Hi, In the book on DSP by Proakis, and in the part where the relation between analog and digital frequencies is given, it is written that As -inf < F < inf (where F is the frequency in Hz of Analog signal) so, -inf < omega < inf (omega is the angular frequency in rad/sec) Now, I can't understand how the angular frequency can be greater than 2pi. Am I missing something? Mathematically, it seems to be correct, as F -> inf, omega = 2piF -> inf, but I'm not satisfied Can some expert explain why is it so? For Vladimir, This may be a STUPIDENT question but certainly not HOMEWORK!
Regarding analog angular frequency
Started by ●July 24, 2009
Reply by ●July 24, 20092009-07-24
On Jul 24, 12:35�am, "commengr" <communications_engin...@yahoo.com> wrote:> Hi, > > In the book on DSP by Proakis, and in the part where the relation between > analog and digital frequencies is given, it is written that > > As -inf < F < inf � (where F is the frequency in Hz of Analog signal) > > so, -inf < omega < inf �(omega is the angular frequency in rad/sec) > > Now, I can't understand how the angular frequency can be greater than 2pi. > Am I missing something?so far they're both analog. so there is no Nyquist frequency yet. the difference between the "regular" frequency (like Hz) and angular frequency is that one measures the number of complete cycles per unit time and the other measures how many radians of turn per unit time. it's just a factor of 2*pi. it's the same difference between Planck's constant and "hbar". no big deal. in the digital world, where we are normalized to the sampling frequency, the angular frequency repeats every 2*pi so we just usually keep it between -pi and +pi. but you *could* exceed that range, but it would just repeat. maybe Vlad will pick on you now. r b-j
Reply by ●July 24, 20092009-07-24
On Jul 23, 9:35�pm, "commengr" <communications_engin...@yahoo.com> wrote:> Hi, > > In the book on DSP by Proakis, and in the part where the relation between > analog and digital frequencies is given, it is written that > > As -inf < F < inf � (where F is the frequency in Hz of Analog signal) > > so, -inf < omega < inf �(omega is the angular frequency in rad/sec) > > Now, I can't understand how the angular frequency can be greater than 2pi. > Am I missing something? > > Mathematically, it seems to be correct, as F -> inf, omega = 2piF -> inf, > but I'm not satisfied > > Can some expert explain why is it so? > > For Vladimir, This may be a STUPIDENT question but certainly not HOMEWORK!Bloody hell - has the world come to this....Will analogue become a lost art! Don't they teach any analogue at all nowadays?
Reply by ●July 24, 20092009-07-24
commengr wrote:> Hi, > > In the book on DSP by Proakis, and in the part where the relation between > analog and digital frequencies is given, it is written that > > As -inf < F < inf (where F is the frequency in Hz of Analog signal) > > so, -inf < omega < inf (omega is the angular frequency in rad/sec) > > > Now, I can't understand how the angular frequency can be greater than 2pi. > Am I missing something? > > Mathematically, it seems to be correct, as F -> inf, omega = 2piF -> inf, > but I'm not satisfied > > Can some expert explain why is it so? > > > For Vladimir, This may be a STUPIDENT question but certainly not HOMEWORK!The difference between F and omega is just a scale factor, like the difference between inches and centimeters. The scale factors are different, but that doesn't matter. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 24, 20092009-07-24
On 24 Jul, 19:43, Jerry Avins <j...@ieee.org> wrote:> The difference between F and omega is just a scale factor, like the > difference between inches and centimeters. The scale factors are > different, but that doesn't matter.The ancient Scandinavian measurement system used a couple of units, 'tomme' and 'alen.' The term 'tomme' is still in use for the English 'inch', while 'alen' was about 60 cm. I have no idea how true this is, but myth has it that it was that the ruling King's anatomy was the reference measures for these units: The 'tomme' was defined by the outer section of the King's thumb (Eng. 'thumb' = Norw. 'tommel') while the length of the King's forearm defined the 'alen'. Rune
Reply by ●July 24, 20092009-07-24
On Jul 24, 5:55=A0pm, Rune Allnor <all...@tele.ntnu.no> wrote:> ... myth has it that it was > that the ruling King's anatomy was the reference measures for > these units: ... the > length of the King's forearm defined the 'alen'.maybe the length of the King's court jester's manhood. that would make for a good anthropometric unit. r b-j
Reply by ●July 24, 20092009-07-24
On 7/24/2009 2:55 PM, Rune Allnor wrote:> On 24 Jul, 19:43, Jerry Avins<j...@ieee.org> wrote: > >> The difference between F and omega is just a scale factor, like the >> difference between inches and centimeters. The scale factors are >> different, but that doesn't matter. > > The ancient Scandinavian measurement system used a couple > of units, 'tomme' and 'alen.' The term 'tomme' is still in > use for the English 'inch', while 'alen' was about 60 cm. > > I have no idea how true this is, but myth has it that it was > that the ruling King's anatomy was the reference measures for > these units: The 'tomme' was defined by the outer section of > the King's thumb (Eng. 'thumb' = Norw. 'tommel') while the > length of the King's forearm defined the 'alen'. > > RuneSupposedly a "cubit" (of Biblical fame) was the distance from an adult male's elbow to the fingertip with fingers extended and the elbow bent at about 90 degrees. The Egyptians (and other contemporary cultures) clearly had precise enough architects, engineers, and builders, that they must have had something standardized with much tighter tolerances than that. It'd be so much fun to have a time machine to go back and see how some of that stuff was really handled. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
Reply by ●July 24, 20092009-07-24
Eric Jacobsen wrote:> On 7/24/2009 2:55 PM, Rune Allnor wrote: >> On 24 Jul, 19:43, Jerry Avins<j...@ieee.org> wrote: >> >>> The difference between F and omega is just a scale factor, like the >>> difference between inches and centimeters. The scale factors are >>> different, but that doesn't matter. >> >> The ancient Scandinavian measurement system used a couple >> of units, 'tomme' and 'alen.' The term 'tomme' is still in >> use for the English 'inch', while 'alen' was about 60 cm. >> >> I have no idea how true this is, but myth has it that it was >> that the ruling King's anatomy was the reference measures for >> these units: The 'tomme' was defined by the outer section of >> the King's thumb (Eng. 'thumb' = Norw. 'tommel') while the >> length of the King's forearm defined the 'alen'. >> >> Rune > > Supposedly a "cubit" (of Biblical fame) was the distance from an adult > male's elbow to the fingertip with fingers extended and the elbow bent > at about 90 degrees. > > The Egyptians (and other contemporary cultures) clearly had precise > enough architects, engineers, and builders, that they must have had > something standardized with much tighter tolerances than that. It'd be > so much fun to have a time machine to go back and see how some of that > stuff was really handled.In medieval times, A yard was defined as the distance from the reigning king's nose to the tip of his thumb when he faced forward with his arm outstretched to the side. The word "fathom" means "encompass". ("It took three men to fathom the tree.") As a length, Parliament defined a fathom as "the length of a swain's arms about the object of his affections." Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●July 24, 20092009-07-24
"Jerry Avins" <jya@ieee.org> wrote in message news:SSsam.33607$YU5.23065@newsfe21.iad...> Eric Jacobsen wrote: >> On 7/24/2009 2:55 PM, Rune Allnor wrote: >>> On 24 Jul, 19:43, Jerry Avins<j...@ieee.org> wrote: >>> >>>> The difference between F and omega is just a scale factor, like the >>>> difference between inches and centimeters. The scale factors are >>>> different, but that doesn't matter. >>> >>> The ancient Scandinavian measurement system used a couple >>> of units, 'tomme' and 'alen.' The term 'tomme' is still in >>> use for the English 'inch', while 'alen' was about 60 cm. >>> >>> I have no idea how true this is, but myth has it that it was >>> that the ruling King's anatomy was the reference measures for >>> these units: The 'tomme' was defined by the outer section of >>> the King's thumb (Eng. 'thumb' = Norw. 'tommel') while the >>> length of the King's forearm defined the 'alen'. >>> >>> Rune >> >> Supposedly a "cubit" (of Biblical fame) was the distance from an adult >> male's elbow to the fingertip with fingers extended and the elbow bent at >> about 90 degrees. >> >> The Egyptians (and other contemporary cultures) clearly had precise >> enough architects, engineers, and builders, that they must have had >> something standardized with much tighter tolerances than that. It'd be >> so much fun to have a time machine to go back and see how some of that >> stuff was really handled. > > In medieval times, A yard was defined as the distance from the reigning > king's nose to the tip of his thumb when he faced forward with his arm > outstretched to the side. The word "fathom" means "encompass". ("It took > three men to fathom the tree.") As a length, Parliament defined a fathom > as "the length of a swain's arms about the object of his affections." > > JerrySo, who first used the 'rch' as a measurement? Bob -- == All google group posts are automatically deleted due to spam ==
Reply by ●July 24, 20092009-07-24
BobW wrote: ...> So, who first used the 'rch' as a measurement?Graucho Marx? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
