Quote:
Originally Posted by JaZZ /img/forum/go_quote.gif
A resonance doesn't just affect the narrow band with maximum intensity, but extends quite largely to both sides. A simple, descriptive example may show you how impossible your scenario is: Let's take some 11-kHz tone bursts, let them pass a sharp 22-kHz low-pass filter. That's one octave below the filter resonance. The 11-kHz tone burst will not stop immediately, unlike it would with full bandwidth, but show significant delay of decay, with a few additional (11-kHz!) cycles before complete silence. That's in the nature of low-pass filtering: Immediate signal stop would call for full bandwidth. Now tell me that's not transient corruption and time-smearing!
|
This is a very good idea, and I have done it.
But I had to find a filter sharp enough to produce significant amounts of ringing. The resampling algorithms of SoundForge did not. Neither its parametric equalizer.
But Foobar2000 0.8.3's graphic equalizer has very sharp transitions between its frequency bands. Setting the 20 kHz slider to the minimum (-20 dB) on a white noise gives this frequency response (65536-samples FFT analysis) :
Complete attenuation is reached only 30 Hz above the last unaffected frequency !
Taking a 96 kHz wav with 11 kHz bursts, and equalizing it this way produces ringing, because of the sharpness of the transition in the frequency domain :
Left, the original file, with sharp transition between silence and sound. Right, the lowpassed file. We could expect that it is the same, since everything below 16730 Hz is unaffected, and the file only contains bursts of 11 kHz sines.
But a burst of 11 kHz sine is not a real 11 kHz sine. The start point and the stop point of the sine are places where the frequency decomposition shows a lot of other frequencies whose effect is to allow the transition between silence and sound.
These frequencies are affected by the lowpass, and the transition looks different. There is
ringing, visible in the right picture.
If we zoom out horizontally, so as to see the whole bursts, and zoom in vertically, so as to see the smallest amount of ringing, we can see that the ringing extends so far that there is no more silence at all between the bursts. The post-ringing of all bursts joins the pre-ringing of the next :
However, I can't hear the difference. I can hear that there are a lot of other noises than just 11 kHz bleeps, but they sound the same in both versions. They are the clicks that start and stop each piece of sine.
Let's look more closely at a given pre-ringing :
Here, we can see something very interesting : the oscillations of the ringing seem closer spaced than the ones of the 11 kHz burst !
Unfortunately, SoundForge is not a practical software to look at this. The zoom is at maximum here. Analyzing frequencies on such short bits of wave is not accurate, but we can ask for the statistics about zero-crossings. First in the burst :
Then in the ringing :
The software shows that the ringing is not an extension of the 11 kHz sine at all, but rather a parasite 16 kHz resonance added.
The spectrogram view shows it much better. Here is a spectrogram showing three bursts in the original file (256 samples FFT) :
The bursts of 11 kHz sine are represented by the three horizontal red lines. the vertical green and blue bars show the sudden burst of all kind of frequencies that account for the brutal "clicks" at the sharp starting and ending of each sine.
Now, here is the lowpassed version :
The vertical bars still extend to the top frequencies. Remember that the filter applied is just an equalization of -20 dB, and that it doesn't delete completely high frequencies.
And the ringing is perfectly visible as a continuous blue line around 16 kHz, which is the transition frequency of the filter (remember the white noise spectrum above).
We can note two important results :
-The ringing is completely restricted to the transition frequency of the filter. It consists in a pure sine wave.
-The sharpness of the frequencies below (and above) the ringing is completely preserved. The verical bars are still there, and the horizontal red lines are not extended the slightest amount, compared to the large duration of the ringing.
With an antialias filter designed to cut frequencies above 20 kHz, the ringing is also completely restricted to this frequency, and the sharpness of the musical content is completely preserved, in spite of visible oscillations that extends from it in the waveform view.
We can also see a curious thing that the waveform did not show : the ringing extends not only outside, but also
inside the 11 kHz sinewaves.
I'd like to post another picture by GBO. He did the same experiment, but with a musical sample. It is the recording of a triangle, made at 96 kHz. He applied a brickwall filter at 22 kHz.
Here is an analysis of the result :
http://3141592.pio2001.online.fr/pic...nglecomp2D.gif
Up, the original, down, the filtered version.
The pre-ringing is clealy visible, does not extends below 20 kHz, and the content below 20 kHz has no time smearing. There is just some noise caused by the processing. Unfortunately, there is no scale on the diagram for us to show the amplitude of this noise.
There was noise also in my stecrograms, but I purposely set the color scaling just above.
I've not illustrated it, but I read that ringing is only triggered if there is some content at the filter frequency in the original signal. That's why he used the recording of a triangle. He needed some 22 kHz harmonics in order to cause ringing.
In our 11 kHz sine, it's the clicks (the vertical bars) that feature the frequency content that triggers the ringing. If our file had already been lowpassed below 16 kHz, the application of the 16 kHz brickwall would have caused no ringing at all (and the absence of time smearing below this frequency would have been obvious).
