Fourier Series Calculator

The Fourier Series Calculator allows users to compute and analyze the Fourier series coefficients, expression, and RMS value for various periodic waveforms such as square, sawtooth, and triangle waves given the period, amplitude, and number of terms.

Use Our Fourier Series Calculator

Using the Fourier Series Calculator

Step 1: Select Function Type

Start by selecting the type of waveform you want to analyze with the Fourier Series. The available options are:

  • Square Wave
  • Sawtooth Wave
  • Triangle Wave

This choice determines how the Fourier coefficients will be computed. Ensure you select the correct function type as it is a required field.

Step 2: Input the Period (T)

Enter the period of the waveform in the ‘Period (T)’ field. The period is crucial as it influences the shape and size of the series representation.

  • Minimum period: 0.1
  • Maximum period: 100
  • Step size: 0.1

This field is mandatory and requires a valid numerical input within the specified range.

Step 3: Input the Amplitude (A)

Input the amplitude of your waveform in the ‘Amplitude (A)’ field. The amplitude controls the height of the waveform’s peaks.

  • Minimum amplitude: 0.1
  • Maximum amplitude: 100
  • Step size: 0.1

This field is required and should be filled with a number falling within the allowed range.

Step 4: Set the Number of Terms (n)

Decide on the number of terms in the Fourier Series you would like to compute by filling in the ‘Number of Terms (n)’ field. More terms generally mean a more accurate representation of the waveform.

  • Minimum number of terms: 1
  • Maximum number of terms: 50
  • Step size: 1

This is a necessary field and requires an integer value.

Step 5: Review the Results

After inputting all the required information, the calculator will provide several outputs:

  • The a₀ (DC Component) will give you the average value over one period.
  • The aₙ Coefficients and bₙ Coefficients are determined based on your selected function type and will dictate the contribution of cosine and sine terms in the series.
  • The Fundamental Frequency (ω₀) is calculated as 2π divided by the period and shown in radians per second.
  • The Fourier Series Expression provides a mathematical representation of your input waveform.
  • The RMS Value offers the root mean square value which is a measure of the waveform’s effective value.

All calculations will appear to four decimal places for precision.