hi, i'm designing a lowpass IIR Butterworth filter (direct form II transposed) in Matlab using fdatool, and there are several different ways of specifying the frequency 1. normalized [0,1] 2. Hz 3. kHz 4. MHz for 2-4, it makes sense because for those selections, i can enter in a Fs (samplerate) and a Fc (cutoff) but for the normalized [0,1] i can only enter in a wc (cutoff) ... how is it possible to design a filter then that seems to be samplerate independent ... ?? i know there are classes of filters that are sr independent but didn't think these were ...i know there is something fundamental i'm overlooking ... thanks for any insights into this regards, sam
Filter Design Question WRT samplerate
Started by ●June 11, 2004
Reply by ●June 11, 20042004-06-11
sambaed wrote:> hi, > i'm designing a lowpass IIR Butterworth filter (direct form II > transposed) in Matlab using fdatool, and there are several different > ways of specifying the frequency > > 1. normalized [0,1] > 2. Hz > 3. kHz > 4. MHz > > for 2-4, it makes sense because for those selections, i can enter in a > Fs (samplerate) and a Fc (cutoff) but for the normalized [0,1] i can > only enter in a wc (cutoff) ... > > how is it possible to design a filter then that seems to be samplerate > independent ... ?? > > i know there are classes of filters that are sr independent but didn't > think these were ...i know there is something fundamental i'm > overlooking ... > > thanks for any insights into this > > regards, > samYour last three cases differ only in scale. Simplified, there are only two cases, normalized and not normalized. When normalized, the sampling frequency is implicit. When not, it's one of the inputs you supply. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●June 11, 20042004-06-11
> > Your last three cases differ only in scale. Simplified, there are only > two cases, normalized and not normalized. When normalized, the sampling > frequency is implicit. When not, it's one of the inputs you supply.Thanks Jerry, agreed there are only two cases ... but where can i go to get some more insight on the implicitness of the sampling frequency in the normalized case? i ask because i'm using this as a final "cleanup filter" after resampling and sr is important. so i want to be certain i'm on the right track ... thanks, sam
Reply by ●June 11, 20042004-06-11
"sammyd" <sammyd@ratpack.com> wrote in message news:6Okyc.52101$8k4.1165523@news20.bellglobal.com...> hi, > i'm designing a lowpass IIR Butterworth filter (direct form II > transposed) in Matlab using fdatool, and there are several different > ways of specifying the frequency > > 1. normalized [0,1] > 2. Hz > 3. kHz > 4. MHz > > for 2-4, it makes sense because for those selections, i can enter in a > Fs (samplerate) and a Fc (cutoff) but for the normalized [0,1] i can > only enter in a wc (cutoff) ... > > how is it possible to design a filter then that seems to be samplerate > independent ... ??Sam, "Normalized" means that the sample rate is 1.0 by definition. This means that all frequencies are referenced or "normalized" to the sampling frequency. Fs > Fs/Fs = 1 Fc > Fc/Fs = something less than 0.5.... etc. Digital filters are sample rate independent only to the extent that we allow the Fc and other frequencies to be represented as a *fraction of* the sampling frequency and not as fixed numbers expressed in Hz. For example, if one were to design a lowpass filter with cutoff at 2kHz and with sample rate of 10kHz then this same filter could be said to have a cutoff frequency of 0.2Fs, right? Then, if you change the sample rate to 16kHz, the cutoff frequency will be 3.2kHz. You can think of it this way: the filter doesn't care what the sample rate is unless the filter is constructed of delay boxes of fixed delay. These delays are the same as the sample interval. But, you're doing it in software and don't have physical delay boxes in your filter implementation. So, the filter only operates on sequences of samples and treats them accordingly. The assumed spacing between the samples doesn't change the filter's internal operation. However, the spacing between the samples does change *your* view of them regarding frequencies. I hope this helps. Fred
Reply by ●June 11, 20042004-06-11
"sammyd" <sammyd@ratpack.com> wrote in message news:6Okyc.52101$8k4.1165523@news20.bellglobal.com...> hi, > i'm designing a lowpass IIR Butterworth filter (direct form II > transposed) in Matlab using fdatool, and there are several different > ways of specifying the frequency > > 1. normalized [0,1] > 2. Hz > 3. kHz > 4. MHz > > for 2-4, it makes sense because for those selections, i can enter in a > Fs (samplerate) and a Fc (cutoff) but for the normalized [0,1] i can > only enter in a wc (cutoff) ... > > how is it possible to design a filter then that seems to be samplerate > independent ... ??Firstly, digital filters are always referenced to the sample rate. So saying that you designed a digital filter with cut-off of 5kHz doesn't make any sense unless you specify the sample rate. So you might as well combine the 2 and specify your cut-off as a ratio of fc/fs. So for example, if you designed (using fdatool), a filter with fc of 5kHz and fs of 20kHz...and you used this exact same filter in another design where the fs is now 40kHz, then your cut-off moves to 10kHz. So when you choose 'normalized', this would be a filter design with a fc at 0.25. You can use this filter at any sample rate and your cutoff freq will be 1/4 of the sample rate. Cheers Bhaskar> i know there are classes of filters that are sr independent but didn't > think these were ...i know there is something fundamental i'm > overlooking ... > > thanks for any insights into this > > regards, > sam >
Reply by ●June 11, 20042004-06-11
sammyd wrote:>> >> Your last three cases differ only in scale. Simplified, there are only >> two cases, normalized and not normalized. When normalized, the sampling >> frequency is implicit. When not, it's one of the inputs you supply. > > > Thanks Jerry, agreed there are only two cases ... but where can i go to > get some more insight on the implicitness of the sampling frequency in > the normalized case? > > i ask because i'm using this as a final "cleanup filter" after > resampling and sr is important. so i want to be certain i'm on the > right track ... > > thanks, > samI don't know Matlab. (There's a Matlab newsgroup you can ask.) If you know how to use the version with explicit sample rate, you don't really have a problem. Most normalized filter programs normalize by dividing by the sample rate, do that becomes 1. Some divide by half the sample rate, to the sample rate is 2 and the highest allowed frequency is 1-. That's unusual. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
