Reply by Nigel Redmon August 1, 20042004-08-01
In <fb78d2e7.0407090927.50acf218@posting.google.com> Luis Fernando wrote:
> 1) why is it necessary to run a filter when I upsample? I won't be > generating any high frequency doing this, will I?
Maybe this will help. You're probably aware that a digital signal has aliased images that mirror and repeat--that is the reason we need to apply a low pass filter ("anti-imaging filter", "reconstruction filter", etc.) when we convert to analog. You've probably seen frequency graphs that look something like this (use a fixed-width font): 0 a b c d | | | | | ______ ___________ __________ ... \ / \ / \ / \ / It goes in the negative direction too, but here I'm showing the positive half, starting at 0 Hz. Your nice audio content is in the band of 0 though a, and your sample rate is b. (If you converted this signal to analog, you would follow the D/A with a low pass filter with a cutoff at a.) If you double the sample rate without doing anything else, you've simply moved the sample rate to d, increasing the available working bandwidth from 0-a to 0-b. So you can see that you have now "revealed" the aliasing in the area from a to b. You need to low pass filter with a cutoff at a to get rid of that aliased image before applying your non- linear processing. So the answer is that while you haven't generated any new high frequencies, you've widened the audio band so that frequencies that were above the audio band before are now in the new audio band.
Reply by Jon Harris July 12, 20042004-07-12
"Jerry Avins" <jya@ieee.org> wrote in message
news:40ef446b$0$1178$61fed72c@news.rcn.com...
> Jon Harris wrote: > > I'm arguing here for a unified filtering-centric treatment of interpolation. > > I've found this to be the most useful way of analyzing and comparing various > > interpolation methods. > > You certainly don't need to argue that with me: I agree. We're trying to > give the OP a feel for what he's doing. (I'm sure he knows by now that > filtering of a sort is in fact needed.) As a matter of practical > implementation, the way it's done is the whole point.
Glad to hear you agree with this. From some of your past comments, it sounded to me like you were considering interpolation and filtering to be different animals. To wit: "One way is do use a good interpolation formula. A better and often simpler way is to insert zeros and then to filter out the new artifacts." and "True enough, but the results of linear interpolation and of low-pass filtering are not the same. Linear interpolation can generate in-band distortion products that defy subsequent filtering." IMHO, realizing that interpolation formulas and zero-stuffing/filtering are just different implementations of LP filtering is an important step in understanding the big picture of sample rate converting.
Reply by Jerry Avins July 9, 20042004-07-09
Jon Harris wrote:


> I'm arguing here for a unified filtering-centric treatment of interpolation. > I've found this to be the most useful way of analyzing and comparing various > interpolation methods.
You certainly don't need to argue that with me: I agree. We're trying to give the OP a feel for what he's doing. (I'm sure he knows by now that filtering of a sort is in fact needed.) As a matter of practical implementation, the way it's done is the whole point. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
Reply by Jon Harris July 9, 20042004-07-09
"Jerry Avins" <jya@ieee.org> wrote in message
news:40ef164b$0$1169$61fed72c@news.rcn.com...
> Jon Harris wrote: > > "Jerry Avins" <jya@ieee.org> wrote in message > > news:40eee85d$0$1169$61fed72c@news.rcn.com... > > > >>One way is do use a good interpolation formula. A > >>better and often simpler way is to insert zeros and then to filter out > >>the new artifacts. > > > > > > The two methods are different ways of conceptualizing, but mathematically
are
> > the same process (i.e. your interpolation formula can be analyzed as a
filter*,
> > and your LP filter can be viewed as an interpolation formula). > > > > *assuming a linear interpolation formula > > True enough, but the results of linear interpolation and of low-pass > filtering are not the same. Linear interpolation can generate in-band > distortion products that defy subsequent filtering. About "my" > interpolation formula, I cited none in particular. The most appropriate > method has to do with the system's specs and the resources available to > meet them.
My point here is that linear interpolation _is_ low pass filtering. It's not very good LP filtering, but it is indeed LP filtering. In fact, you can design a FIR LP filter that does give you the _exact_ same result as a LP filter (it has a triangular impulse response). Or conversely, you can find the impulse of any linear interpolation method and implement it as a filter. You can also measure the response of a linear interpolator and observe the LP characteristic (complete with some really nasty sidelobes, the main source of the aliasing you are speaking of). I'm arguing here for a unified filtering-centric treatment of interpolation. I've found this to be the most useful way of analyzing and comparing various interpolation methods.
Reply by Jerry Avins July 9, 20042004-07-09
Jon Harris wrote:
> "Jerry Avins" <jya@ieee.org> wrote in message > news:40eee85d$0$1169$61fed72c@news.rcn.com... > >>Luis Fernando wrote: >> >> >>>thanks! that's a very nice text, but I still have some doubts: >>> >>>1) why is it necessary to run a filter when I upsample? I won't be >>>generating any high frequency doing this, will I? >> >>One way is do use a good interpolation formula. A >>better and often simpler way is to insert zeros and then to filter out >>the new artifacts. > > > The two methods are different ways of conceptualizing, but mathematically are > the same process (i.e. your interpolation formula can be analyzed as a filter*, > and your LP filter can be viewed as an interpolation formula). > > *assuming a linear interpolation formula
True enough, but the results of linear interpolation and of low-pass filtering are not the same. Linear interpolation can generate in-band distortion products that defy subsequent filtering. About "my" interpolation formula, I cited none in particular. The most appropriate method has to do with the system's specs and the resources available to meet them. Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
Reply by Jon Harris July 9, 20042004-07-09
"Jerry Avins" <jya@ieee.org> wrote in message
news:40eee85d$0$1169$61fed72c@news.rcn.com...
> Luis Fernando wrote: > > > thanks! that's a very nice text, but I still have some doubts: > > > > 1) why is it necessary to run a filter when I upsample? I won't be > > generating any high frequency doing this, will I? > > One way is do use a good interpolation formula. A > better and often simpler way is to insert zeros and then to filter out > the new artifacts.
The two methods are different ways of conceptualizing, but mathematically are the same process (i.e. your interpolation formula can be analyzed as a filter*, and your LP filter can be viewed as an interpolation formula). *assuming a linear interpolation formula
Reply by Jerry Avins July 9, 20042004-07-09
Luis Fernando wrote:

> thanks! that's a very nice text, but I still have some doubts: > > 1) why is it necessary to run a filter when I upsample? I won't be > generating any high frequency doing this, will I?
You will. When you insert extra samples, the new sequence rill represent a waveform with new frequencies unless you have a way to know what those samples would have been if they had been taken from the original source. (Whew! Long sentence sorry!) You don't have a way to know that, but you can calculate it. One way is do use a good interpolation formula. A better and often simpler way is to insert zeros and then to filter out the new artifacts. ... Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;
Reply by Luis Fernando July 9, 20042004-07-09
thanks! that's a very nice text, but I still have some doubts:

1) why is it necessary to run a filter when I upsample? I won't be
generating any high frequency doing this, will I?

2)  I tried to implement my distortion like:
input -> interpolate -> "distortion" (cut amplitude) -> lowpass filter
-> decimate -> output

i'm using this simple "distortion" algorithm:

---------
x = input / DISTORTION_LEVEL;
	
if (x < -1) y = -2/3;
else if (x > 1) y = 2/3;
else y = x - (x*x*x)/3;

y *= NIVEL_DISTORCAO;

output = y;
---------

i'm working on 48000 Hz sample ratio and interpolating four "0", so it
would become 240000 Hz

but, if I understand correct:
"when I receive an input, for example '10000', I act like I had
received 5 inputs: '10000', '0', '0', '0', '0', then I apply the
distortion to them, run the lowpass filter, and return just the first
one"

the problem is that I end up in the same thing as if I hadn't
upsampled/decimated:

let's again suppose I received '10000', and suppose my "limit"
amplitude (DISTORTION_LEVEL) is '5000'

what will happen?

input: 10000
interpolate: 10000 0 0 0 0
apply distortion: 5000 0 0 0 0
apply lowpass filter: 5000 0 0 0 0
decimate: 5000
output: 5000

it's the same output as:
input: 10000
apply distortion: 5000
output: 5000

:(

the problem is probably on "apply lowpass filter"

is it right to interpolate putting "0" instead putting average values?
won't the filter get "crazy" (instead receiving a sinusoid, it's
receiving a weird thing that goes up and down every time)?

BTW, i'm using a 5 bi-quad IIR filter with sample ratio of 240000 Hz.

thanks in advance,
Luis Fernando
Reply by Stephan M. Bernsee July 9, 20042004-07-09
And here: http://www.musicdsp.com

--smb

Erik de Castro Lopo <nospam@mega-nerd.com> wrote in message news:<40EDB05C.486C4C9C@mega-nerd.com>...
> Luis Fernando wrote: > > > > Hello > > > > I'm trying to implement a distortion effect (following > > http://music.calarts.edu/%7Eglmrboy/musicdsp/FAQs/guitar_distortion_FAQ.html > > ) with 48000 Hz sampling and minimum "useful" frequency = 20 Hz. My > > problem is with aliasing. > > This issue has been rasied here hundreds of times. See for instance > this: > > http://groups.google.com/groups?&selm=401AF523.A2C504A8%40mega-nerd.com&rnum=1 > > Erik
Reply by Erik de Castro Lopo July 8, 20042004-07-08
Luis Fernando wrote:
> > Hello > > I'm trying to implement a distortion effect (following > http://music.calarts.edu/%7Eglmrboy/musicdsp/FAQs/guitar_distortion_FAQ.html > ) with 48000 Hz sampling and minimum "useful" frequency = 20 Hz. My > problem is with aliasing.
This issue has been rasied here hundreds of times. See for instance this: http://groups.google.com/groups?&selm=401AF523.A2C504A8%40mega-nerd.com&rnum=1 Erik -- +-----------------------------------------------------------+ Erik de Castro Lopo nospam@mega-nerd.com (Yes it's valid) +-----------------------------------------------------------+ "I want to make sure (a user) can't get through ... an online experience without hitting a Microsoft ad." - Microsoft CEO, Steve Ballmer on the Microsoft search engine.