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Understanding Fourier Series and Synthesis in Signal Representation

In today's lecture, we delve into the representation of the spectrum of synthetic vowels as periodic signals. We explore Fourier series synthesis, detailing how any periodic signal can be synthesized using a sum of harmonically related sinusoids. Key concepts include properties of the exponential function, Fourier coefficients, and the Fourier analysis equation, which is essential for performing Fourier analysis. We also highlight the integral properties and orthogonality of exponential functions. Finally, we present an example of harmonic signals and their synthesis strategies.

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Understanding Fourier Series and Synthesis in Signal Representation

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Presentation Transcript

  1. Today's lecture • Spectrum Representation • Synthetic Vowel as a Periodic Signal • Fourier Series Synthesis • Properties of exp(j) • Fourier coefficients

  2. Spectrum Representation • Fourier Series (3-4) • Any periodic signal can be synthesized with a sum of harmonically related sinusoids • Fourier series/ Fourier Synthesis Equation • Fourier series integral (to perform Fourier analysis) is known as Fourier Analysis Equation • Fourier series coefficients

  3. Fourier Series Synthesis

  4. Synthesis Example: Harmonic Signal (3 Frequencies)

  5. Strategy: x(t)---->ak

  6. Synthesis Vs. Analysis

  7. Integral Property of exp (j)

  8. Orthogonality of exp (j)

  9. Isolate one FS Coefficient

  10. Beautiful Belief: • Jab meri DUA qabool ho tu khushi hoti hay kay is main meri marzi hay…..aur jab na ho tu khushi or bhi barh jati hay kay is main allah ki marzi hay(HAZRAT ALI R.A)

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