1 review of continuous-time fourier series. 2 example 3.5 t/2 t1t1 -t/2 -t 1 this periodic signal...
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1
Review of Continuous-Time Fourier Series
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Example 3.5
T/2T1-T/2 -T1
This periodic signal x(t) repeats every T seconds.x(t)=1, for |t|<T1 , and x(t)=0, for T1 <|t|< T/2
Fundamental period= T,Fundamental frequency Choosing the period of integration to be between-T/2 and +T/2. Use eqn 3.39 to get at Fourier Series Coefficients.
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Example 3.5 continued
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Continuous-Time Fourier Transform
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Continuous-Time Fourier Transform
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Bode Plotrepresentationof the FourierTransform of
an exponentialtime function
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Properties of Fourier Transform
• Linearity• Time Shifting• Conjugation• Differentiation in the time-domain• Integration in the time-domain• Time and Frequency Scaling.• Duality• Parseval’s Relation• Convolution• Multiplication
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FT Property associated with Linearity
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FT Properties associated with Time shifting & Conjugation
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FT Properties associated with Differentiation & Integration in Time Domian
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FT Properties associated with Time & Frequency Scaling.
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FT Properties associated with Duality
.||,1)(sin
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FT Properties –Duality continued.
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FT Properties – Duality continued.
}.{))(()(
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FT Properties-Duality continued
domian}.frequency in on {integrati
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FT Properties- Duality continued
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FT Property associated with Convolution in time domain
domain) (freqtion multiplicadomain) (timen convolutio
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)()(
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FT Property associated with Multiplication in time domain
domain.equency in time/fr
cation n/multipliconvolutio ofDuality
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