EE3008_Lecture2 - 1 Lecture 2 Deterministic Signal Analysis...

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1 Lecture 2. Deterministic Signal Analysis • Fourier Transform • Energy Spectrum, Power Spectrum and Signal Bandwidth • Signal Transmission through a Linear System Lin Dai (City University of Hong Kong) EE3008 Principles of Communications Lecture 2
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2 Signals in Time Domain ü Periodic signal vs. Aperiodic signal 2 | ( ) | s E s t dt −∞ = /2 2 /2 1 lim | ( ) | T s T T P s t dt T →∞ = ü Continuous-time vs. Discrete-time signal A signal is a set of data or information, which can be represented as a function of time : ( ) s t ü Signal Energy: ü Signal Power: Signal Classification: Deterministic signal is a signal whose physical description is known completely, either in a mathematical form or a graphical form. ü …… Lin Dai (City University of Hong Kong) EE3008 Principles of Communications Lecture 2
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3 Signals in Frequency Domain f f 0 Time domain Frequency domain f nf 0 n s t • Periodic signal with fundamental period 1/ f 0 : ( ) S f Lin Dai (City University of Hong Kong) EE3008 Principles of Communications Lecture 2 s ( t ) = s n e j 2 π nf 0 t n = −∞ s ( t ) = cos(2 π f 0 t )
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4 Fourier Transform Lin Dai (City University of Hong Kong) EE3008 Principles of Communications Lecture 2
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5 Given a time domain signal s ( t ), its Fourier transform is defined as follows. Fourier transform : The time domain signal s ( t ) can be expressed by S ( f ) using an inverse transform. Inverse Fourier transform : ( ) 2 ( ) j ft S f s t e dt π −∞ = ( ) 2 ( ) j ft s t S f e df π −∞ = ( ) S f Fourier Transform (Fourier) spectrum of s ( t ) : Magnitude spectrum of s ( t ) : ( ) S f s ( t ) S ( f ) Lin Dai (City University of Hong Kong) EE3008 Principles of Communications Lecture 2
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6 Example 1: Spectrum of Unit Impulse ( ) 1 t dt δ −∞ = is a unit impulse, which is zero everywhere except at t =0 , and has unit area. and S ( f ) = δ ( t ) e j 2 π ft dt −∞ = 1 f 1 S ( f ) 0 t ε 0 1/ ε →∞ area =1 1 s ( t ) 0 t ( ) ( ) s t t δ = Lin Dai (City University of Hong Kong) EE3008 Principles of Communications Lecture 2 δ ( t ) δ ( t ) δ ( t ) δ ( t ) = t = 0 0 t 0
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