Today's lecture Spectrum Representation

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Presentation transcript:

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

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

Fourier Series Synthesis

Synthesis Example: Harmonic Signal (3 Frequencies)

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

Synthesis Vs. Analysis

Integral Property of exp (j)

Orthogonality of exp (j)

Isolate one FS Coefficient

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)