Two square-wave signals share the same period but have different amplitudes: and

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Fourier analysis and integral transforms · Fourier analysis and integral transforms

Mathematical Methods for Physics, Ch Fourier series and periodic decomposition

Problem

Two square-wave signals share the same period

L = 4.0\,\mathrm{ms}

but have different amplitudes:

A_1 = 3.0\,\mathrm{V}

and

A_2 = 9.0\,\mathrm{V}

. For a Fourier partial sum with

N = 9

non-zero terms, the peak beside the jump has height

1.180A

at position

x = L/(4N)

. ((a)) Find the peak voltage of the

N=9

partial sum for each signal. ((b)) Find the (common) position of that peak, and state the ratio of the two peak voltages.

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