orthogonal or orthonormal?

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#1
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Hi,

I don't know if it is the right place to post such a question. In my textbook "Digital Communications" there are two similar English words: orthogonal and orthonormal. Do they mean the same?

Thanks
Owen

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According to that great sage, wikipedia:

In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal and unit vectors.

Then, about orthogonal (my clumsy definition)-

Orthogonal means that the vectors are independent. That is, if a second vector is NOT orthogonal to the first, then the second can, itself, be decomposed into a component that is proportional to the first AND a component that is normal to the first.

This definition extends to signals, though I find that extension a bit awkward. But, signal theorists seem to like it.

Jim

Jim Wagner Oregon Research Electronics, Consulting Div. Tangent, OR, USA http://www.orelectronics.net

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It's been a long time since I did this stuff, but IIRC, in the usual definition, two vectors are orthogonal if their inner product is zero.

- S

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Surely, the textbook must define the two terms in the context of communications.

Jim

Jim Wagner Oregon Research Electronics, Consulting Div. Tangent, OR, USA http://www.orelectronics.net

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I always thought of orthogonal as @ 90 degrees. (which I suppose is a less formal version of Jim's findings)

In communications terms 2 orthogonal signals, (I & Q or sin & cos) having 90degs phase difference, are independent in nature by virtue that they don't transition at the same time. (Thinking square wave)

This can allow for more bits/Hz in transmission bandwidth. It can extend to many phases to, not just orthogonal.

Steve

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Vectors are orthogonal if they're at right angles to each other. Orthonormal vectors are orthogonal AND have unit length so that they may easily be used as basis vectors. That is, any other vector may be expressed as a linear combination of the orthonormal vectors.

Greg

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Thank you very much.

Owen :D