The Fourier expansion of an odd function F(1) must use sines instead of cosines: 2. 2nRI de F(r) = Bn sin with Bn = F(x) sin %3D %3D nere, the B are the Fourier coefficients. Consider the square wave...

The Fourier expansion of an odd function F(1) must use sines instead of cosines:<br>2.<br>2nRI<br>de<br>F(r) = Bn sin<br>with<br>Bn =<br>F(x) sin<br>%3D<br>%3D<br>nere, the B are the Fourier coefficients. Consider the square wave shown below as an example of a<br>periodic odd function F(r). (a) Write down an expression for F(r) valid for the range 0<r< A. (b) by<br>evaluating the integral in the equation above, show that the Fourier coefficients B, for this square wave<br>are given by<br>f(r)<br>a = X/2<br>0.<br>for even n<br>Bn =<br>%3D<br>A<br>4A<br>for odd n<br>nR<br>

Extracted text: The Fourier expansion of an odd function F(1) must use sines instead of cosines: 2. 2nRI de F(r) = Bn sin with Bn = F(x) sin %3D %3D nere, the B are the Fourier coefficients. Consider the square wave shown below as an example of a periodic odd function F(r). (a) Write down an expression for F(r) valid for the range 0<>< a.="" (b)="" by="" evaluating="" the="" integral="" in="" the="" equation="" above,="" show="" that="" the="" fourier="" coefficients="" b,="" for="" this="" square="" wave="" are="" given="" by="" f(r)="" a="X/2" 0.="" for="" even="" n="" bn="%3D" a="" 4a="" for="" odd="" n="">

Jun 04, 2022

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The Fourier expansion of an odd function F(1) must use sines instead of cosines: 2. 2nRI de F(r) = Bn sin with Bn = F(x) sin %3D %3D nere, the B are the Fourier coefficients. Consider the square wave...

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