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.
Table of Contents
How to Use
- Enter the DC term a0 and comma-separated an/bn coefficients.
- Specify the fundamental period and the point x where you want to evaluate the series.
- 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.