orthogonal signals

Started by Dave Henry May 22, 2004
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?


"Dave Henry"  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
thanks

"Randy Yates"  wrote in message
news:xxpekpcc7me.fsf@usrts005.corpusers.net...
> "Dave Henry" 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
Randy Yates wrote:
> "Dave Henry" 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
Randy Yates wrote:
> "Dave Henry" 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
thanks

"Randy Yates"  wrote in message
news:xxpekpcc7me.fsf@usrts005.corpusers.net...
> "Dave Henry" 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
"Dave Henry"  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
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?