what are orthogonal signals?? Why is CODFM modulation used for terrestrial digital TV? I can't find the correct info on the web. can anyone help me?

# orthogonal signals

Started by ●May 22, 2004

Posted by ●May 22, 2004

"Dave Henry" <davehenry82@ntlworld.com> writes:> what are orthogonal signals??Hi Dave, I'm no expert on OFDM, but here are some basics that I believe to be correct. Two functions f(t) and g(t) are said to be orthogonal over T_0 if \int_{T_0} f(t) g(t) dt = 0. [1] For example, sin t and cos t are orthogonal over 2*pi because \int_{0}^{2*pi} cos(t) sin(t) dt = 0.> Why is CODFM modulation used for terrestrial > digital TV? I can't find the correct info on the web.Orthogonal Frequency Division Multiplexing (OFDM) utilizes a set of N carrier waves (k_0, k_1, ..., k_{N-1}) to transmit information such that k_n = cos(2*pi*f_0*n*t). It can be shown that k_i is orthogonal to k_j when i != j. "COFDM" is "Coded OFDM" where forward error-correction coding is added to the mix. The reason this is chosen for TV is that by splitting the entire transmission bandwidth B (I believe B is the same for HDTV as it was for NTSC in the U.S., i.e., 6 MHz) into smaller pieces, B/N, each subchannel is relatively undisturbed by fading and multipath. For some web references, see [2] and [3]. [1] I am using the somewhat arcane TeX typesetting system syntax here in which \int denotes the integral symbol, a "_" is used for subscript or lower limit and a "^" is used for a superscript or upper limit. [2] http://www.bbc.co.uk/rd/pubs/papers/paper_15/paper_15.html [3] http://home.earthlink.net/~yatescr/esb96rc.pdf. -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA randy.yates@sonyericsson.com, 919-472-1124

Posted by ●May 23, 2004

thanks "Randy Yates" <randy.yates@sonyericsson.com> wrote in message news:xxpekpcc7me.fsf@usrts005.corpusers.net...> "Dave Henry" <davehenry82@ntlworld.com> writes: > > > what are orthogonal signals?? > > Hi Dave, > > I'm no expert on OFDM, but here are some basics that I > believe to be correct. > > Two functions f(t) and g(t) are said to be orthogonal over > T_0 if > > \int_{T_0} f(t) g(t) dt = 0. [1] > > For example, sin t and cos t are orthogonal over 2*pi because > > \int_{0}^{2*pi} cos(t) sin(t) dt = 0. > > > Why is CODFM modulation used for terrestrial > > digital TV? I can't find the correct info on the web. > > Orthogonal Frequency Division Multiplexing (OFDM) utilizes a set > of N carrier waves (k_0, k_1, ..., k_{N-1}) to transmit information > such that > > k_n = cos(2*pi*f_0*n*t). > > It can be shown that k_i is orthogonal to k_j when i != j. > > "COFDM" is "Coded OFDM" where forward error-correctioncoding> is added to the mix. > > The reason this is chosen for TV is that by splitting the entire > transmission bandwidth B (I believe B is the same for HDTV as > it was for NTSC in the U.S., i.e., 6 MHz) into smaller pieces, B/N, > each subchannel is relatively undisturbed by fading and multipath. > > For some web references, see [2] and [3]. > > [1] I am using the somewhat arcane TeX typesetting system > syntax here in which \int denotes the integral symbol, > a "_" is used for subscript or lower limit and a "^" is > used for a superscript or upper limit. > > [2] http://www.bbc.co.uk/rd/pubs/papers/paper_15/paper_15.html > > [3] http://home.earthlink.net/~yatescr/esb96rc.pdf. > -- > Randy Yates > Sony Ericsson Mobile Communications > Research Triangle Park, NC, USA > randy.yates@sonyericsson.com, 919-472-1124

Posted by ●May 25, 2004

Randy Yates wrote:> "Dave Henry" <davehenry82@ntlworld.com> writes:>>what are orthogonal signals??> I'm no expert on OFDM, but here are some basics that I > believe to be correct.> Two functions f(t) and g(t) are said to be orthogonal over > T_0 if> \int_{T_0} f(t) g(t) dt = 0. [1]You should also have a weighting function w(t), though in many cases it is constant. \int_{T_0} w(t) f(t) g(t) dt = 0 -- glen

Posted by ●May 25, 2004

Randy Yates wrote:> "Dave Henry" <davehenry82@ntlworld.com> writes:>>what are orthogonal signals??> I'm no expert on OFDM, but here are some basics that I > believe to be correct.> Two functions f(t) and g(t) are said to be orthogonal over > T_0 if> \int_{T_0} f(t) g(t) dt = 0. [1]You should also have a weighting function w(t), though in many cases it is constant. \int_{T_0} w(t) f(t) g(t) dt = 0 -- glen

Posted by ●May 23, 2004

thanks "Randy Yates" <randy.yates@sonyericsson.com> wrote in message news:xxpekpcc7me.fsf@usrts005.corpusers.net...> "Dave Henry" <davehenry82@ntlworld.com> writes: > > > what are orthogonal signals?? > > Hi Dave, > > I'm no expert on OFDM, but here are some basics that I > believe to be correct. > > Two functions f(t) and g(t) are said to be orthogonal over > T_0 if > > \int_{T_0} f(t) g(t) dt = 0. [1] > > For example, sin t and cos t are orthogonal over 2*pi because > > \int_{0}^{2*pi} cos(t) sin(t) dt = 0. > > > Why is CODFM modulation used for terrestrial > > digital TV? I can't find the correct info on the web. > > Orthogonal Frequency Division Multiplexing (OFDM) utilizes a set > of N carrier waves (k_0, k_1, ..., k_{N-1}) to transmit information > such that > > k_n = cos(2*pi*f_0*n*t). > > It can be shown that k_i is orthogonal to k_j when i != j. > > "COFDM" is "Coded OFDM" where forward error-correctioncoding> is added to the mix. > > The reason this is chosen for TV is that by splitting the entire > transmission bandwidth B (I believe B is the same for HDTV as > it was for NTSC in the U.S., i.e., 6 MHz) into smaller pieces, B/N, > each subchannel is relatively undisturbed by fading and multipath. > > For some web references, see [2] and [3]. > > [1] I am using the somewhat arcane TeX typesetting system > syntax here in which \int denotes the integral symbol, > a "_" is used for subscript or lower limit and a "^" is > used for a superscript or upper limit. > > [2] http://www.bbc.co.uk/rd/pubs/papers/paper_15/paper_15.html > > [3] http://home.earthlink.net/~yatescr/esb96rc.pdf. > -- > Randy Yates > Sony Ericsson Mobile Communications > Research Triangle Park, NC, USA > randy.yates@sonyericsson.com, 919-472-1124

Posted by ●May 22, 2004

"Dave Henry" <davehenry82@ntlworld.com> writes:> what are orthogonal signals??Hi Dave, I'm no expert on OFDM, but here are some basics that I believe to be correct. Two functions f(t) and g(t) are said to be orthogonal over T_0 if \int_{T_0} f(t) g(t) dt = 0. [1] For example, sin t and cos t are orthogonal over 2*pi because \int_{0}^{2*pi} cos(t) sin(t) dt = 0.> Why is CODFM modulation used for terrestrial > digital TV? I can't find the correct info on the web.Orthogonal Frequency Division Multiplexing (OFDM) utilizes a set of N carrier waves (k_0, k_1, ..., k_{N-1}) to transmit information such that k_n = cos(2*pi*f_0*n*t). It can be shown that k_i is orthogonal to k_j when i != j. "COFDM" is "Coded OFDM" where forward error-correction coding is added to the mix. The reason this is chosen for TV is that by splitting the entire transmission bandwidth B (I believe B is the same for HDTV as it was for NTSC in the U.S., i.e., 6 MHz) into smaller pieces, B/N, each subchannel is relatively undisturbed by fading and multipath. For some web references, see [2] and [3]. [1] I am using the somewhat arcane TeX typesetting system syntax here in which \int denotes the integral symbol, a "_" is used for subscript or lower limit and a "^" is used for a superscript or upper limit. [2] http://www.bbc.co.uk/rd/pubs/papers/paper_15/paper_15.html [3] http://home.earthlink.net/~yatescr/esb96rc.pdf. -- Randy Yates Sony Ericsson Mobile Communications Research Triangle Park, NC, USA randy.yates@sonyericsson.com, 919-472-1124

Posted by ●May 22, 2004