why do we use complex exponential mathematics in dig comm

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wajahat

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hi everyone ,i want to know why do we use complex exponential mathematics in digital cammunication, but we transmit only real part of the signal .We recover the complex part by using hilbert transformer at receiver.

One reason that i found out was that it simplifies arithmatic operations.
Is there any other reason?
Any response would be helpful.
 

Re: why do we use complex exponential mathematics in dig com

Using complex notation for signals helps in easy understanding and implementation. We only take the mathematical representation so that it helps in easy mathematical manipulation...
When implementing a transmitter, the I and Q components (In-phase=real, Quadrature=imaginary) are actually cosine (real) and sine (imaginary) components. They are orthogonal to each other and are sent on the same carrier. But can be easily understood with complex representation.
 

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    wajahat

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Re: why do we use complex exponential mathematics in dig com

the noice cancellation is easier in additiion to ease of implementation. So, BER is lower.
 

Re: why do we use complex exponential mathematics in dig com

It is basically, we can easily analyze the systems. In real schemes we have to deal with inphase and quadrature parts seperatly. But in the complex representation we can do the operations easily on the combined version as the complex signal.

The other advantage is we can work on baseband signals avoiding the effect of carrier frequency:

This is called the complex baseband model.

Janath
 

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    wajahat

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Re: why do we use complex exponential mathematics in dig com

It's for the same reason we consider both positive and negative frequencies in Fourier transform while the negative ones do not have any physical meanning.It makes calculations and representations of types much easier to understand and use.
 

Re: why do we use complex exponential mathematics in dig com

Also, sometimes we need phase information, that can only be derived using exponential means. I.e Real and Imaginary, and when you convert that to polar notation you get the phase and magnitude, for example when you do power spectrum calculations and when working with digital modulation schemes.
 

In Meyr book, it state that:

if we use rael mathematic, like cos(wt), it only one dimension signal space.

if we use the complex exponential mathematics, like cos(wt) and j*sin(wt), it represents two dimension signal space, then we can carry more infirmation in a symbol time interval.
 

Dear wajahat,

The book name is IGITAL COMMUNICATION RECEIVERS
Synchronization, Channel Estimation,And Signal Processing

Author: Heinrich Meyr, Marc Moeneclaey, Stefan A. Fechtel
 

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    wajahat

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