Lecture3

# Lecture3 - A Volts Complex Fourier Series and Line Spectra...

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Fourier Transform and Spectra
Fourier Transform and Spectra w(t) here is a periodic function (x To on the first slide)

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Definition W(t) here refers to the non periodic signal (x(t) on the first slide)
Fourier Transform and Spectra

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Complex function In general the Fourier transform ) ( t w of a function is complex, even if that function ) ( t w is real.
Inverse transform and conditions for existence In general the Fourier transform ) ( t w of a function is complex, even if that function ) ( t w is real.

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Example 2-2 SPECTRUM OF AN EXPONENTILA PULSE By means of direct integration find the Fourier transform of ) ( t w < = - 0 , 0 0 , ) ( t t e t w t Properties of Fourier Transforms
Parseval’s Theorem Definition

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Example 2-3 SPECTRUM OF A DAMPED SINUSOID < = - 0 , 0 0 , 0 , sin ) ( 0 / t T t t e t w T t ϖ
FOURIER TRANSFORM THEOREMS

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Dirac Delta and Unit Step Function Or
Unit Step Function

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SPECTRUM OF A SINEWAVE Find the spectrum of a sinusoidal voltage that has a frequency 0 f and a peak value of

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Unformatted text preview: A Volts Complex Fourier Series and Line Spectra Rectangular and Triangular Pulses Rectangular and Triangular Pulses Rectangular and Triangular Pulses SOME FOURIER TRANSFORM PAIRS Spectra of rectangular, (sinx)/x, and triangular pulses Spectra of rectangular, (sinx)/x, and triangular pulses Convolutiom Energy Spectral Density review Definition Being Energy Signal I sufficient condition for existence In general the Fourier transform ) ( t w of a function is complex, even if that function ) ( t w is real. What about power signals? ) ( t w is a power waveform if the normalized average power P is finite and nonzero. ) ( t w is an energy waveform if the normalized energy E is finite and nonzero. We are assuming the power signal has a Fourier Transform in the limit Power Spectral Density Power Spectral Density Periodic Signals Power Spectral Density Polar Fourier Series...
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Lecture3 - A Volts Complex Fourier Series and Line Spectra...

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