ece306-2 - ECE 306 -2 ECE 306 Continuous-Time and...

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1 ECE 306-2 1 ECE 306 Continuous-Time and Discrete-Time Signal Sampling of Analog Signals Z. Aliyazicioglu Electrical and Computer Engineering Department Cal Poly Pomona ECE 306 -2 ECE 306-2 2 Outline •C o n t i n u o u s T im e S i g n a l • Discrete-Time Sinusoidal Signal • Analog-to-Digital Conversion (ADC) • Sampling of Analog Signals
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2 ECE 306-2 3 Continuous Time Signal Let s have the following continuous-time sinusoidal signal: () cos ( ) , a xt A t t θ =Ω + < < where A : the amplitude of the signal : the frequency in radians per second θ : the phase in radians The frequency can be expressed in cycles/s or Hertz (Hz) 2 F π = The period is define as 1 p T F = ECE 306-2 4 Continuous Time Signal The analog sinusoidal signal can repeat every period T p θ A ( ) ap a x tT xt + = Increasing the frequency means decreasing the period of the signal, so that increase the rate of oscillation of the signal
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3 ECE 306-2 5 Continuous Time Signal The analog sinusoidal signal can be expressed in complex exponent for as () cos ( ) 22 jt a A A xt A t e e θ +− + =Ω + = + Re Im t+ θ -( t+ θ ) A/2 A/2 ECE 306-2 6 Discrete-Time Sinusoidal Signal A discrete-time sinusoidal signal may be expressed as ( ) cos( ), xn A n n ω =+ < < where n : integer variable A : the amplitude of the signal ω : the frequency in radians per sample θ : the phase in radians The frequency can be expressed in cycles per sample 2 f π = c o s ( 2 ) , x nA f n n = < < and the signal is
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4 ECE 306-2 7 Discrete-Time Sinusoidal Signal A sinusoidal signal with the amplitude A, frequency ω = π /6 radians per sample (f=1/12) and phase θ = π /3 Example:
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This note was uploaded on 03/11/2008 for the course ECE 306 taught by Professor Aliyazicioglu during the Winter '08 term at Cal Poly Pomona.

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ece306-2 - ECE 306 -2 ECE 306 Continuous-Time and...

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