# multi-band equalizer

Started by June 7, 2004
```For CD signals (sampling rate 44100Hz), Butterworth method is applied to
design 10 bandpass filters. Center frequencies of these 10 bands are: 31,
63, 125, 250, 500, 1K, 2K, 4K, 8K, 16KHz, respectively. As weighting values
(0.5, 0.5, 0.5, 0.8, 1.1, 1.3, 1.6, 1.6, 1.6, 1.6) are set to these
corresponding 10 badns, the "Full Treble" style of music is achieved. It
seems that the function of "Full Treble" is to emphasize the feeling of high
frequency components .

Question:
If the sampling rate of input signal is changed to 11025Hz, should I modify
the multi-band equalizer and the weighting values? Or just remove the last
band (16KHz)?

```
```"WYChen" <wychen@sounding.com.tw> wrote in message
news:2ikjs5Fo0pftU1@uni-berlin.de...
> For CD signals (sampling rate 44100Hz), Butterworth method is applied to
> design 10 bandpass filters. Center frequencies of these 10 bands are: 31,
> 63, 125, 250, 500, 1K, 2K, 4K, 8K, 16KHz, respectively. As weighting
values
> (0.5, 0.5, 0.5, 0.8, 1.1, 1.3, 1.6, 1.6, 1.6, 1.6) are set to these
> corresponding 10 badns, the "Full Treble" style of music is achieved. It
> seems that the function of "Full Treble" is to emphasize the feeling of
high
> frequency components .
>
> Question:
> If the sampling rate of input signal is changed to 11025Hz, should I
modify
> the multi-band equalizer and the weighting values? Or just remove the last
> band (16KHz)?

What difference would it make one way or the other?  Set sampling that low,
and you will have what sounds like a cheap AM radio with a ten band graphic
equalizer.  :)  -Dave

```
```"WYChen" <wychen@sounding.com.tw> wrote in message
news:2ikjs5Fo0pftU1@uni-berlin.de...
> For CD signals (sampling rate 44100Hz), Butterworth method is applied to
> design 10 bandpass filters. Center frequencies of these 10 bands are: 31,
> 63, 125, 250, 500, 1K, 2K, 4K, 8K, 16KHz, respectively. As weighting
values
> (0.5, 0.5, 0.5, 0.8, 1.1, 1.3, 1.6, 1.6, 1.6, 1.6) are set to these
> corresponding 10 badns, the "Full Treble" style of music is achieved. It
> seems that the function of "Full Treble" is to emphasize the feeling of
high
> frequency components .
>
> Question:
> If the sampling rate of input signal is changed to 11025Hz, should I
modify
> the multi-band equalizer and the weighting values? Or just remove the last
> band (16KHz)?

If you sample at 1/4 the sampling rate then all those frequencies you listed
will be lowered by a factor of 1/4.  That is, the frequencies of your new
filter would be 15.75 Hz, 31.25 Hz, 62.5 Hz, 125 Hz, ..., 4 kHz.  That means
your corresponding weights will be messed up as you'll be emphasizing
frequencies at 1/4 the frequency you were before.  So if you removed any
filters you should remove the "low" filters since at the new sampling rate
your "high" filter will be at 4 kHz.

Also as someone else pointed out sampling at 11.025 kHz will make the sound
pretty crappy.  The highest frequency you could have in your signal would be
5.5125 kHz.  For comparison a telephone gives you 3 kHz for your maximum
frequency so you're not doing too much better!

```
```In alt.music.mp3.hardware Brad Griffis <bradgriffis@hotmail.com> wrote:
>
> "WYChen" <wychen@sounding.com.tw> wrote in message
> news:2ikjs5Fo0pftU1@uni-berlin.de...
>> For CD signals (sampling rate 44100Hz), Butterworth method is applied to
>> design 10 bandpass filters. Center frequencies of these 10 bands are: 31,
>> 63, 125, 250, 500, 1K, 2K, 4K, 8K, 16KHz, respectively. As weighting
> values
>> (0.5, 0.5, 0.5, 0.8, 1.1, 1.3, 1.6, 1.6, 1.6, 1.6) are set to these
>> corresponding 10 badns, the "Full Treble" style of music is achieved. It
>> seems that the function of "Full Treble" is to emphasize the feeling of
> high
>> frequency components .
>>
>> Question:
>> If the sampling rate of input signal is changed to 11025Hz, should I
> modify
>> the multi-band equalizer and the weighting values? Or just remove the last
>> band (16KHz)?
>
> If you sample at 1/4 the sampling rate then all those frequencies you listed
> will be lowered by a factor of 1/4.  That is, the frequencies of your new

Err, no.
That'd be the case if you wanted a 9 band graphic equaliser, designed for
0-5512Hz, but you don't.
Leave the frequencies as they are, and just ignore the last two, will
give as similar effect as you can get.
You get the same output signal, minus any frequencies past around 5Khz.
```
```WYChen wrote:

> For CD signals (sampling rate 44100Hz), Butterworth method is
> applied to design 10 bandpass filters. Center frequencies of these
> 10 bands are: 31, 63, 125, 250, 500, 1K, 2K, 4K, 8K, 16KHz,
> respectively. As weighting values (0.5, 0.5, 0.5, 0.8, 1.1, 1.3,
> 1.6, 1.6, 1.6, 1.6) are set to these corresponding 10 badns, the
> "Full Treble" style of music is achieved. It seems that the
> function of "Full Treble" is to emphasize the feeling of high
> frequency components .
>
> Question:
> If the sampling rate of input signal is changed to 11025Hz, should
> I modify the multi-band equalizer and the weighting values? Or
> just remove the last band (16KHz)?

signal is band-limited to frequencies lower than Fs/2=5.5 kHz.

If this is not the case, you'll get aliasing errors.

If you use the same filter (i.e. the same coefficients) with 1/4 of
the original sample rate, you'll get a filter with 1/4 of the
original band frequency, which is
8, 16, 31, 62.5, 125, 250, 500, 1K, 2K, 4KHz
Since you don't need the lowest two filters, you could remove them
together with the weights from the higher end.
Should result in 8 bands as:
31, 62.5, 125, 250, 500, 1K, 2K, 4KHz
0.5, 0.5, 0.5, 0.8, 1.1, 1.3, 1.6, 1.6

My guess is, that the weights will not work as fine as before,
because the lack of high frequency content misleads the ear.
You'll probably do better with bigger values for the higher
frequencies. But that's guessing - I didn't try it...

Bernhard
```
```"Ian Stirling" <root@mauve.demon.co.uk> wrote in message
> >
> > "WYChen" <wychen@sounding.com.tw> wrote in message
> > news:2ikjs5Fo0pftU1@uni-berlin.de...
> >> For CD signals (sampling rate 44100Hz), Butterworth method is applied
to
> >> design 10 bandpass filters. Center frequencies of these 10 bands are:
31,
> >> 63, 125, 250, 500, 1K, 2K, 4K, 8K, 16KHz, respectively. As weighting
> > values
> >> (0.5, 0.5, 0.5, 0.8, 1.1, 1.3, 1.6, 1.6, 1.6, 1.6) are set to these
> >> corresponding 10 badns, the "Full Treble" style of music is achieved.
It
> >> seems that the function of "Full Treble" is to emphasize the feeling of
> > high
> >> frequency components .
> >>
> >> Question:
> >> If the sampling rate of input signal is changed to 11025Hz, should I
> > modify
> >> the multi-band equalizer and the weighting values? Or just remove the
last
> >> band (16KHz)?
> >
> > If you sample at 1/4 the sampling rate then all those frequencies you
listed
> > will be lowered by a factor of 1/4.  That is, the frequencies of your
new
>
> Err, no.
> That'd be the case if you wanted a 9 band graphic equaliser, designed for
> 0-5512Hz, but you don't.
> Leave the frequencies as they are, and just ignore the last two, will
> give as similar effect as you can get.
> You get the same output signal, minus any frequencies past around 5Khz.

Whoops - I left off the very first frequency band.  The new filters would be
at 7.75 Hz, 15.75 Hz, 31.25 Hz, 62.5 Hz, 125 Hz, ..., 4 kHz

Ian, you're being misleading.  In discrete-time filtering the cutoff
frequencies are always between 0 and pi radians.  This corresponds to 0 and
Fs/2 in the original analog signal.  If you change your sampling rate that
doesn't matter to your discrete signal.  Its cutoffs are still somewhere
between 0 and pi.  The thing that changes is the corresponding "analog"
frequency.  This is why changing your sampling rate by a factor of 4 changes
all the positions of the filters by the corresponding factor of 4.

```
```In alt.music.mp3.hardware Brad Griffis <bradgriffis@hotmail.com> wrote:
>
> "Ian Stirling" <root@mauve.demon.co.uk> wrote in message
>> >
>> > "WYChen" <wychen@sounding.com.tw> wrote in message
>> > news:2ikjs5Fo0pftU1@uni-berlin.de...
>> >> For CD signals (sampling rate 44100Hz), Butterworth method is applied
> to
>> >> design 10 bandpass filters. Center frequencies of these 10 bands are:
> 31,
>> >> 63, 125, 250, 500, 1K, 2K, 4K, 8K, 16KHz, respectively. As weighting
>> > values
>> >> (0.5, 0.5, 0.5, 0.8, 1.1, 1.3, 1.6, 1.6, 1.6, 1.6) are set to these
>> >> corresponding 10 badns, the "Full Treble" style of music is achieved.
> It
>> >> seems that the function of "Full Treble" is to emphasize the feeling of
>> > high
>> >> frequency components .
>> >>
>> >> Question:
>> >> If the sampling rate of input signal is changed to 11025Hz, should I
>> > modify
>> >> the multi-band equalizer and the weighting values? Or just remove the
> last
>> >> band (16KHz)?
>> >
>> > If you sample at 1/4 the sampling rate then all those frequencies you
> listed
>> > will be lowered by a factor of 1/4.  That is, the frequencies of your
> new
>>
>> Err, no.
>> That'd be the case if you wanted a 9 band graphic equaliser, designed for
>> 0-5512Hz, but you don't.
>> Leave the frequencies as they are, and just ignore the last two, will
>> give as similar effect as you can get.
>> You get the same output signal, minus any frequencies past around 5Khz.
>
> Whoops - I left off the very first frequency band.  The new filters would be
> at 7.75 Hz, 15.75 Hz, 31.25 Hz, 62.5 Hz, 125 Hz, ..., 4 kHz
>
> Ian, you're being misleading.  In discrete-time filtering the cutoff
> frequencies are always between 0 and pi radians.  This corresponds to 0 and
> Fs/2 in the original analog signal.  If you change your sampling rate that
> doesn't matter to your discrete signal.  Its cutoffs are still somewhere
> between 0 and pi.  The thing that changes is the corresponding "analog"
> frequency.  This is why changing your sampling rate by a factor of 4 changes
> all the positions of the filters by the corresponding factor of 4.

Well, yes of course if you leave the filter unchanged.
But it's not going to obtain similar audio effects.
To do that, you need to leave the frequency bands alone, and modify
the filter so that this happens.

```