Hi,
Try this - may be helpful.
https://www.dsprelated.com/freebooks/filters/
Regards,
Shadders.
Likewise, I have a link for your enjoyment - your best friends at Xivero make a very nice apodization software and appear to be fully backing the overall "elimination of the pre-ringing" approach in the entire recording/playback chain.
https://www.xivero.com/xipodizer/
XIPODIZER
Remove pre-ringing caused by steep linear phase antialiasing filters
From their website:
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Standard resolution CD quality records with a sample rate of 44.1kHz ask for steep low-pass filters at around 22kHz to avoid any aliasing during the analog to digital conversion process. The same principle applies during playback, where the digital to analog converter must use a low-pass filter to reconstruct the analog signal.
Filters used to suppress aliasing and to reconstruct the analog signal are usually “linear phase”, which implies that they create pre-ringing and post-ringing (pls. see Figure 1) by limiting the bandwidth of the input signal.
The ringing amplitude is significant because the spectral energy of music above 20kHz is still quite high.
There is quite a debate in the Hi-Fi community that the unnatural and none-causal impulse response of a linear-phase filter, plagued by pre-ringing, causes artifacts that sound inferior.
In contrast to High Resolution Audio we do not have the possibility to apply the filtering outside of the audio spectrum but we can use algorithms like “Apodization” that are quite efficiently used within different fields of optics like microscopy and astronomy.
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And, more SHOCKINGLY:
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APODIZATION IN THE WHOLE RECORDING AND PLAYBACK CHAIN
Figure 5 represents the full recording and playback chain, including the analog to digital and digital to analog processing but
no apodization.
The resulting output signal (pls. see figure 6) exhibits strong pre- and post-ringing.
In figure 7 the recorded signal is apodized by applying the
XiPodizer to reduce the effect of pre-ringing.
The
XiPodizer is very effective in suppressing the pre-ringing (pls. see figure 8) by compromising a bit of the available audio bandwidth.
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Is this FRAUD? Should I report them? I think I am being CONNED!