"iarif" <108405@DSPRelated> writes:>>"iarif" <108405@DSPRelated> writes: >> >>> Hi all, as you know, saturation arithmetic can be employed to avoid >>> overflow oscillations in discrete time systems. I want to know that if > we >>> have calculated the saturation limit, how can the word-length (number > of >>> bits) be calculated from this information? Is there any specific >>> relation? >> >>If you assume two's complement representation, the relationship >>is >> >> N >= log_2(MAX), unsigned >> >> N >= log_2(MAX) + 1, signed, including -MAX but excluding +MAX >> >> N >= log_2(MAX) + 2, signed, including -MAX and +MAX >> >>-- >>Randy Yates >>Digital Signal Labs >>http://www.digitalsignallabs.com > > Does it imply that if saturation bound is +/-1 (as in case of global > saturation arithmetic to avoid overflow), no of bits chosen should be > greater than 2?Instead of asking us if Park Ave. is a one-way street south, try asking us how to get to Central Park. "overflow oscillations in discrete time systems" doesn't make any sense to me. Tell us what you're trying to do instead of asking for information on low-level operations. It also doesn't make any sense to ask about a saturation bound of +/- 1 for integers. So I'm afraid our semantic phase-lock is slipping quite a few degrees. -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
relationship between wordlength and saturation limit/bound
Started by ●September 4, 2015
Reply by ●September 5, 20152015-09-05
Reply by ●September 5, 20152015-09-05
>"iarif" <108405@DSPRelated> writes: > >>>"iarif" <108405@DSPRelated> writes: >>> >>>> Hi all, as you know, saturation arithmetic can be employed to avoid >>>> overflow oscillations in discrete time systems. I want to know thatif>> we >>>> have calculated the saturation limit, how can the word-length(number>> of >>>> bits) be calculated from this information? Is there any specific >>>> relation? >>> >>>If you assume two's complement representation, the relationship >>>is >>> >>> N >= log_2(MAX), unsigned >>> >>> N >= log_2(MAX) + 1, signed, including -MAX but excluding +MAX >>> >>> N >= log_2(MAX) + 2, signed, including -MAX and +MAX >>> >>>-- >>>Randy Yates >>>Digital Signal Labs >>>http://www.digitalsignallabs.com >> >> Does it imply that if saturation bound is +/-1 (as in case of global >> saturation arithmetic to avoid overflow), no of bits chosen should be >> greater than 2? > >Instead of asking us if Park Ave. is a one-way street south, try asking >us how to get to Central Park. > >"overflow oscillations in discrete time systems" doesn't make any sense >to me. Tell us what you're trying to do instead of asking for >information on low-level operations. It also doesn't make any sense to >ask about a saturation bound of +/- 1 for integers. So I'm afraid our >semantic phase-lock is slipping quite a few degrees. >-- >Randy Yates >Digital Signal Labs >http://www.digitalsignallabs.comi am doing overflow oscillation elimination analysis in discrete time systems, which occur due to representation of number using fixed point arithmetic. I have applied saturation arithmetic as overflow correction technique. In my analysis, for a given disturbance energy (that occur in cascaded filters) and interference attenuation level, i have calculated (or got an idea) about saturation limit, such that under this saturation limit, overflow oscillations will be eliminated. So i want to know for that value of saturation bound, how i can calculate no of bits (word-length) for implementation of digital filter. I hope my question makes sense now. Thanku --------------------------------------- Posted through http://www.DSPRelated.com
Reply by ●September 5, 20152015-09-05
>>"iarif" <108405@DSPRelated> writes: >> >>>>"iarif" <108405@DSPRelated> writes: >>>> >>>>> Hi all, as you know, saturation arithmetic can be employed to avoid >>>>> overflow oscillations in discrete time systems. I want to know that >if >>> we >>>>> have calculated the saturation limit, how can the word-length >(number >>> of >>>>> bits) be calculated from this information? Is there any specific >>>>> relation? >>>> >>>>If you assume two's complement representation, the relationship >>>>is >>>> >>>> N >= log_2(MAX), unsigned >>>> >>>> N >= log_2(MAX) + 1, signed, including -MAX but excluding +MAX >>>> >>>> N >= log_2(MAX) + 2, signed, including -MAX and +MAX >>>> >>>>-- >>>>Randy Yates >>>>Digital Signal Labs >>>>http://www.digitalsignallabs.com >>> >>> Does it imply that if saturation bound is +/-1 (as in case of global >>> saturation arithmetic to avoid overflow), no of bits chosen should be >>> greater than 2? >> >>Instead of asking us if Park Ave. is a one-way street south, try asking >>us how to get to Central Park. >> >>"overflow oscillations in discrete time systems" doesn't make any sense >>to me. Tell us what you're trying to do instead of asking for >>information on low-level operations. It also doesn't make any sense to >>ask about a saturation bound of +/- 1 for integers. So I'm afraid our >>semantic phase-lock is slipping quite a few degrees. >>-- >>Randy Yates >>Digital Signal Labs >>http://www.digitalsignallabs.com >i am doing overflow oscillation elimination analysis in discrete time systems, which occur due to representation of number using fixed point arithmetic. I have applied saturation arithmetic as overflow correction technique. In my analysis, for a given disturbance energy (that occur in cascaded filters) and interference attenuation level, i have calculated (or got an idea) about saturation limit, such that under this saturation limit, overflow oscillations will be eliminated. For example, if we apply global saturation arithmetic property, the saturation bound is +/-1. So i want to know for some value of saturation bound, how i can calculate no of bits (word-length) for implementation of digital filter. I hope my question makes sense now. Thanku>--------------------------------------- >Posted through http://www.DSPRelated.com--------------------------------------- Posted through http://www.DSPRelated.com
Reply by ●September 5, 20152015-09-05
"iarif" <108405@DSPRelated> writes:>>>"iarif" <108405@DSPRelated> writes: >>> >>>>>"iarif" <108405@DSPRelated> writes: >>>>> >>>>>> Hi all, as you know, saturation arithmetic can be employed to avoid >>>>>> overflow oscillations in discrete time systems. I want to know that >>if >>>> we >>>>>> have calculated the saturation limit, how can the word-length >>(number >>>> of >>>>>> bits) be calculated from this information? Is there any specific >>>>>> relation? >>>>> >>>>>If you assume two's complement representation, the relationship >>>>>is >>>>> >>>>> N >= log_2(MAX), unsigned >>>>> >>>>> N >= log_2(MAX) + 1, signed, including -MAX but excluding +MAX >>>>> >>>>> N >= log_2(MAX) + 2, signed, including -MAX and +MAX >>>>> >>>>>-- >>>>>Randy Yates >>>>>Digital Signal Labs >>>>>http://www.digitalsignallabs.com >>>> >>>> Does it imply that if saturation bound is +/-1 (as in case of global >>>> saturation arithmetic to avoid overflow), no of bits chosen should be >>>> greater than 2? >>> >>>Instead of asking us if Park Ave. is a one-way street south, try asking >>>us how to get to Central Park. >>> >>>"overflow oscillations in discrete time systems" doesn't make any sense >>>to me. Tell us what you're trying to do instead of asking for >>>information on low-level operations. It also doesn't make any sense to >>>ask about a saturation bound of +/- 1 for integers. So I'm afraid our >>>semantic phase-lock is slipping quite a few degrees. >>>-- >>>Randy Yates >>>Digital Signal Labs >>>http://www.digitalsignallabs.com >> > i am doing overflow oscillation elimination analysis in discrete time > systems, which occur due to representation of number using fixed point > arithmetic. I have applied saturation arithmetic as overflow correction > technique. In my analysis, for a given disturbance energy (that occur in > cascaded filters) and interference attenuation level, i have calculated > (or got an idea) about saturation limit, such that under this saturation > limit, overflow oscillations will be eliminated. For example, if we apply > global saturation arithmetic property, the saturation bound is +/-1. So i > want to know for some value of saturation bound, how i can calculate no of > bits > (word-length) for implementation of digital filter. > I hope my question makes sense now.A little more, thank you. I suggest you take a look at work already done by, e.g., [mitra], e.g., sections 9.10, "Reduction of Product Round-Off Errors Using Error Feedback" and 9.11, "Limit Cycles in IIR Digital Filters" before trying your own solutions (I believe the term "limit cycles" is what you are referring to as "overflow oscillations). There are undoubtedly several other sources as well. --Randy @BOOK{mitra, title = "{Digital Signal Processing: A Computer-Based Approach}", author = "Sanjit~K.~Mitra", publisher = "McGraw-Hill", edition = "second", year = "2001"} -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●September 5, 20152015-09-05
>"iarif" <108405@DSPRelated> writes: > >>>>"iarif" <108405@DSPRelated> writes: >>>> >>>>>>"iarif" <108405@DSPRelated> writes: >>>>>> >>>>>>> Hi all, as you know, saturation arithmetic can be employed toavoid>>>>>>> overflow oscillations in discrete time systems. I want to knowthat>>>if >>>>> we >>>>>>> have calculated the saturation limit, how can the word-length >>>(number >>>>> of >>>>>>> bits) be calculated from this information? Is there any specific >>>>>>> relation? >>>>>> >>>>>>If you assume two's complement representation, the relationship >>>>>>is >>>>>> >>>>>> N >= log_2(MAX), unsigned >>>>>> >>>>>> N >= log_2(MAX) + 1, signed, including -MAX but excluding +MAX >>>>>> >>>>>> N >= log_2(MAX) + 2, signed, including -MAX and +MAX >>>>>> >>>>>>-- >>>>>>Randy Yates >>>>>>Digital Signal Labs >>>>>>http://www.digitalsignallabs.com >>>>> >>>>> Does it imply that if saturation bound is +/-1 (as in case ofglobal>>>>> saturation arithmetic to avoid overflow), no of bits chosen shouldbe>>>>> greater than 2? >>>> >>>>Instead of asking us if Park Ave. is a one-way street south, tryasking>>>>us how to get to Central Park. >>>> >>>>"overflow oscillations in discrete time systems" doesn't make anysense>>>>to me. Tell us what you're trying to do instead of asking for >>>>information on low-level operations. It also doesn't make any senseto>>>>ask about a saturation bound of +/- 1 for integers. So I'm afraid our >>>>semantic phase-lock is slipping quite a few degrees. >>>>-- >>>>Randy Yates >>>>Digital Signal Labs >>>>http://www.digitalsignallabs.com >>> >> i am doing overflow oscillation elimination analysis in discrete time >> systems, which occur due to representation of number using fixed point >> arithmetic. I have applied saturation arithmetic as overflowcorrection>> technique. In my analysis, for a given disturbance energy (that occurin>> cascaded filters) and interference attenuation level, i havecalculated>> (or got an idea) about saturation limit, such that under thissaturation>> limit, overflow oscillations will be eliminated. For example, if weapply>> global saturation arithmetic property, the saturation bound is +/-1. Soi>> want to know for some value of saturation bound, how i can calculateno>of >> bits >> (word-length) for implementation of digital filter. >> I hope my question makes sense now. > >A little more, thank you. > >I suggest you take a look at work already done by, e.g., [mitra], e.g., >sections 9.10, "Reduction of Product Round-Off Errors Using Error >Feedback" and 9.11, "Limit Cycles in IIR Digital Filters" before trying >your own solutions (I believe the term "limit cycles" is what you are >referring to as "overflow oscillations). There are undoubtedly several >other sources as well. > >--Randy > >@BOOK{mitra, > title = "{Digital Signal Processing: A Computer-Based Approach}", > author = "Sanjit~K.~Mitra", > publisher = "McGraw-Hill", > edition = "second", > year = "2001"} > >-- >Randy Yates >Digital Signal Labs >http://www.digitalsignallabs.comsir, thanku very much for your help. I have gone through such kind of topics earlier. Can you pls see the following paper http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6508866&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel7%2F8920%2F4358609%2F06508866.pdf%3Farnumber%3D6508866 I am doing such analysis. The saturation arithmetic employed in this paper says that saturation limit is +/-1. My question is very simple. What does it mean by +/-1?. how can it be related to word-length? --------------------------------------- Posted through http://www.DSPRelated.com
Reply by ●September 5, 20152015-09-05
"iarif" <108405@DSPRelated> writes:>>"iarif" <108405@DSPRelated> writes: >> >>>>>"iarif" <108405@DSPRelated> writes: >>>>> >>>>>>>"iarif" <108405@DSPRelated> writes: >>>>>>> >>>>>>>> Hi all, as you know, saturation arithmetic can be employed to > avoid >>>>>>>> overflow oscillations in discrete time systems. I want to know > that >>>>if >>>>>> we >>>>>>>> have calculated the saturation limit, how can the word-length >>>>(number >>>>>> of >>>>>>>> bits) be calculated from this information? Is there any specific >>>>>>>> relation? >>>>>>> >>>>>>>If you assume two's complement representation, the relationship >>>>>>>is >>>>>>> >>>>>>> N >= log_2(MAX), unsigned >>>>>>> >>>>>>> N >= log_2(MAX) + 1, signed, including -MAX but excluding +MAX >>>>>>> >>>>>>> N >= log_2(MAX) + 2, signed, including -MAX and +MAX >>>>>>> >>>>>>>-- >>>>>>>Randy Yates >>>>>>>Digital Signal Labs >>>>>>>http://www.digitalsignallabs.com >>>>>> >>>>>> Does it imply that if saturation bound is +/-1 (as in case of > global >>>>>> saturation arithmetic to avoid overflow), no of bits chosen should > be >>>>>> greater than 2? >>>>> >>>>>Instead of asking us if Park Ave. is a one-way street south, try > asking >>>>>us how to get to Central Park. >>>>> >>>>>"overflow oscillations in discrete time systems" doesn't make any > sense >>>>>to me. Tell us what you're trying to do instead of asking for >>>>>information on low-level operations. It also doesn't make any sense > to >>>>>ask about a saturation bound of +/- 1 for integers. So I'm afraid our >>>>>semantic phase-lock is slipping quite a few degrees. >>>>>-- >>>>>Randy Yates >>>>>Digital Signal Labs >>>>>http://www.digitalsignallabs.com >>>> >>> i am doing overflow oscillation elimination analysis in discrete time >>> systems, which occur due to representation of number using fixed point >>> arithmetic. I have applied saturation arithmetic as overflow > correction >>> technique. In my analysis, for a given disturbance energy (that occur > in >>> cascaded filters) and interference attenuation level, i have > calculated >>> (or got an idea) about saturation limit, such that under this > saturation >>> limit, overflow oscillations will be eliminated. For example, if we > apply >>> global saturation arithmetic property, the saturation bound is +/-1. So > i >>> want to know for some value of saturation bound, how i can calculate > no >>of >>> bits >>> (word-length) for implementation of digital filter. >>> I hope my question makes sense now. >> >>A little more, thank you. >> >>I suggest you take a look at work already done by, e.g., [mitra], e.g., >>sections 9.10, "Reduction of Product Round-Off Errors Using Error >>Feedback" and 9.11, "Limit Cycles in IIR Digital Filters" before trying >>your own solutions (I believe the term "limit cycles" is what you are >>referring to as "overflow oscillations). There are undoubtedly several >>other sources as well. >> >>--Randy >> >>@BOOK{mitra, >> title = "{Digital Signal Processing: A Computer-Based Approach}", >> author = "Sanjit~K.~Mitra", >> publisher = "McGraw-Hill", >> edition = "second", >> year = "2001"} >> >>-- >>Randy Yates >>Digital Signal Labs >>http://www.digitalsignallabs.com > > sir, thanku very much for your help. I have gone through such kind of > topics earlier. Can you pls see the following paper > > http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6508866&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel7%2F8920%2F4358609%2F06508866.pdf%3Farnumber%3D6508866 > > I am doing such analysis. The saturation arithmetic employed in this paper > says that saturation limit is +/-1. My question is very simple. What does > it mean by +/-1?. how can it be related to word-length?Without seeing the paper I am not sure I can give you a good answer. However, many times in fixed-point arithmetic integers are scaled so that their maximum magnitude is 1. For example, a 16-bit signed integer scaled A(0, 15) (my notation from http://www.digitalsignallabs.com/fp.pdf ) is related to its fixed-point value by x = X / 2^15, where x is the fixed-point value and X is the integer value. So, for example, the negative full-scale of such an integer, -32678, is the fixed-point value -1, and the positive full-scale of such an integer, +32767, is +1 - 1 / 2^15 (just under +1). This scaling is easy to work with and is often used for that reason. So the answer is that the full-scale fixed-point value really can't be related to word length, e.g., a full-scale value of +/- 1 could be 16 bits, 32 bits, 64 bits, etc. What the wordlength determines is the resolution of the value represented, and this is also related to the (fixed-point) round-off error you can expect to get in the expected manner. -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●September 6, 20152015-09-06
>"iarif" <108405@DSPRelated> writes: > >>>"iarif" <108405@DSPRelated> writes: >>> >>>>>>"iarif" <108405@DSPRelated> writes: >>>>>> >>>>>>>>"iarif" <108405@DSPRelated> writes: >>>>>>>> >>>>>>>>> Hi all, as you know, saturation arithmetic can be employed to >> avoid >>>>>>>>> overflow oscillations in discrete time systems. I want to know >> that >>>>>if >>>>>>> we >>>>>>>>> have calculated the saturation limit, how can the word-length >>>>>(number >>>>>>> of >>>>>>>>> bits) be calculated from this information? Is there anyspecific>>>>>>>>> relation? >>>>>>>> >>>>>>>>If you assume two's complement representation, the relationship >>>>>>>>is >>>>>>>> >>>>>>>> N >= log_2(MAX), unsigned >>>>>>>> >>>>>>>> N >= log_2(MAX) + 1, signed, including -MAX but excluding +MAX >>>>>>>> >>>>>>>> N >= log_2(MAX) + 2, signed, including -MAX and +MAX >>>>>>>> >>>>>>>>-- >>>>>>>>Randy Yates >>>>>>>>Digital Signal Labs >>>>>>>>http://www.digitalsignallabs.com >>>>>>> >>>>>>> Does it imply that if saturation bound is +/-1 (as in case of >> global >>>>>>> saturation arithmetic to avoid overflow), no of bits chosenshould>> be >>>>>>> greater than 2? >>>>>> >>>>>>Instead of asking us if Park Ave. is a one-way street south, try >> asking >>>>>>us how to get to Central Park. >>>>>> >>>>>>"overflow oscillations in discrete time systems" doesn't make any >> sense >>>>>>to me. Tell us what you're trying to do instead of asking for >>>>>>information on low-level operations. It also doesn't make any sense >> to >>>>>>ask about a saturation bound of +/- 1 for integers. So I'm afraidour>>>>>>semantic phase-lock is slipping quite a few degrees. >>>>>>-- >>>>>>Randy Yates >>>>>>Digital Signal Labs >>>>>>http://www.digitalsignallabs.com >>>>> >>>> i am doing overflow oscillation elimination analysis in discretetime>>>> systems, which occur due to representation of number using fixedpoint>>>> arithmetic. I have applied saturation arithmetic as overflow >> correction >>>> technique. In my analysis, for a given disturbance energy (thatoccur>> in >>>> cascaded filters) and interference attenuation level, i have >> calculated >>>> (or got an idea) about saturation limit, such that under this >> saturation >>>> limit, overflow oscillations will be eliminated. For example, if we >> apply >>>> global saturation arithmetic property, the saturation bound is +/-1.So>> i >>>> want to know for some value of saturation bound, how i can calculate >> no >>>of >>>> bits >>>> (word-length) for implementation of digital filter. >>>> I hope my question makes sense now. >>> >>>A little more, thank you. >>> >>>I suggest you take a look at work already done by, e.g., [mitra],e.g.,>>>sections 9.10, "Reduction of Product Round-Off Errors Using Error >>>Feedback" and 9.11, "Limit Cycles in IIR Digital Filters" beforetrying>>>your own solutions (I believe the term "limit cycles" is what you are >>>referring to as "overflow oscillations). There are undoubtedly several >>>other sources as well. >>> >>>--Randy >>> >>>@BOOK{mitra, >>> title = "{Digital Signal Processing: A Computer-Based Approach}", >>> author = "Sanjit~K.~Mitra", >>> publisher = "McGraw-Hill", >>> edition = "second", >>> year = "2001"} >>> >>>-- >>>Randy Yates >>>Digital Signal Labs >>>http://www.digitalsignallabs.com >> >> sir, thanku very much for your help. I have gone through such kind of >> topics earlier. Can you pls see the following paper >> >> >http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumbere08866&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel7%2F8920%2F4358609%2F06508866.pdf%3Farnumber%3D6508866 >> >> I am doing such analysis. The saturation arithmetic employed in this >paper >> says that saturation limit is +/-1. My question is very simple. Whatdoes>> it mean by +/-1?. how can it be related to word-length? > >Without seeing the paper I am not sure I can give you a good answer. >However, many times in fixed-point arithmetic integers are scaled so >that their maximum magnitude is 1. For example, a 16-bit signed integer >scaled A(0, 15) (my notation from > > http://www.digitalsignallabs.com/fp.pdf > >) is related to its fixed-point value by > > x = X / 2^15, > >where x is the fixed-point value and X is the integer value. So, for >example, the negative full-scale of such an integer, -32678, is the >fixed-point value -1, and the positive full-scale of such an integer, >+32767, is +1 - 1 / 2^15 (just under +1). > >This scaling is easy to work with and is often used for that reason. > >So the answer is that the full-scale fixed-point value really can't >be related to word length, e.g., a full-scale value of +/- 1 could >be 16 bits, 32 bits, 64 bits, etc. > >What the wordlength determines is the resolution of the value >represented, and this is also related to the (fixed-point) round-off >error you can expect to get in the expected manner. >-- >Randy Yates >Digital Signal Labs >http://www.digitalsignallabs.comThanku, Your ans was very helpful :) So it implies that if i have chosen x = 1.2633 X = 121 then no of bits required for hardware implementation is 8. Now, in case i want to represent my number 121 by 4 bits, and i apply rounding i.e 121 (decimal) = 01111001 (binary) after rounding to 4 bits = 0111 = 7 (decimal value) then does it mean that rounding error = 121-7 = 114? --------------------------------------- Posted through http://www.DSPRelated.com
Reply by ●September 7, 20152015-09-07
"iarif" <108405@DSPRelated> writes:>>"iarif" <108405@DSPRelated> writes: >> >>>>"iarif" <108405@DSPRelated> writes: >>>> >>>>>>>"iarif" <108405@DSPRelated> writes: >>>>>>> >>>>>>>>>"iarif" <108405@DSPRelated> writes: >>>>>>>>> >>>>>>>>>> Hi all, as you know, saturation arithmetic can be employed to >>> avoid >>>>>>>>>> overflow oscillations in discrete time systems. I want to know >>> that >>>>>>if >>>>>>>> we >>>>>>>>>> have calculated the saturation limit, how can the word-length >>>>>>(number >>>>>>>> of >>>>>>>>>> bits) be calculated from this information? Is there any > specific >>>>>>>>>> relation? >>>>>>>>> >>>>>>>>>If you assume two's complement representation, the relationship >>>>>>>>>is >>>>>>>>> >>>>>>>>> N >= log_2(MAX), unsigned >>>>>>>>> >>>>>>>>> N >= log_2(MAX) + 1, signed, including -MAX but excluding +MAX >>>>>>>>> >>>>>>>>> N >= log_2(MAX) + 2, signed, including -MAX and +MAX >>>>>>>>> >>>>>>>>>-- >>>>>>>>>Randy Yates >>>>>>>>>Digital Signal Labs >>>>>>>>>http://www.digitalsignallabs.com >>>>>>>> >>>>>>>> Does it imply that if saturation bound is +/-1 (as in case of >>> global >>>>>>>> saturation arithmetic to avoid overflow), no of bits chosen > should >>> be >>>>>>>> greater than 2? >>>>>>> >>>>>>>Instead of asking us if Park Ave. is a one-way street south, try >>> asking >>>>>>>us how to get to Central Park. >>>>>>> >>>>>>>"overflow oscillations in discrete time systems" doesn't make any >>> sense >>>>>>>to me. Tell us what you're trying to do instead of asking for >>>>>>>information on low-level operations. It also doesn't make any sense >>> to >>>>>>>ask about a saturation bound of +/- 1 for integers. So I'm afraid > our >>>>>>>semantic phase-lock is slipping quite a few degrees. >>>>>>>-- >>>>>>>Randy Yates >>>>>>>Digital Signal Labs >>>>>>>http://www.digitalsignallabs.com >>>>>> >>>>> i am doing overflow oscillation elimination analysis in discrete > time >>>>> systems, which occur due to representation of number using fixed > point >>>>> arithmetic. I have applied saturation arithmetic as overflow >>> correction >>>>> technique. In my analysis, for a given disturbance energy (that > occur >>> in >>>>> cascaded filters) and interference attenuation level, i have >>> calculated >>>>> (or got an idea) about saturation limit, such that under this >>> saturation >>>>> limit, overflow oscillations will be eliminated. For example, if we >>> apply >>>>> global saturation arithmetic property, the saturation bound is +/-1. > So >>> i >>>>> want to know for some value of saturation bound, how i can calculate >>> no >>>>of >>>>> bits >>>>> (word-length) for implementation of digital filter. >>>>> I hope my question makes sense now. >>>> >>>>A little more, thank you. >>>> >>>>I suggest you take a look at work already done by, e.g., [mitra], > e.g., >>>>sections 9.10, "Reduction of Product Round-Off Errors Using Error >>>>Feedback" and 9.11, "Limit Cycles in IIR Digital Filters" before > trying >>>>your own solutions (I believe the term "limit cycles" is what you are >>>>referring to as "overflow oscillations). There are undoubtedly several >>>>other sources as well. >>>> >>>>--Randy >>>> >>>>@BOOK{mitra, >>>> title = "{Digital Signal Processing: A Computer-Based Approach}", >>>> author = "Sanjit~K.~Mitra", >>>> publisher = "McGraw-Hill", >>>> edition = "second", >>>> year = "2001"} >>>> >>>>-- >>>>Randy Yates >>>>Digital Signal Labs >>>>http://www.digitalsignallabs.com >>> >>> sir, thanku very much for your help. I have gone through such kind of >>> topics earlier. Can you pls see the following paper >>> >>> >>http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumbere08866&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel7%2F8920%2F4358609%2F06508866.pdf%3Farnumber%3D6508866 >>> >>> I am doing such analysis. The saturation arithmetic employed in this >>paper >>> says that saturation limit is +/-1. My question is very simple. What > does >>> it mean by +/-1?. how can it be related to word-length? >> >>Without seeing the paper I am not sure I can give you a good answer. >>However, many times in fixed-point arithmetic integers are scaled so >>that their maximum magnitude is 1. For example, a 16-bit signed integer >>scaled A(0, 15) (my notation from >> >> http://www.digitalsignallabs.com/fp.pdf >> >>) is related to its fixed-point value by >> >> x = X / 2^15, >> >>where x is the fixed-point value and X is the integer value. So, for >>example, the negative full-scale of such an integer, -32678, is the >>fixed-point value -1, and the positive full-scale of such an integer, >>+32767, is +1 - 1 / 2^15 (just under +1). >> >>This scaling is easy to work with and is often used for that reason. >> >>So the answer is that the full-scale fixed-point value really can't >>be related to word length, e.g., a full-scale value of +/- 1 could >>be 16 bits, 32 bits, 64 bits, etc. >> >>What the wordlength determines is the resolution of the value >>represented, and this is also related to the (fixed-point) round-off >>error you can expect to get in the expected manner. >>-- >>Randy Yates >>Digital Signal Labs >>http://www.digitalsignallabs.com > > Thanku, Your ans was very helpful :) > So it implies that if i have chosen > x = 1.2633 > X = 121Where did these numbers come from? They make absolutely no sense to me. If you're using the notation I proposed above, then the scaling factor b in a signed, fixed-point number that is scaled A(a,b) can be given by b = log_2(X / x) and should be an integer. For your numbers, b = log_2(121 / 1.2633) = 6.58 Makes no sense.> then no of bits required for hardware implementation is 8. > Now, in case i want to represent my number 121 by 4 bits, and i apply > rounding i.e > 121 (decimal) = 01111001 (binary) > after rounding to 4 bits = 0111 = 7 (decimal value) > then does it mean that rounding error = 121-7 = 114?I really have no idea what you are talking about. It seems we're not really communicating. -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●September 7, 20152015-09-07
On 9/7/15 1:57 PM, Randy Yates wrote:> "iarif"<108405@DSPRelated> writes: >...>> >> Thanku, Your ans was very helpful :) >> So it implies that if i have chosen >> x = 1.2633 >> X = 121 > > Where did these numbers come from? They make absolutely no sense > to me. > > If you're using the notation I proposed above, then the scaling factor b > in a signed, fixed-point number that is scaled A(a,b) can be given > by > > b = log_2(X / x) > > and should be an integer. For your numbers, > > b = log_2(121 / 1.2633) > > = 6.58 > > Makes no sense. > >> then no of bits required for hardware implementation is 8. >> Now, in case i want to represent my number 121 by 4 bits, and i apply >> rounding i.e >> 121 (decimal) = 01111001 (binary) >> after rounding to 4 bits = 0111 = 7 (decimal value) >> then does it mean that rounding error = 121-7 = 114? > > I really have no idea what you are talking about. It seems we're not > really communicating.Randy, you have much more patience than me. i gave up on him days ago. the guy's a wanker. On 9/5/15 2:23 PM, iarif wrote:> > i am doing overflow oscillation elimination analysis in discrete time > systems, which occur due to representation of number using fixed point > arithmetic. I have applied saturation arithmetic as overflow correction > technique. In my analysis, for a given disturbance energy (that occur in > cascaded filters) and interference attenuation level, i have calculated > (or got an idea) about saturation limit, such that under this saturation > limit, overflow oscillations will be eliminated. For example, if we apply > global saturation arithmetic property, the saturation bound is +/-1. So i > want to know for some value of saturation bound, how i can calculate no of > bits (word-length) for implementation of digital filter. > I hope my question makes sense now.like the https://en.wikipedia.org/wiki/Bogdanov_affair , this person is using big words and tying them together in sentences that are syntactically correct, but the content makes no sense. he's in way over his head. he needs remedial or elementary training, first in binary arithmetic, and perhaps in other basic mathematical concepts before even beginning to do DSP. there was briefly a post to dsp.stackexchange (by someone named "zarif") about the same thing, but i think it was withdrawn. i can't see it anymore. sorry to be so harsh. perhaps i am channeling Vlad. for those in the U.S., have a happy Labor Day. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
Reply by ●September 7, 20152015-09-07
robert bristow-johnson <rbj@audioimagination.com> writes:> [...] > sorry to be so harsh.I have been giving him the benefit of the doubt, but the doubt's growing pretty big!> for those in the U.S., have a happy Labor Day.You too, Robert! -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
