Hi Does anyone have some guidelines on how to implement a 4'th order low-pass Butterworth IIR filter in fixed point. My cut-off frequency is relatively close to the DC frequency so high precision is needed for the coefficients. What about realization structure and so on! I have implemented the bit-flipping algorithm in http://www.cmsa.wmin.ac.uk/~artur/pdf/Paper16.pdf for quantization of coefficients and it indeed works, but does some other techniques allow for further reductions of number of bits used to represent the coefficients. Thomas

# Fixed point implementation of 4'th order IIR filters

I've found the normalized lattice-ladder approach yields low distortion even at low frequencies. The cost is more multiplies per filter. Is this a hardware/FPGA implementation? "Heureka" <stoltzo@hotmail.com> wrote in message news:boc1up$l86$1@news.cybercity.dk...> Hi > > Does anyone have some guidelines on how to implement a 4'th order low-pass > Butterworth IIR filter in fixed point. My cut-off frequency is relatively > close to the DC frequency so high precision is needed for thecoefficients.> What about realization structure and so on! > > I have implemented the bit-flipping algorithm in > http://www.cmsa.wmin.ac.uk/~artur/pdf/Paper16.pdf for quantization of > coefficients > and it indeed works, but does some other techniques allow for further > reductions of number of bits used to represent the coefficients. > > Thomas > >

Might have to go with 32 bit filter states and/or coefficients. Or you can try some of the noise shaping that's been described in here every now and then. I would cascade 2, 2nd order biquads ( if it's being done in software ). Robert www.gldsp.com "Heureka" <stoltzo@hotmail.com> wrote:>Hi > >Does anyone have some guidelines on how to implement a 4'th order low-pass >Butterworth IIR filter in fixed point. My cut-off frequency is relatively >close to the DC frequency so high precision is needed for the coefficients. >What about realization structure and so on! > >I have implemented the bit-flipping algorithm in >http://www.cmsa.wmin.ac.uk/~artur/pdf/Paper16.pdf for quantization of >coefficients >and it indeed works, but does some other techniques allow for further >reductions of number of bits used to represent the coefficients. > >Thomas >( modify address for return email ) www.numbersusa.com www.americanpatrol.com

Heureka wrote:> Hi > > Does anyone have some guidelines on how to implement a 4'th order > low-pass Butterworth IIR filter in fixed point. My cut-off > frequency is relatively close to the DC frequency so high > precision is needed for the coefficients. What about realization > structure and so on! > > I have implemented the bit-flipping algorithm in > http://www.cmsa.wmin.ac.uk/~artur/pdf/Paper16.pdf for quantization > of coefficients > and it indeed works, but does some other techniques allow for > further reductions of number of bits used to represent the > coefficients. > > ThomasWhich is your relative cut-off frequency Fc/Fs? How many real bits has your signal? How many bits do you need after the filter stage? Bernhard

Hello: Basic Guidelines: Use 2 2nd order Direct Form I (two delay lines, to avoid overflow of internal filter states) cascaded sections. You most likely will need to halve the a1 coeficient in each stage (if it is greater than 1) and do two macs on that part of the calculation. For low fc/fs, you may need 32 bit recursive data paths. Matlab has tools to take general transfer functions B(z)/A(z) and restructure them to cascaded second order sections. Regards -S www.appliedsignalprocessing.com "Heureka" <stoltzo@hotmail.com> wrote in message news:boc1up$l86$1@news.cybercity.dk...> Hi > > Does anyone have some guidelines on how to implement a 4'th order low-pass > Butterworth IIR filter in fixed point. My cut-off frequency is relatively > close to the DC frequency so high precision is needed for thecoefficients.> What about realization structure and so on! > > I have implemented the bit-flipping algorithm in > http://www.cmsa.wmin.ac.uk/~artur/pdf/Paper16.pdf for quantization of > coefficients > and it indeed works, but does some other techniques allow for further > reductions of number of bits used to represent the coefficients. > > Thomas > >

Sorry for my late reply! The filters are to be implemented on a FPGA. The cutoff frequency is fs/64. When I convert the floating point coefficients linearly I have to use 30 bit in order to have a stop band attenuation at 70 dB. With the bit.flipiing algorithm I can get the bit number down to 20 bit. I need to use as few multiplications as possible, since power consumption is of the essence - but area is too. Can anyone recommend some nice litterature adressing this issue! Thomas "Bernhard Holzmayer" <holzmayer.bernhard@deadspam.com> wrote in message news:1097769.KRe6XMYa8L@holzmayer.ifr.rt...> Heureka wrote: > > > Hi > > > > Does anyone have some guidelines on how to implement a 4'th order > > low-pass Butterworth IIR filter in fixed point. My cut-off > > frequency is relatively close to the DC frequency so high > > precision is needed for the coefficients. What about realization > > structure and so on! > > > > I have implemented the bit-flipping algorithm in > > http://www.cmsa.wmin.ac.uk/~artur/pdf/Paper16.pdf for quantization > > of coefficients > > and it indeed works, but does some other techniques allow for > > further reductions of number of bits used to represent the > > coefficients. > > > > Thomas > > Which is your relative cut-off frequency Fc/Fs? > How many real bits has your signal? > How many bits do you need after the filter stage? > > Bernhard >

FPGA with minimal multiplies? In that case, scratch my previous idea of the normalized Lattice-Ladder implementation. "Heureka" <stoltzo@hotmail.com> wrote in message news:3faaa32c$0$69926$edfadb0f@dread12.news.tele.dk...> Sorry for my late reply! > > The filters are to be implemented on a FPGA. The cutoff frequency isfs/64.> When I convert the floating point coefficients > linearly I have to use 30 bit in order to have a stop band attenuation at70> dB. With the bit.flipiing algorithm I can get the bit number down to 20bit.> I need to use as few multiplications as possible, since power consumptionis> of the essence - but area is too. > > Can anyone recommend some nice litterature adressing this issue! > > Thomas > > > "Bernhard Holzmayer" <holzmayer.bernhard@deadspam.com> wrote in message > news:1097769.KRe6XMYa8L@holzmayer.ifr.rt... > > Heureka wrote: > > > > > Hi > > > > > > Does anyone have some guidelines on how to implement a 4'th order > > > low-pass Butterworth IIR filter in fixed point. My cut-off > > > frequency is relatively close to the DC frequency so high > > > precision is needed for the coefficients. What about realization > > > structure and so on! > > > > > > I have implemented the bit-flipping algorithm in > > > http://www.cmsa.wmin.ac.uk/~artur/pdf/Paper16.pdf for quantization > > > of coefficients > > > and it indeed works, but does some other techniques allow for > > > further reductions of number of bits used to represent the > > > coefficients. > > > > > > Thomas > > > > Which is your relative cut-off frequency Fc/Fs? > > How many real bits has your signal? > > How many bits do you need after the filter stage? > > > > Bernhard > > > >

Hi Thomas! You can also use Lattice Digital Wave filter sections to implement 1-st and 2-nd order allpass sections in cascade. From these allpass sections in cascade one can form a sum or difference dependent on how the filter should act (LP, HP etc.). The resulting filter require minimal number of multipliers and wordlength. Jon Harris wrote:> FPGA with minimal multiplies? In that case, scratch my previous idea of the > normalized Lattice-Ladder implementation. > > "Heureka" <stoltzo@hotmail.com> wrote in message > news:3faaa32c$0$69926$edfadb0f@dread12.news.tele.dk... > >>Sorry for my late reply! >> >>The filters are to be implemented on a FPGA. The cutoff frequency is > > fs/64. > >>When I convert the floating point coefficients >>linearly I have to use 30 bit in order to have a stop band attenuation at > > 70 > >>dB. With the bit.flipiing algorithm I can get the bit number down to 20 > > bit. > >>I need to use as few multiplications as possible, since power consumption > > is > >>of the essence - but area is too. >> >>Can anyone recommend some nice litterature adressing this issue! >> >>Thomas >> >> >>"Bernhard Holzmayer" <holzmayer.bernhard@deadspam.com> wrote in message >>news:1097769.KRe6XMYa8L@holzmayer.ifr.rt... >> >>>Heureka wrote: >>> >>> >>>>Hi >>>> >>>>Does anyone have some guidelines on how to implement a 4'th order >>>>low-pass Butterworth IIR filter in fixed point. My cut-off >>>>frequency is relatively close to the DC frequency so high >>>>precision is needed for the coefficients. What about realization >>>>structure and so on! >>>> >>>>I have implemented the bit-flipping algorithm in >>>>http://www.cmsa.wmin.ac.uk/~artur/pdf/Paper16.pdf for quantization >>>>of coefficients >>>>and it indeed works, but does some other techniques allow for >>>>further reductions of number of bits used to represent the >>>>coefficients. >>>> >>>>Thomas >>> >>>Which is your relative cut-off frequency Fc/Fs? >>>How many real bits has your signal? >>>How many bits do you need after the filter stage? >>> >>>Bernhard >>> >> >> > >