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# Discussion Groups | Comp.DSP | orthogonal signals

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# orthogonal signals - Dave Henry - 2004-05-22 13:50:00

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?

# Re: orthogonal signals - 2004-05-22 20:25:00

"Dave Henry" <d...@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

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

--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
r...@sonyericsson.com, 919-472-1124

# Re: orthogonal signals - Dave Henry - 2004-05-23 08:31:00

thanks

"Randy Yates" <r...@sonyericsson.com> wrote in message
news:x...@usrts005.corpusers.net...
> "Dave Henry" <d...@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
>
> --
> Randy Yates
> Sony Ericsson Mobile Communications
> Research Triangle Park, NC, USA
> r...@sonyericsson.com, 919-472-1124

# Re: orthogonal signals - glen herrmannsfeldt - 2004-05-25 17:45:00

Randy Yates wrote:
> "Dave Henry" <d...@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