Physical Layer (Part 2) Srinidhi Varadarajan Fourier Series Even - - PowerPoint PPT Presentation

Physical Layer (Part 2)

Srinidhi Varadarajan

Fourier Series

• Even and Odd functions:

– Even functions mirror around the Y-axis (cos θ) – Odd functions invert around the Y axis (sin θ)

• A Fourier series expresses a time-domain function

as a series of harmonics of sines and cosines.

– The basic Fourier series expresses are periodic function. – Aperiodic functions are involve a continuum of frequencies – leads to the Fourier transform

• Why is it useful?

– Hint: Tells you something about the frequency

Fourier Series

Take a look at :

– http://sunlightd.virtualave.net/Fourier/

∫ ∫ ∫ ∑ ∑

= = = + + =

∞ = ∞ = T n T n T n n n n

dt nft t g T B dt nft t g T A dt t g T A nft B nft A A t g

1 1

) 2 cos( ) ( 2 ) 2 sin( ) ( 2 ) ( 2 ) 2 cos( ) 2 sin( 2 ) ( π π π π

Nyquist’s Sampling Theorem

• The bit and the baud

– Using multiple signaling levels. Baud * log2(signaling levels) = bits/sec

• If a signal is passed through an arbitrary low pass

filter of bandwidth B, it can be reconstructed by a sampler collecting 2B samples/sec

– Reasoning: Frequency components higher than the sampling rate are already filtered out.

• Max data rate = 2B log2 V bits/sec,

– Where V is the number of discrete levels in the signal.

Thermal Noise: Shannon’s Theorem

• Nyquist theorem is used for noiseless channels.

– Real world communication channels are noisy. At the minimum, you have thermal noise

• Signal to Noise ration S/N is expressed in dB as

10log10(S/N).

– Recall the -3db cutoff point.

• Shannon’s Theorem:

– Max data rate = B log2(1+S/N) – This is an upper bound independent of the number of signaling levels and sampling rate.

Module at Node A Module at Node B “Link”

Point-to-Point Protocols and Links (1)

• Point-to-point protocols involve exactly two

peer entities or modules that are connected by some “link”

• The modules must interact to ensure the

proper transfer of information using the link

Point-to-Point Protocols and Links (2)

• For example, the link may be:

– Physical link (e.g. RS-232 is a point-to-point protocol) – Virtual bit pipe (e.g. at the data link layer) – A connection or virtual connection (e.g. at the transport or session layer)

Data Link Control -- DLC (1)

• For each point-to-point link in a network there are

two data link control (DLC) peer modules, one at each end

• DLC modules use a distributed algorithm to

transfer packets

– Received from and delivered the network layer

• Usual objective is to deliver packets in order of

arrival (from the network layer) without errors or repeated packets

Network DLC Physical Network DLC Physical

Data Link Control -- DLC (2)

• DLC modules must use the unreliable

“virtual bit pipe” provided by the physical layer

Data Link Control -- DLC (3)

• DLC must:

– Detect errors (using redundancy bits) – Request retransmission if data is lost (using automatic repeat request -- ARQ) – Perform framing (detect packet start and end) – Support initialization and disconnection

• perations

service data unit header trailer frame

Data Link Control -- DLC (4)

• These functions require that extra bits be added to

the packet to be transmitted

– Header bits are added to the front of each each packet – Trailer bits are added to the rear of each packet – The header, packet from upper layer (service data unit), and trailer form a frame

service data unit header trailer frame

Frame Format

• The packet from the upper layer is the service data

unit (SDU)

• The frame (header, network layer packet, and

trailer) is the protocol data unit (PDU)

• Note that the DLC does not care what is in the

network layer packet and the physical layer does not care what is in the frame generated by the data link layer