Fourier transform ( ) LED Audio Spectrum Analyzer. Fourier transform: Example. Asst. Prof. Dr. Prapun Suksompong

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ICT Elementary for Embedded Systems Signal/Electronic Fundamental Fourier Transform and Communication Systems Fourier transform ( ) The Fourier transform is a frequency domain representation of the

1 ICT Elementary for Embedded Systems Signal/Electronic Fundamental Fourier Transform and Communication Systems Fourier transform ( ) The Fourier transform is a frequency domain representation of the original signal. The term Fourier transform refers to both the frequency domain representation and the corresponding mathematical operation ( ). f t f f f f Asst. Prof. Dr. Prapun Suksompong prapun@siit.tu.ac.th t -f 0 f 0 f 1 9 LED Audio Spectrum Analyzer Fourier transform: Example t f t 8 [ 10

2 Euler s Formula Fourier Transform Pairs (1) 12 Complex exponential e j j ja ja ja Ae e e ja ja ja Ae e e j x x x x x x xx x x d x x dx xy x y x y (product-to-sum formula) x 17 Time Domain Frequency Domain j ft j ft gt G f e df G f gte dt e j f t f t t f f f -f 0 f f f f 0 f 0 f f (Continuous-Time) Fourier Transform Time Domain Frequency Domain j ft j ft gt G f e df G f gte dt Capital letter is used to represent corresponding signal in the frequency domain. j ft Complex exponential: e ft j ft g G f df G g t dt Fourier Transform Pairs (2) Time Domain Frequency Domain j ft j ft gt G f e df G f gte dt x x x

3 Fourier Transform Pairs (3) Time Domain Frequency Domain j ft j ft gt G f e df G f gte dt Modulation The term baseband is used to designate the band of frequencies of the signal delivered by the source. Modulation is a process that causes a shift in the range of frequencies in a signal. Motivation Frequency-Division Multiplexing (FDM) and Frequency-Division Multiple Access (FDMA) Reasonable antenna size for effective radiation of power over a radio link Communication channel matching (avoiding frequencies that suffer from large attenuation/distortion) More realistic signal 22 Important Properties of x yt xytd xtyd Convolution Properties: Shifting Properties: Modulation: x y X Y x y X Y j ft t f g t e G j ft e g t G f f g t t G f G f Note that the magnitude of this is simply f f f c c c

4 Simple Modulation Simple Modulation Message (modulating signal) fct Modulator Message (modulating signal) fct Modulator g t t G f G f f f f c c c c c c xt mt ft M f f M f f 23 M f fc M f f c 25 Simple Modulation Electromagnetic Spectrum [Gosling, 1999, Fig 1.1 and 1.2] c f Wavelength Frequency

5 [ Radio-frequency spectrum Commercially exploited bands LTE on iphones (sold in Thailand) Upto 150Mbps download speed. 27 c f Wavelength Frequency Note that the freq. bands are given in decades; the VHF band has 10 times as much frequency space as the HF band. More LTE bands help you benefit from the growing number of roaming agreements around the world 29 [ Cellular Support in iphone 6 FDD and TDD LTE frequency bands FDD LTE frequency band allocations TDD LTE frequency band allocations [

32 Terrestrial TV in BKK VHF.(Low Band) Channel Picture Bandwidth.. Carrier. Audio Carrier. 2 47-54 48.25 53.75 3 54-61 55.25 60.75 4 61-68 62.25 67.75 VHF.(Hight Band) Channel. Bandwidth. Picture Carrier.

6 32 Terrestrial TV in BKK VHF.(Low Band) Channel Picture Bandwidth.. Carrier. Audio Carrier VHF.(Hight Band) Channel. Bandwidth. Picture Carrier. Audio Carrier UHF.(Band 4) Channel. ( ) Bandwidth. Picture Carrier. Audio Carrier MUX 1 MUX 2 MUX 3 MUX 4 MUX 5 UHF.(Band 5) Channel Picture Bandwidth.. Carrier. Audio Carrier Upper limits on radio use GHz [Gosling, 1999, Fig 1.3] Make commu. very dependent on weather conditions Atmospheric absorption Atmospheric Opacity/Transparency Quasi-optical propagation Short wavelength = Deep shadows behind obscuring objects = Unreliable coverage. Increased absorption by building and structural materials Lower limits on radio use Efficiency of an antenna in radiating radio energy is dependent on its length expressed as a fraction of wavelength. Too low frequency = too large antenna Ex. The Sanguine submarine communication system 30 Hz (10,000 km wavelength) Designed (but never built) for the US Navy Base antenna: 24 km square mesh of wires. 10MW RF input Radiate only 147 W All the remainder of the power dissipates as heat. Spectrum Allocation Spectral resource is limited. Most countries have government agencies responsible for allocating and controlling the use of the radio spectrum. Commercial spectral allocation is governed globally by the International Telecommunications Union (ITU) ITU Radiocommunication Sector (ITU-R) is responsible for radio communication. in the U.S. by the Federal Communications Commission (FCC) in Europe by the European Telecommunications Standards Institute (ETSI) in Thailand by the National Broadcasting and Telecommunications Commission (NBTC; ;.) Blocks of spectrum are now commonly assigned through spectral auctions to the highest bidder. 33 [Gosling, 1999, p 11] 35

Spectrum Allocation (Final Words) y Spectrum is a scarce resource.

y Spectrum is allocated in chunks in frequency domain. y Chunks are licensed to (cellular/wireless) operators.

y Each channel has its own band of frequency.

y For example, AMPS, D-AMPS, N-AMPS and IS-95 all use the 36 38 2011 800 MHz frequency chunk.

7 Spectrum Allocation (Final Words) y Spectrum is a scarce resource. y Radio spectrum will be the first of our finite resources to run out, long before oil, gas or mineral deposits. y Spectrum is allocated in chunks in frequency domain. y Chunks are licensed to (cellular/wireless) operators. y Within a single cellular operator, the chunk is further divided into many channels. y Each channel has its own band of frequency. y Mobile networks based on different standards may use the same frequency chunk. y For example, AMPS, D-AMPS, N-AMPS and IS-95 all use the MHz frequency chunk. y This is achieved by the use of different channels. [ Oct 2012: Thailand 2.1GHz Auction Thailand Freq. Allocations Chart y 4.5bn baht per license (freq chunk) y 1 license (chunk) = 5 MHz (UL) + 5 MHz (DL) y 450 million baht per MHz y 30 million baht per MHz per year

LPF mt fct fct xt vt mt 44 Scaling and Suppressing Frequency Components DSB-SC (Zoomed in time) Note how

8 [Demo_DSBSC_Sound_ReadWAV.m] DSB-SC DSB-SC Message (modulating signal) Channel fct fct Modulator Demodulator LPF 42 Key equation: LPF mt fct fct xt vt mt 44 Scaling and Suppressing Frequency Components DSB-SC (Zoomed in time) Note how the baseband signal becomes the envelope of the modulated signal. Note how the high-frequency content is riding on top of the original baseband signal. Note the delay caused by the LPF

Electromagnetic silence in a town where wireless signals are forbidden 13,000 sq miles (33,000 sq km) National Radio Quiet Zone Green Bank, West Virginia Wi-Fi, cellphones, Bluetooth, AM radio are

Residents are allowed to use land-line phones and wired internet The only way anyone just passing through can reach the rest of the world is by using the pay phone on the side of a road in town Only

The Interference Protection Group was formed to hunt down rogue signals. Unforeseen newcomers Diane Schou She believed the cell-phone tower near her home in Iowa is the source of her illness.

She spent months living in a Faraday cage (shielded cage), a wood-framed box with metal meshing that blocked out cell signals. 46 49 Robert C.

9 Electromagnetic silence in a town where wireless signals are forbidden 13,000 sq miles (33,000 sq km) National Radio Quiet Zone Green Bank, West Virginia Wi-Fi, cellphones, Bluetooth, AM radio are banned under state law. Residents are allowed to use land-line phones and wired internet The only way anyone just passing through can reach the rest of the world is by using the pay phone on the side of a road in town Only diesel vehicles are allowed on-site, because a gasoline-powered engine s spark plugs give off interfering radiation. The cafeteria s microwave is kept in a shielded cage. The Interference Protection Group was formed to hunt down rogue signals. Unforeseen newcomers Diane Schou She believed the cell-phone tower near her home in Iowa is the source of her illness. Symptoms range from acute headaches, skin burning, muscle twitching and chronic pain. She spent months living in a Faraday cage (shielded cage), a wood-framed box with metal meshing that blocked out cell signals Robert C. Byrd radio telescope Green Bank is the site of the gigantic Robert C. Byrd radio telescope. In recent years, the telescopes have been used to track NASA s Cassini probe to Saturn s moon and to examine Mercury s molten core. So sensitive that it can pick up the energy equivalent of a single snowflake hitting the ground. Even a basic AM radio transmission is enough to overpower faint readings from outer space. Unforeseen newcomers Electrosensitivity Formally, Electromagnetic Hypersensitivity (EHS) Or Idiopathic environmental intolerance attributed to electromagnetic fields (IEI- EMF) 5%? of Americans. (Estimates vary widely.) Claim that exposure to electromagnetic fields (EMF) (typically created by mobile phones, wi-fi and other electronic equipment) makes them physically ill. Whether EHS is real is still debatable. Not medically recognized in the US. Sweden is the first country to recognize EHS as a disability. Since 2007, electrosensitives started to move into Green Bank. Electrosensitives demands clash with locals. They demand that local businesses uninstall fluorescent lights, and want a church to stop using wireless microphones [ [ [ [

Many extremely successful wireless systems operate in unlicensed bands, including wireless LANs, Bluetooth, and cordless phones.

10 [TseViswanath, 2005, Section 4.1] 53 Unlicensed bands Frequency bands that are free to use according to a specific set of etiquette rules. The purpose of these unlicensed bands is to encourage innovation and low-cost implementation. Many extremely successful wireless systems operate in unlicensed bands, including wireless LANs, Bluetooth, and cordless phones. Major difficulty: If many unlicensed devices in the same band are used in close proximity, they generate much interference to each other, which can make the band unusable. 55 Licensed vs. Unlicensed Spectra Licensed Typically nationwide. Over a period of a few years. From the spectrum regulatory agency. Bandwidth is very expensive. No hard constraints on the power transmitted within the licensed spectrum but the power is expected to decay rapidly outside. Provide immunity from any kind of interference outside of the system itself. Unlicensed For experimental systems and to aid development of new wireless technologies. Very cheap to transmit on. There is a maximum power constraint over the entire spectrum. Have to deal with interference. 54 Unlicensed bands (2) Unlicensed spectrum is allocated by the governing body within a given country. Often countries try to match their frequency allocation for unlicensed use so that technology developed for that spectrum is compatible worldwide. The following table shows the unlicensed spectrum allocations in the U.S. (ISM = Industrial, Scientific, and Medical) 900 MHz 2.4 GHz 5.8 GHz 5 GHz 5 GHz 5.8 GHz (U-NII = Unlicensed National Information Infrastructure) 56 Ex. Wi-Fi Standards a/b/g/n operate in the 2.4 GHz band n optionally supporting the 5 GHz band. The new ac standard mandates operation only in the 5 GHz band. 2.4 GHz band is susceptible to greater interference from crowded legacy Wi-Fi devices as well as many household devices. The 5 GHz band has relatively reduced interference and there are a greater number of nonoverlapping channels available (25 non-overlapping channels in US) compared to the 2.4 GHz band (3 non-overlapping channels in the US).

2.4 GHz has > 10 Channels? 2.4 GHz Channels in Various Parts of the World 57 59 [Sohraby, Minoli, and Znati, 2007] 2.4 GHz has > 10 Channels? The 802.

Channel 14, where available, is restricted to 802.11b operation only. [http://www.ieeeghn.org/wiki/index.php/wireless_lan_802.

11 2.4 GHz has > 10 Channels? 2.4 GHz Channels in Various Parts of the World [Sohraby, Minoli, and Znati, 2007] 2.4 GHz has > 10 Channels? The b Spectral Mask 58 The channels are spaced 5 MHz apart. In the US, FCC regulations permit channels 1 to 11 to be used. Channels 10 and 11 are the only channels which are common throughout the world. Channel 14, where available, is restricted to b operation only. [ Can many networks generally operate in close proximity without interfering with each other? 60 Simulated spectrum of a filtered 1 Mbps transmission [Maxfield and Bird, 2008] The b (and g) standards do not specify the width of a channel. Rather, they specify the center frequency of the channel and a spectral mask for that channel. The energy radiated by the transmitter extends well beyond the 22-MHz bandwidth of the channel (11 MHz from f c ). At 11 MHz from the center of the channel, the energy must be 30 db lower than the maximum signal level. At 22 MHz away, the energy must be 50 db below the maximum level.

WiFi in the 2.4 GHz bands It is common to hear that channels 1, 6 and 11 do not overlap.

attenuated to minimally interfere with a transmitter on any other channel. Same for any two channels that are 5 or more ch. numbers away.

11g Spectral Mask At 11 MHz from the center, the transmitter energy level is only 20 db below the maximum (as opposed to 35 db for 802.

12 WiFi in the 2.4 GHz bands It is common to hear that channels 1, 6 and 11 do not overlap. It is more correct to say that, given the separation between channels 1, 6, and 11, the signal on any channel should be sufficiently attenuated to minimally interfere with a transmitter on any other channel. Same for any two channels that are 5 or more ch. numbers away. Tools such as Vistumbler or inssider can help you visualize the WiFi landscape g Spectral Mask At 11 MHz from the center, the transmitter energy level is only 20 db below the maximum (as opposed to 35 db for b) At 22 MHz away, the energy is only about 30 db below (as opposed to 50 db for b). Even as far out as 40 MHz, the energy is still only 40 db below the maximum Spectral Mask Comparison 62 [ 64

introduced by the channel Receiver Channel Decoder Digital Modulator Map digital sequence to analog signal Digital Demodulator Channel Transmitted Signal Received Signal Noise&Interference 65 67 66

13 5 GHz Band Channels Elements of digital commu. sys. Message Transmitter Information Source Recovered Message Destination Source Encoder Remove redundancy (compression) Source Decoder Channel Encoder Add systematic redundancy to combat errors introduced by the channel Receiver Channel Decoder Digital Modulator Map digital sequence to analog signal Digital Demodulator Channel Transmitted Signal Received Signal Noise&Interference Unlicensed 60 GHz Frequency Band A lot of bandwidth available Worldwide spectrum availability Even for the smallest allocation, there is more than 3 GHz of bandwidth available, and most regions allow use of at least 7 GHz. In comparison, the 5 GHz unlicensed band has about 500 MHz of total usable bandwidth. The 2.4 GHz band has less than 85 MHz of bandwidth in most regions. 68 Information Source Destination Digital Modulation/Demodulation Message Recovered Message Source Encoder Remove redundancy (compression) Source Decoder Transmitter Channel Encoder Add systematic redundancy to combat errors introduced by the channel Receiver Channel Decoder Digital Modulator Map digital sequence to analog signal Digital Demodulator Channel Transmitted Signal Received Signal Noise&Interference

14 Simple ASK: ON-OFF Keying (OOK) Digital Modulator? ASK: Higher Order Modulation Digital Modulator? f c = 4 Hz Bit rate = 1 bps t f c = 100 Hz Bit rate = 20 bps [ASK_playTones_Demo.m] t 71 f c = 100 Hz Symbol rate = 20 symbols per second Bit rate = 40 bps Simple ASK : ON-OFF Keying FSK M = 4 f f f f f c Smoke signal [FSK_playTones_Demo.m]

FSK 11110011100001101111 Digital Modulator?

15 FSK Digital Modulator? Spectrum of ON-OFF Keying M = 4 f f f f f c [ ] [ ] Hz f c = 100 Hz Bit rate = 1 bps 73 [FSK_playTones_Demo.m] 75 FSK Digital Modulator? Five Frequencies M = 4 f f f f f c [ ] [ ] Hz Each tone lasts 1/R s sec. Rate = R s frequency-changes per second 74 [FSK_playTones_Demo.m] 76

16 Spectrum of Five Frequencies Spectrum of ON-OFF Keying 100 Hz 200 Hz 300 Hz 400 Hz 500 Hz M = R s = 0.5 f c = 5 Hz R s = Cos vs. Cos Pulse Spectrum of ON-OFF Keying otherwise M = f c = 100 Hz R s = 1

17 Spectrum of ON-OFF Keying Spectrum of Five Frequencies (2/5) M = 2 f c = 100 Hz R s = R s = Hz 200 Hz 300 Hz 400 Hz 500 Hz Spectrum of Five Frequencies (1/5) Spectrum of Five Frequencies (3/5) 100 Hz 200 Hz 300 Hz 400 Hz 500 Hz 100 Hz 200 Hz 300 Hz 400 Hz 500 Hz R s = 0.5 R s =

18 Spectrum of Five Frequencies (4/5) Spectrum of FSK (1/2) 100 Hz 200 Hz 300 Hz 400 Hz 500 Hz Freq. = [ ] Hz R s = 50 M = 4 R s = Spectrum of Five Frequencies (5/5) Spectrum of FSK (2/2) 100 Hz 200 Hz 300 Hz 400 Hz 500 Hz Freq. = [ ] Hz M = 5 R s = 0.5 R s =

ECS 455 Chapter 1 Introduction & Review

ECS 455 Chapter 1 Introduction & Review 1.4 Spectrum Allocation 1 Dr.Prapun Suksompong prapun.com/ecs455 Office Hours: BKD 3601-7 Tuesday 9:30-10:30 Tuesday 13:30-14:30 Thursday 13:30-14:30 Electromagnetic