Derive fourier series for constant function
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f(x)≈A02+∑∞1Ancos(2πLnx)+Bnsin(2πLnx)f(x)≈A02+∑1∞Ancos(2πLnx)+Bnsin(2πLnx)
If f(x)f(x) is equal to a constant; f(x)=cf(x)=c, it should be clear that the sines and cosines must have no contribution to the Fourier series. Their coefficients An,Bn,if n>0An,Bn,if n>0 are zero.
Then the Fourier series reduces to f(x)≈A02f(x)≈A02, a constant.
If f(x)f(x) is equal to a constant; f(x)=cf(x)=c, it should be clear that the sines and cosines must have no contribution to the Fourier series. Their coefficients An,Bn,if n>0An,Bn,if n>0 are zero.
Then the Fourier series reduces to f(x)≈A02f(x)≈A02, a constant.
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