Derive expressions for the amplitude An and phase angle n of the Fourier series of the sawtooth

Derive expressions for the amplitude An and phase angle ϕn of the Fourier series of the sawtooth wave in Figure 13–4. Sketch the amplitude and phase spectra of a sawtooth wave with A= 5 and T0 = 4 ms

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Waveform Constant (dc) A Fourier Coefficients a=0 all n b=0 all Cosine wave fit) -To- AM Sine wave f(r) AL-To- AM Square wave K(1) A a=0 a = A 4 01 ba=0 all n Q=0 =0 all b = A b=0n 1 4 =0 4-0 all n To- b = nodd b=0 neven Rectangular pulse fin To A AT an=24sin (XT) b=0 all Waveform Fourier Coefficients Sawtooth wave fir) %=0 all in all n To Triangular wave -To- -A 9=0 a = 81 (x) %=0 b=0 nodd even Half-wave rectified sine wave a = fit) 2A/x even 1-2 A-T- Full-wave rectified sine wave =0 odd b =4 a=1 b=0 1 %=2A/x 4A/x 1-2 neven %=0 b=0 odd Parabolic wave =0 Q=0 all n 32A b = nodd (x3 b=0 neven