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Numerical Analysis Versus Analytical Analysis

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channel_coding84

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I am confused about the terms

Numerical Analysis and Analytical Analysis

Please help somone understand the difference.

please find some time ..
 

In analytical analysis we should use related formulas to obtain the analysis results. However many systems possess complex functionality that it is hard to track the system behavior by formulas. in such cases, we should simulate the system and analyze it in some well defined situation to estimate its behavior.
 
Thank you very much for your reply:

I still have little confusion:

You mean results got with simulation are called numerical analysis, and with formulas, called analytical ??


I have a probability of errror formula, for example

Pe=Q(SNR); Q is q-function

Now, if I get some curve between SNR and Pe, using some values for SNR (-5:15), what type of analysis the resulting curve show ??

I hope you will help.
 

If the author have obtained the formula that relate Pe to SNR (e.g. Q-function) and plot the curve based on that formula, then the curve returns analytical results. On the other hand if the problem is complicated and the author could not obtain the analytical results, he can setup a simulation. some random sequences are transmitted through the channel; in the receiver the signal demodulate; exploiting the transmitted sequence, he may calculate the Pe in each SNR and plot them as a curve. This is the routine that many use in their papers and is definitely numerical analysis.

Regards
 
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