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the subject of communication systems is immense.

what is communication system?

the communication systems are designed to transfer information between transmitter and receiver. however, noise limits our ability to communicate. communication systems are designed to transmit information bearing waveforms to the receiver. and there are many possibilities for selecting waveforms to represent the information.

communication system designers have four main concerns:

• selection of the information-bearing waveform
• bandwidth and power of the waveform
• effect of system noise on the received information
• cost of the system

• 1. introduction
• 2.

• DC value
• root-mean-square (RMS) value
• normalized power
• magnitude spectrum
• phase spectrum
• power spectral density
• bandwidth

• in addition, effects of linear filtering

will be established.

• the DC value of a wave
  
   is given by its time average, thus

• for any physical wave, we are actually interested in evaluating the DC value only over a finite interval of interest. in such a case, the DC value is

power

• for physics, power는 energy을 단위시간으로 나눈 물리양이다. 이러한 기본개념을 바탕으로 여러 다양한 분야에서 각 학문영역에 적용되어 활용되고 있다. electrical field의 경우 voltage와 current에 의해서 power와 energy를 정의한다.

it is known that power is defined as work per unit time, voltage is work per unit charge, and current is charge per unit time. this is the basic for the definition of power in terms of electrical quantities.

• the instantaneous power is given by

• the average power is

• if a load is resistive (i.e. with unity power factor), the average power is

• using RMS value concept,

RMS (root-mean square) value of

for the case of district function, formula become

• computing average (normalized) power of sinusoidal waveform
  using RMS value concept, RMS value of sinusoidal waveform is
  
  .

• concept of normalized power is assuming that
  
   is
  
  .

instantaneous normalized power is
average normalized power is

• underlying ideas can be extended to nonperiodic phenomena. this leads to Fourier integrals and transforms. a common name for the whole area is Fourier analysis.
• in the most important of PDEs of physics and engineering is the area in which Fourier analysis has its most basic applications, related to boundary and initial value problems of mechanics, heat flow, electrostatics, and other fields.

Fourier analysis



Fourier series

• periodic function
• a function
  
   is called a periodic function if
  
   is defined for all real x (perhaps except at some points, like
  
   and if there is some positive number p, called a period of
  
  , such that

• first few case, we will study various functions
  
   of period
  
  .

• given function of period
  
  , Fourier series
• given function of period
  
   can be represented by a trigonometric series; Fourier series,

• coefficients of Fourier series are the so-called Fourier coefficients of
  
  , given by the Euler formulas

dddd

Fourier series expansion and function approximation

less..

lecture note. Partial fraction expansion and Fourier series expansion

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Partial fraction expansion
Fourier series expansion
     periodic function (definition and example)
     Fourier series representation of periodic function, f(x)
     Fourier series coefficient: Euler's formula when period is 2*pi and p

lecture note. function approximation and the square error of function, frequency and amplitude

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fourier series expansion of f(x)
approximation of f(x), f_N(x)
the square error of f_N(x), E_N: definition, derivation formula which in practrical using
limitation of the square error of f_N(x), E*: definition, parseval's equality
frequency and amplitude spectrum, derivation other form of fourier series
     frequency spectrum of f(x)
     nth harmonic frequency of f(x)
     amplitude spectrum of f(x)
     nth harmonic of f(x)

less..

sinc function

• the ESD is defined for energy waveforms by

where

 (FT pairs).

 has units of joules per hertz.

(FYI) chap 2. signals and spectra: useful wave characteristic, wave의 power에 대해 정리한 내용 참고. 

• the PSD for a deterministic power waveform is

where

 (FT paris).
and

 has units of watts per hertz.

• dial-up,
• landline (coaxial cable, fiber optic, copper wires),
• T-lines,
• Wi-Fi: IEEE 802.11 standard을 바탕으로 wireless devices 상호간 operatable(interoperability) 한 기기에 부여하는 TM
• stellite 
• cell phones.
  

dial-up internet access
dial-up internet access is form of internet access via telephone line(telephone network). the client uses a modem connected to a computer and a telephone line to dial into an ISP's node to establish a modem to modem link, which is then routed to internet.

• modern dial-up modems typically have a maximum theoretical speed of 56 kbit/s^[각주:1]
• 상용 전화선의 음성 데이터 처리와 model rate 사이의 상관관계

voice 주파수 대역 및 max frequency에 따른 nyquist frequency 는 8KHz 로 결정되었다. 샘플링되는 음성 신호의 quantization level은 256개 로서 2의 8승 개에 해당된다. 따라서 초당 처리 bit 는 8 KHz * 8 bits = 64 Kbits/sec.
오랫동안 64 Kbits/sec 로 통신을 하다가 음성신호의 전송은 8 bit가 아니라 7 bit로도 충분하다는 것을 발견하였다. 하지만 이미 8 bit의 규약으로 인프라(회선)가 건설되었기에 7 bit는 voice 전송을 위해 1 bit는 administration 목적을 위해 사용하고 있다. modem 의 경우 56 Kbit/s가 이론적인 최고 속도 (using the V.90 or V.92 protocol)

• broadband internet access

broadband internet access (or just broadband) is high data rate internet access - typically contrasted with dial-up access over a 56k modem. it is often called 'high speed' internet.

• DSL: ADSL (asymmetric digital subscriber line)

DSL is a family of technologies that provides digital data transmission over the wires of a local telephone network. DSL can be used at the same time and on the same telephone line with regular telephone, as it uses high frequency, while regular telephone uses low frequency.
ADSL is a data communications technology that enables faster data transmission over copper telephone lines than a conventional voiceband modem can provide.

landline


T-lines


Wi-Fi
Wi-Fi is a trademark for certified products based on the IEEE 802.11 standards. this certification warrants interoperability between different wireless devices. the term Wi-Fi is often used by the public as a synonym for WLAN; but not every wireless Lan product has a Wi-Fi certification, which may be because of certification costs that must be paid for each certified device type.

• Wi-Fi logo and practical example

(우) router, unicorn WB-1500N 의 제품상자에 표시되어 있는 Wi-Fi 로고

• Wi-Fi 에 대한 좀더 자세한 정보에 대해서는 별도의 posting을 통해 정리한다.

satellite


cell phone

큰제목 complex analysis에 대한 내용

many engineering problems can be modeled, investigated, and solved by functions of a complex variable. for simpler problems, such as simpler electric circuits and mechanical vibrating systems, some acquaintance with complex numbers will suffice. for more complicated problems in heat conduction, fluid flow, electrostatics, etc., one needs the theory of complex analytic function, briefly called complex analysis.

comlex analysis의 최종 목적은 analytic function을 이해하고 활용하는데 있다.
그러기 위해서 기본적인 complex number의 정의부터 시작하여 논의를 시작한다.

• in probability theory and statistics, correlation (ofter measured as a correlation coefficient) indicates the strength and direction of a linear relationship between two random variables. that is in contrast with the usage of the term in colloquial speech, denoting any relationship, not necessarily linear.^[각주:1]

• correlation functions contain information about the distribution of points or events, or things across some space/time.^[각주:2]
• a normalized correlation function for functions of time can be defined as,

when

 and

 represent the same function, this definition geves the auto-correlation, whereas when the represent separate functions, the cross correlation is determined.^[각주:3]

different definitions of auto-correlation are in use depending on the field of study.^[각주:4]

auto-correlation,

• cross-correlation function

• for binary sequences, it turns out that
  
   can be determined relatively simply by noting that the variable
  
   is the number of bits or digits by which the second sequence is shifted with respect to the first. then by comparing the two sequences bit by bit, the normalized correlation function is determined from