Joseph Fourier s claim: all signals are sums of sinusoids of differen frequencies. weighed sine curves weigh: ampliude of sine curve all : no exacly bu doesn maer for us in pracice
Example: 3 sin() + sin(*) + sin(3*) 1-1 - -3 4 6 8 1 1 14 3 sin() 1-1 - -3 4 6 8 1 1 14 3 sin(*) 1-1 - -3 4 6 8 1 1 14 3 sin(3*) 1-1 - -3 4 6 8 1 1 14
Top signal equals sin +sin +sin3 frequencies 1 Hz, Hz, and 3 Hz weigh?
Anoher example: signal creaed by sin +3sin +sin3 6 sin() + 3 * sin(*) + sin(3*) 4 - -4-6 4 6 8 1 1 14 frequency 1 Hz: weigh 1 frequency Hz: weigh 3 frequency 3 Hz: weigh 1 Weighs of sine curves are called specrum of he signal hey creae. specrum: a lis or able of weighs like DNA (or fingerprin/signaure) of signal
Ye anoher example: signal creaed by sin 1 + 3 sin + sin 3 6 sin(1 * ) + 3 * sin( *) + sin(3 *) 4 - -4-6 4 6 8 1 1 14 specrum of signal?
Anoher view of specra: signals creaed by.1 sin 1 +sin +.1 sin 3.5 sin 1 +sin +.5 sin 3 sin 3.1 * sin(1 * ) + 1 * sin( *) +.1 * sin(3 *) 1-1 - -3 4 6 8 1 1 14 3.5 * sin(1 * ) + 1 * sin( *) +.5 * sin(3 *) 1-1 - -3 3 4 6 8 1 1 14 sin(*) 1-1 - -3 4 6 8 1 1 14
Sine curves wih small weighs in a specrum don conribue much may be ignored rea as if weighs were zero same aiude as compression (video, image, audio) called lossy compression lossless compression?
Back o neworking: pure sine curve of frequency f = 1 MHz pure sine curve morphed ino 1 1 1 no a sine curve anymore specrum before ampliude modulaion? specrum aferwards?
Specrum before and afer ampliude modulaion o ransmi bis: weigh (ampliude) 1 frequency (MHz) weigh (ampliude) afer modulaion o carry bis 1 frequency (MHz) Ac of morphing sine curve o carry bis inroduces energy around carrier frequency. amoun of spreading: called bandwidh of signal
If spreading is limied: zero or near zero beyond a cerain poin signal is called bandlimied much of communicaion engineering deals wih bandlimied signals Quesion: can he amoun of spreading depend on he daa (i.e., bi paern) being carried by a carrier frequency? Quesion: wha is he negaive impac of spreading?
Iner-channel inerference (ICI): wo parallel bi sreams carried on wo carrier frequencies 1 MHz and 11 MHz Good case: weigh (ampliude) 1 11 frequency (MHz) parallel bi sreams weigh (ampliude) 1 11 frequency (MHz) signal bandwidhs around 1 MHz and 11 MHz don overlap: no ICI
Bad case: weigh (ampliude) 1 11 frequency (MHz) iner channel inerference (ICI) weigh (ampliude) frequency (MHz) 1 11 signal bandwidhs around 1 MHz and 11 MHz overlap ampliude deeced by receiver is disored ICI resuling in bi flips
Overlap (i.e., inerference) causes weighs from he wo specra o be added disorion of original weigh values bi flips likely bi value 1 or is represened by weigh (ampliude) How o preven ICI?
Allocae sufficien spacing guardband beween adjacen carrier frequencies. Drawback: limis how many carrier frequencies can be squeezed in a given frequency range. e.g., 1 MHz 1 MHz esimaing guardband is par of hardcore radio engineering limiaion of radiional FDM
Recen advance: acually a small revoluion orhogonal FDM (OFDM) used in high-speed wired and wireless sysems (e.g., ADSL, WiFi, cellular) he sae-of-he-ar using carrier sine curves ha are orhogonal o each oher, can overcome radiional guardband requiremen orhogonal: a righ angles
Similar idea also used in CDMA wireless neworks (e.g., Verizon, Sprin) wha remains: CDMA followed by OFDM covers sae-of-he-ar hopefully will las a few decades Quesion before moving on: modulaion ha spreads signal specrum is no good can cause ICI however: are here scenarios where spreading is a good hing?
Guardband example: IEEE 8.11 WLAN U.S.: 11 channels for.4 GHz sysems channel: analogous o carrier frequency.41,.417,.4,.47,.43,.437,.44,.447,.45,.457,.46 GHz channel separaion mus be a leas by 5 channels o avoid iner-channel inerference (ICI) oherwise bleeding over and bi flips hree ho spos in neighboring coffee houses: 1, 6, 11 same in office buildings, residenial areas