::
::
:: > > I think this should be a seperate utility outside of lame? Most people
:: > > encode from CDs, which usually are already correctly filtered for stuff
:: > > below 20 Hz.
:: > >
:: > For pop music this is (mostly) true. I will test several CDs. Next week.
:: > The psycho part I would nevertheless filter with a 8rd order Chebychew
:: > high pass @80 Hz. Remember active controlled boxes by B&O. But also
:: > normal vented tubes have a relatively sharp cut off at low frequencies,
:: > so don't rely on masking.
:: >
::
:: The windowed FFT used for the psycho acoustics surely has better
:: frequency responce than an 8th order Chebychev filter,
:: so there will negligable leakage of this 80Hz tone into
:: other frequencies. If you think this is a problem, I would
:: try some experiemnts by removing (from the psycho acoustics)
:: the coefficients up to 80hz.
::
1. Chebychev filters (LTI system) have no leakage at all
2. Chebychev highpass filters (like all IIR filters) have a worse
frequency resolution for high frequencies ( -> oo) and a extremly
good for low frequencies ( -> 0).
3. You can program a FFT like filterbank with simple 2nd order
lowpass filters. But this filterbank has problems with
detecting high frequencies if there are high level low
frequency signals are present.
Calculate yourself:
#include <stdio.h>
#include <math.h>
#define PASS_BAND_RIPPLE 0.1 // dB
#define ORDER 8
#define STOP_BAND 84.22 // Hz, note damping is not
// -3 dB, but -PASS_BAND_RIPPLE dB
double cheychev_polynom ( double x, int n )
{
// NOTE: These are really polynoms, but the trigonometric
// represenation is much easier to remember
if ( x <= 1 )
return cos ( n*acos (x) );
else
return cosh ( n*acosh (x) ); // would be the same formula for complex numbers
}
int step ( int i )
{
if ( i < 200 ) return 1;
if ( i < 500 ) return 2;
if ( i < 1000 ) return 10;
if ( i < 2000 ) return 50;
if ( i < 5000 ) return 200;
if ( i < 10000 ) return 1000;
if ( i < 25000 ) return 5000;
return i;
}
int main (void)
{
int i;
double poly;
double damp;
double ripple = pow ( 10., 0.1*PASS_BAND_RIPPLE ) - 1.;
for ( i = 1; i <= 20000; i += step (i) ) {
poly = cheychev_polynom ( (double) STOP_BAND / i, ORDER );
damp = 10. * log10 ( 1. + ripple * poly * poly )
+ ( ORDER & 1 ? 0. : -PASS_BAND_RIPPLE );
printf ( "%5u Hz%9.2f dB\n", i, -damp );
}
return 0;
}
--
Mit freundlichen Grüßen
Frank Klemm
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