## orthogonal or orthonormal?

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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

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

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

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

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