domain:
FFT frequency response:
Comment: Dominant notch at 250 Hz. Even the FFT frequency response is very rugged above center freq of 3 kHz, the modulation domain is clean above 3 kHz up to the modulation freq of 100 Hz.
One ideal 0 dB reflection at 5 ms
WAV file of ideal reflection:
Response in AM modulation domain:
FFT frequency response:
Comment: Despite of heavy notches in FFT frequency response, the modulation domain is clean above center freq of 1 kHz up to the modulation freq of 50 Hz. Also the depth of the notch at center freq of 100 Hz is much less in the modulation domain than in the FFT freq response.
One ideal 0 dB reflection at 10 ms
WAV file of ideal reflection:
Response in AM modulation domain:
FFT frequency response:
Comment: The signal in the modulation domain is clean above center freq of 500 Hz up to the modulation freq of 20 Hz.
One ideal 0 dB reflection at 20 ms
WAV file of ideal reflection:
Response in AM modulation domain:
FFT frequency response:
Comment: When the gap between direct sound and the reflection is 20 ms, the modulation domain is practically clean in the whole center frequency band of 20 Hz - 20 kHz up to the modulation freq of 10 Hz. However above the modulation freq of 10 Hz the modulation domain is severly affected.
One ideal 0 dB reflection at 50 ms
WAV file of ideal reflection:
Response in AM modulation domain:
FFT frequency response:
Comment: When the reflection gap is 50 ms, there will be problems with signals having modulation speed higher than 5 Hz as seen in the modulation domain.
One ideal 0 dB reflection at 100 ms
WAV file of ideal reflection:
Response in AM modulation domain:
FFT frequency response:
Comment: When the reflection gap is 100 ms, speech intelligibility is affected since the signal in the modulation domain is having loss of modulation above modulation freq of 3 Hz, which is close to the typical modulation speed (syllabic rate) of human speech.
One ideal 0 dB reflection at 200 ms
WAV file of ideal reflection:
Response in AM modulation domain:
FFT frequency response:
Comment: When the reflection gap is 200 ms, modulation domain is severly rugged above modulation freq of 1 Hz.
Analysis of One Ideal Reflection in a Real Room
In a typical European size living room of 25 m2, the distance between a loudspeaker and the listening position could be for example 2 m. Also the reflection coefficient of the room boundaries could be for example 90 %. Normally the first order room reflections could occur in the time range between 2 ms and 20 ms. The level of the reflection depends also on the travel path difference compared to the direct sound. Here is presented the modulation domain analysis in some of such cases.
One ideal -3 dB reflection at 2 ms
WAV file of ideal reflection:
Response in AM modulation domain:
FFT frequency response:
Comment: In the modulation domain there is a dominant notch at 250 Hz. Even the FFT frequency response is very rugged above center freq of 3 kHz, the modulation domain is clean above 3 kHz up to the modulation freq of 100 Hz.
One ideal -6 dB reflection at 5 ms
WAV file of ideal reflection:
Response in AM modulation domain:
FFT frequency response:
Comment: Despite of heavy notches in FFT frequency response, the modulation domain is clean above center freq of 1 kHz up to the modulation freq of 50 Hz.
One ideal -10 dB reflection at 10 ms
WAV file of ideal reflection:
Response in AM modulation domain:
FFT frequency response:
Comment: The signal in the modulation domain is clean above center freq of 500 Hz up to the modulation freq of 20 Hz.
One ideal -14 dB reflection at 20 ms
WAV file of ideal reflection:
Response in AM modulation domain:
FFT frequency response:
Comment: When the gap between direct sound and the reflection is 20 ms, the modulation domain is practically clean in the whole center frequency band of 20 Hz - 20 kHz up to the modulation freq of 10 Hz. However above the modulation freq of 10 Hz the modulation domain is slightly affected.
Conclusions
FFT frequency response is a poor indicator of psychoacoustic relevance of comb filtering caused by a room reflection.
Modulation domain analysis gives indications when comb filtering is potentially perceived and when it may not affect the perception.
Some rule of thumbs can be made based on the modulation domain analysis here:
Reflection happening before 1 ms is relatively bad above center frequencies of 500 Hz.
Reflection between 1 ms and 5 ms affect mostly the midrange center frequencies between 100 Hz and 2 kHz.
If the reflection gap is 5 ms or longer, the center frequencies above 1 kHz will be clean in the modulation domain.
If the reflection gap is 10 ms or longer, the center frequencies above 500 Hz will be clean in the modulation domain.
Longer reflection gaps than 50 ms start to affect speech intelligibility.
In a typical European size living room of 25 m2 the gap between the direct sound and the first reflection is usually between 5 - 10 ms.
In the real room case, the amplitude of the reflections compared to the 0 dB has only a slight effect compared to the idealised results.
