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These functions can be rewritten in terms of polar coordinates using x = r cos , y = r sin : 2r sin 1 r2 u= and , v= (1 + r cos )2 + r 2 sin 2 (1 + r cos )2 + r 2 sin 2 u 2r sin = v 1 r2 Hence f = 1 1 2r sin tan 1 1 r2

Network Address Translation (NAT)

The best part about digital telephony is that most of the aspects you ve already learned about computer networking work roughly the same way in a telephone network In fact, most of the concepts that created computer networking came from the telephone industry

Cisco's Network Address Translation (NAT) process converts one IP address safely into another IP address NAT is used primarily in the following roles:

EXAMPLE 125 Consider a disk 0 r < R and solve Laplace s equation with Neumann boundary conditions given by u ( R, ) = g( ) r u(r , ) is bounded as r 0 and

For example, the telephone industry was the first technology to heavily adopt the idea of digital packets It was the first to do what we now call switching Heck, the telephone industry even made the first working topologies! Let s take advantage of what you already know about how networks work to learn about how the telephone industry invented the idea of digital networks When you learned about networks in the first few chapters of this book, you learned about cabling, frame types, speeds, switching, and so on All of these are important for computer networks Well, let s do it again (in a much simpler format) to see the cabling, frame types, speed, and switching used in telephone systems Don t worry Unlike computer networks, in which a certain type of cable might run different types of frames at different speeds, most of the remote connections used in the telephony world tend to have one type of cable that only runs one type of frame at one type of speed The only real question is where to start The best place to begin is with the most basic data chunk you get in the telephone world: DS0

NAT allows you to hide your internal IP address scheme, for security purposes If you have an internal network configured with nonregistered IP addresses, NAT allows safe connectivity to a public network by translating these addresses to registered IP addresses before forwarding the traffic onto the public network This saves you the time of redoing your internal IP address scheme Internal machines that match up to static NAT IP addresses (mail servers, for instance) can be swapped without having to update records stored on the Internet Following are the advantages and disadvantages of NAT

When AT&T decided to go digital, it knew all phone calls had to be broken into a digital sample AT&T chose (some people say guessed or compromised ) and decided that if it took an analog signal of a human voice and converted it into 8-bit chunks 8000 times a second, that would be good enough to re-create the sound later Figure 14-11 shows an example of the analog human voice seen earlier being converted into a digital sample

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NAT conserves the number of legally registered IP addresses taken up for public network interaction Network design is simplified because of unlimited availability of addressing schemes (no more growth restrictions relating to lack of IP addresses) When mergers occur, NAT allows for a seamless integration by maintaining previously implemented IP address schemes NAT eliminates the need to re-address a network that requires public network interaction Security is increased by masking the internal IP address scheme

NOTE A device that takes an analog signal and converts it into a digital signal is a modulator A device that takes a digital signal and converts it into an analog signal is a demodulator A device that does both is called a modulatordemodulator, better known as a modem

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