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Topic: new article about noise shaping (Read 14824 times) previous topic - next topic
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new article about noise shaping

Hi!

I've added a new article about noise shaping. I guess it doesn't fully qualify as a proper encyclopdia article due to the occasional personal/tutorial tone and lack of references but it's a start.

Noise shaping

Cheers!
SG

new article about noise shaping

Reply #1 –
Many, many thanks Sebastian!
lossyWAV -q X -a 4 -s h -A --feedback 2 --limit 15848 --scale 0.5 | FLAC -5 -e -p -b 512 -P=4096 -S- (having set foobar to output 24-bit PCM; scaling by 0.5 gives the ANS headroom to work)

new article about noise shaping

Reply #2 –
Darn!
I just wanted to fix a typo and pressed reply instead of edit.
Please ignore this.

new article about noise shaping

Reply #3 –
Is it „encyclopdia” you wanted to fix?

For me, typos are not relevant unless they completely change the meaning of a word. Then they are dangerous

Your wiki article is of very good quality!
If age or weaknes doe prohibyte bloudletting you must use boxing

new article about noise shaping

Reply #4 –
Many thanks indeed. Fascinating stuff!

Cheers, Slipstreem. 

new article about noise shaping

Reply #5 –
Thank you Sebastian!

The "Decoupling filtering and quantization" was particularly useful and clear.


Please mention somewhere appropriate that SACD is not dithered - or at least, not dither correctly, since this would leave no room for the signal! Hence SACD falls under the criticism you make within the first sentence of the "Limits & filter design restrictions" section. Its placement above implies that it does not have this problem.

Cheers,
David.

new article about noise shaping

Reply #6 –
Thank you for your kind responses.

As for the SACD dithering issue I think it's on the verge to being off-topic but I added it nonetheless because I covered "undithered quantization" and the SACD example as well.

Cheers!
SG

new article about noise shaping

Reply #7 –
Thx Sebastian for great article.

At the moment I'm adding dither routine based on your algoritm to mplayers ogg and mp3 decoder.
I implemented your article in integer only routine, which takes about 1% CPU on P3@1GHz for stereo 44.1kHz.
Haven't tested with music yet, but on a low amplitude sine generated in C, algoritm works like a charm!

#include "tgmath.h"
#include "stdlib.h"


int NoiseShapedDither(in,ch)
int ch;
long in;
{
    /* 32 bit integer in
    relation 32bit input sample <==> 16 bit audio output:  aud32=aud16<<11;
    This gives 11 bits resolution for dither, 5 bits peak headroom    */

    #define MAXCH 8 /* multi channel audio 8 ch should suffice.
                              CHANGING MAXCH breaks array initializations!!  */
    static unsigned long rnd=256;  /* 32bits fibonacci shift reg PRNG. Init at any value but 0....*/
    long wanted,quantized;
    static long h_out [5] [MAXCH] =
    { {0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0} };
    static long last_error [4] [MAXCH] =
    { {0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0} };
   
   
    h_out[4][ch]=h_out [3][ch];
    h_out[3][ch]=h_out [2][ch];
    h_out[2][ch]=h_out [1][ch];
    h_out[1][ch]=h_out [0][ch];
    /* based on 44.1k LAME ath IIR formula for hearing treshold */
    h_out[0][ch]= (-17346*h_out[1][ch] -1108*h_out[2][ch] + 9919*h_out[3][ch] + 4486*h_out[4][ch]
    +36145*last_error[0][ch] -7710*last_error[1][ch] -4152*last_error[2][ch] -10181*last_error[3][ch]) ;

    h_out[0][ch]= h_out[0][ch] >> 14 ; /* compensate for scaling in previous line */

    wanted=in-h_out[0][ch];

    /* GENERATE 22 new random bits. Generator based on 32 bit  Fibonacci shift register. */
    rnd= (rnd<<22) + (  0x003FFFFF & ( (rnd>>9) ^ (rnd>>7) ^ (rnd>>6) ^ rnd )  ); 
    /* from 32bits, use 2 11 bits parts as random numbers (=triangularPDF), offset and quantize ......*/
    quantized=0xFFFFF800 & ( wanted  - 1024 +  ( (rnd>>11)&0x000007FF ) + (rnd&0x000007FF)  );

    last_error[3][ch]=last_error[2][ch];
    last_error[2][ch]=last_error[1][ch];
    last_error[1][ch]=last_error[0][ch];
    last_error[0][ch]=quantized-wanted;
    quantized=quantized>>11;
    if ( quantized > 32767)
   return(32767);
    else if ( quantized < -32768 )
   return(-32768);
    else return(quantized);
}

new article about noise shaping

Reply #8 –
The noise shaping part looks good at the first glance.

If you like you could get rid of the last_error arrays when swithing from Direct Form I to Direct Form II for H(z). But this would also require to quantize twice to get the filter's output. The danger of getting overflows in DFII is also a bit higher when working with integers.

Your quantization part seems to introduce a bias towards negative infinity which makes the error samples unnecessarily large. I don't think you need the "-1024" here because the binarry "AND" with 0xFFFFF800 already leads to an average reduction of 1024.

inline int zero11LSBs(int x) { return (x+0x400) & (-0x800); } // correct rounding

So, the +1024 for the correct rounding and your -1024 to offset the dither cancel each other out.


Cheers,
SG

new article about noise shaping

Reply #9 –
The line having the -1024 in it needs some comment:
Basically, it performs this function (in floating point):
floor(input+0.5+TPDF)
where tpdf is trianguler PDF dither in range -1....+1
The 0.5 is needed to compensate for offset in floor function

However, my dither is triangular based in range 0....+2 so to compensate, I have to subtract 1, leading to
floor(input-0.5+TPDFoffset1)

I'll have to look into DirectFormII later on...

new article about noise shaping

Reply #10 –
Quote from: DualIP on
However, my dither is triangular based in range 0....+2 so to compensate, I have to subtract 1, leading to
floor(input-0.5+TPDFoffset1)

You're right. I was mistakenly thinking about a rectangular dither with a range of 0...+1

Cheers,
SG

new article about noise shaping

Reply #11 –
Most textbooks mention 2LSB peak-peak TPD dither as dither source to fully get rid of quantization errors.
Previous code was based on this 2 LSB peak-peak value:
quantized=0xFFFFF800 & ( wanted - 1024 + ( (rnd>>11)&0x000007FF ) + (rnd&0x000007FF) );


However, with the noise shaping loop added, it seems you can get away with a lower value:
I just tried by halving this TPD white noise to 1 LSB peak-peak, and don't see any distorsion showing up on the spectrum using a two-tone test signal, but overall noise floor is lowered a couple of dBs!
quantized=0xFFFFF800 & ( wanted  +  ( (rnd>>11)&0x000003FF ) + (rnd&0x000003FF)    );

For this noise shaping, what's the optimal internal dither source? There's nothing about it in the topic-start wiki.

new article about noise shaping

Reply #12 –
Quote from: DualIP on
However, with the noise shaping loop added, it seems you can get away with a lower value:
[...]
For this noise shaping, what's the optimal internal dither source? There's nothing about it in the topic-start wiki.

From what I know you still need 2 LSBs peak-to-peak to be able to guarantee that there won't be nasty distortions. My personal favorite dither method is a morphed PDF between rectangular and triangular:
Code: [Select]
dither_k = (random()-0.5) + s * (random()-0.5);

with random() returning random numbers between 0 and 1 (rectangular probability density) and 's' being a scalar between 0 (=> rectangular) and 1 (=> triangular). This way it's always at least as good as a rectangular dither (important feature!). I also noticed that when noise shaping is in use it's okay to use lower values for 's' like 0.6 without getting noise modulation. The noise floor wil be 1 dB below of what you'd expect from a full triangular dither. However, I know of no proof for it to work all the time. It just does in the cases I checked.

Cheers,
SG

new article about noise shaping

Reply #13 –
Quote from: SebastianG on
From what I know you still need 2 LSBs peak-to-peak to be able to guarantee that there won't be nasty distortions. My personal favorite dither method is a morphed PDF between rectangular and triangular:
Code: [Select]
dither_k = (random()-0.5) + s * (random()-0.5);

with random() returning random numbers between 0 and 1 (rectangular probability density) and 's' being a scalar between 0 (=> rectangular) and 1 (=> triangular). This way it's always at least as good as a rectangular dither (important feature!). I also noticed that when noise shaping is in use it's okay to use lower values for 's' like 0.6 without getting noise modulation. The noise floor wil be 1 dB below of what you'd expect from a full triangular dither. However, I know of no proof for it to work all the time. It just does in the cases I checked.

Cheers,
SG
Interesting, very interesting....
lossyWAV -q X -a 4 -s h -A --feedback 2 --limit 15848 --scale 0.5 | FLAC -5 -e -p -b 512 -P=4096 -S- (having set foobar to output 24-bit PCM; scaling by 0.5 gives the ANS headroom to work)

new article about noise shaping

Reply #14 –
Well seeing that I am writer and not much of a Mathmatician I did manage to add a few sources in your article in particular the one on SACD dithering. Cheers.  Excellent article btw. I think there are a few other ones that need to be rewritten in the Signal Processing section and we will be in good shape.
budding I.T professional

new article about noise shaping

Reply #15 –
Quote from: DualIP on
Most textbooks mention 2LSB peak-peak TPD dither as dither source to fully get rid of quantization errors.
However, with the noise shaping loop added, it seems you can get away with a lower value:
I just tried by halving this TPD white noise to 1 LSB peak-peak, and don't see any distorsion showing up on the spectrum using a two-tone test signal, but overall noise floor is lowered a couple of dBs!


Here's an example of this causing a problem with a single test tone, though I suspect that away from test tones, you'd get away with it.

  -bandpass