Introduction to Communications Prof. R. C. T. Lee National Chi Nan University

Fourier Transform

What does the above signal contain?

A Music Signal

What does the above signal contain? For human voice signals, Fourier Transform shows that the significant frequency components are under 3k Hertz. This in turn means that the wavelength of the signal is around meters. Again, this means that the antenna has to be exceedingly long.

What does the above signal contain? This means that the human voice can not be transmitted wirelessly because of the problem about the required length of the antenna. This leads to the concept of modulation.

(a) Rectangular pulse in time. (b) The FT of x(t).

This means that a smaller width of the impulse will imply the existence of higher frequencies. Smaller width also means higher bit rate. This is why a transmission line transmitting a large number of pulses in one second is called the broadband system.

Modulation The main effect of modulation is to increase the frequency of the signals significantly such that a wireless transmitting of these signals can be done.

Modulation Modulation: The letter is put onto a horse by the person who wants to deliver the letter. Demodulation: The letter is taken down from the horse by the person who receives the letter.

Amplitude Modulation m(t): signal to be transmitted (baseband signal, usually of relatively low frequency) c(t): the carrier wave signal (usually of relatively high frequency)

For AM broadcast, fc is in the range of 500k to 1.6 Amplitude Modulation For AM broadcast, fc is in the range of 500k to 1.6 mega Hertz

Amplitude Modulation (a) Baseband signal m(t) (b) AM wave for all t (c) AM wave for for some t

Demodulation Envelop detector

Demodulation (a) The message signal (b) The AM signal (c) The demodulated signal

Demodulation (a) Spectrum of baseband signal (b) Spectrum of AM wave

Double Sideband (DSB)

Double Sideband (DSB) The RC-ckt can no longer be used to demodulate (a) The message signal (b) The DSB-SC modulated signal

Double Sideband (DSB) Spectrum of the message signal (b) Spectrum of the DSB-SC modulated signal

Double Sideband (DSB) Demodulation

Double Sideband (DSB) Coherent detection of DSB-SC modulated signal

Double Sideband (DSB) Illustrating the spectrum of the demodulation process

Frequency Modulation We change frequency, instead of amplitude.

Frequency Modulation Sinusoidal message signal (b) Carrier wave (c) Frequency-modulated signal

Frequency Modulation Demodulation: After differentiation

Frequency Modulation Block diagram of a slope detector for FM demodulation

Frequency Modulation The envelope of v(t) is

Digital Modulation Baseband Pulse Transmission

Digital Modulation Amplitude Shift Keying

Digital Modulation Phase Shift Keying Demodulation

Digital Modulation Coherent detector for BPSK Threshold x Say “1” if x> decision device Say “0” if x< Coherent detector for BPSK

Digital Modulation (a) Transmitted signal (b) The signal (c) The output of the correlator and the corresponding sampling points

Digital Modulation Frequency Shift Keying

Digital Modulation FSK

Digital Modulation FSK Demodulation

Digital Modulation FSK if 1 is transmitted, . if 0 is transmitted, .

Digital Modulation FSK

Digital Modulation FSK Coherent detector for FSK system

Digital Modulation FSK

Multiple Access Communication Frequency Division Multiple Access(FDMA)

Multiple Access Communication Spectrum of an FDMA system

Multiple Access Communication Time Division Multiple Access(TDMA)

Multiple Access Communication Code Division Multiple Access(CDMA)

Multiple Access Communication CDMA : Two users : 1 and 2.   User i transmits to send 1 and to send 0.

Multiple Access Communication CDMA To find what (i=1,2) is, we multiply r(t) by and integrate

Multiple Access Communication CDMA  

Multiple Access Communication CDMA

Multiple Access Communication K-User CDMA System

Multiple Access Communication Carrier Sense Multiple Access (CSMA)

Electromagnetic Waves (Maxwell Equations) Solution:

Electromagnetic Waves (Maxwell Equations) A wave at t=0

Electromagnetic Waves (Maxwell Equations) A wave at t=t

Electromagnetic Waves (Maxwell Equations) The Electric and Magnetic Fields in a Plane Electromagnetic Wave

Electromagnetic Waves (Maxwell Equations) Hertz, f = 1800 mega Hertz (mobile phone),  

Transmission Lines A Co-Axial Cable Transmission Line.

Transmission Lines Twin-Strip Parallel Plate Transmission Line.

Transmission Lines An Equivalent Circuit of a Lossless Transmission Line.

Transmission Lines

The Waves on a Transmission Line.

Without great mathematicians such as Fourier, Maxwell and so on, there can be no modern communication technology. Even the ADSL technology is based upon the Fourier transform.