Question

Provide the steps and calculations involved in determining the Fourier series representation for a square wave signal. Include any relevant formulas and coefficients.

Answer 1

To determine the Fourier series for a square wave signal, one must write it as a sum of sine functions, calculate the coefficients via integration for each odd harmonic, and write the series sum.

Step-by-step explanation:

The Fourier series representation for a square wave signal involves writing it as a sum of sinusoidal functions. Here are the steps and calculations:

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3. Write down the square wave signal, specifying its period, amplitude, and any phase shifts.
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6. Calculate the Fourier coefficients. For a square wave, only the sine terms (odd harmonics) will be present, and the coefficients are given by:
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9. An = (2/A) ∫ f(x) sin(nx) dx for n=1,3,5,...
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12. Integrate over one period of the square wave to find the coefficients.
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15. Write the Fourier series sum using the coefficients and the sine functions for the odd harmonics: f(x) = A0/2 + Σ An sin(nωt + φn), where ω is the fundamental angular frequency and φn the phase angle for the nth term.

Calculating the coefficients involves integrating the product of the square wave function and the sin(nx) function over one period of the wave