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Fourier Series Calculator

Compute partial Fourier series values

Fourier Series Calculator

The calculator evaluates f(x) = a0/2 + Σ [an cos(nωx) + bn sin(nωx)] with ω = 2π/T.

Separate coefficients with commas (e.g., 1, 0.5, -0.25). Leave blank if not needed.

Separate coefficients with commas (e.g., 1, 0.5, -0.25). Leave blank if not needed.

How to Use

  1. Enter the DC term a0 and comma-separated an/bn coefficients.
  2. Specify the fundamental period and the point x where you want to evaluate the series.
  3. Run the calculator to see the partial sum, harmonic tally, and contribution table.

Interpreting the coefficients

Each an coefficient scales the cosine term for harmonic n while each bn coefficient scales the sine term. Longer coefficient lists mean more harmonics and a closer match to the underlying signal.

Practical tips

  • Keep units consistent: x and the period must use the same units.
  • Leaving an or bn blank is equivalent to setting all terms to zero.
  • Symmetric signals often have either only cosine or only sine terms, so you can omit the other list.

Frequently Asked Questions

How many harmonics can I enter?
Enter as many comma-separated coefficients as you need. The calculator evaluates up to the longest list of an or bn values.
Does the tool integrate or differentiate the series?
No. It focuses on evaluating the partial sum at a specific x using the coefficients you provide.

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