FOURIER Function (LibreOffice Calc)

• Introduced: LibreOffice 6.3, explicitly stated in function-specific Help.
• Supported in: 26.8 Help and 26.8.1.1 registration; no retirement is established.
• Scope: Desktop Calc, English semicolon-separated formulas. The documented ORG.LIBREOFFICE.FOURIER namespace is outside OpenFormula 1.3.
• Checked: October 14, 2026. Ten listed examples were recalculated in LibreOfficeDev 26.8.0.0.alpha0 using headless XLSX import. Stable releases, 26.8.1.1 and GUI array entry were not executed.

FOURIER computes a discrete Fourier transform of a numeric sequence. It returns a two-column array: real and imaginary components by default, or magnitude and phase when Polar is TRUE. The input grouping flag tells Calc how to read the source; it does not turn the returned spectrum into a horizontal two-row result. Function Help.

FOURIER(Array; GroupedByColumns [; Inverse [; Polar [; MinimumMagnitude]]])

Square brackets mark optional arguments; do not type them. Array contains real values in one column or row, or real and imaginary components in two columns or rows. GroupedByColumns is required: TRUE reads columns, FALSE reads rows. Inverse defaults to FALSE; TRUE selects the inverse transform. Polar defaults to FALSE. MinimumMagnitude defaults to zero and is used only for polar output to suppress small components. Complex input is represented by two numeric components, not strings such as “1+i”.

Enter the real sequence 1, 2, 3, 4 down H2:H5 and the same sequence across H7:K7. For the three-point complex example, enter:

The native column is from LibreOfficeDev 26.8.0.0.alpha0, build 2c87e51eeaa2b413ff4ae097b2705eea1995d8e5, using headless XLSX import and forced recalculation. Decimal values are rounded to twelve places; quoted text excludes the surrounding quotation marks from the returned value.

The real sequence 1, 2, 3, 4 has forward-transform components 10, −2+2i, −2 and −2−2i. The first output row is the zero-frequency or DC component, equal to the sum 10. Result row 2 corresponds to frequency index 1, not frequency index 2. =INDEX(FOURIER(H2:H5;TRUE());2;2) selects the imaginary part 2. This separation of frequency row and component column is essential when checking a spectrum.

The forward reference uses X[k]=Σ x[j] exp(−2πijk/N), with j and k from 0 through N−1. The inverse changes the sign and divides by N. The nested inverse example recovers the third original value, 3, from the Cartesian forward result. Do not feed a magnitude/phase result directly into the inverse: the input parser would treat those two columns as real and imaginary components. For the second frequency component, magnitude is √8 and phase is 3π/4 radians. A polar cutoff of 3 suppresses that component to zero magnitude and phase. Inspected callback.

The three-point complex example demonstrates a non-power-of-two length; the retained source chooses among FFT algorithms rather than requiring every sequence length to be a power of two. All input components must be numeric, and the grouping orientation permits at most two component columns or rows. Those invalid-input guards were source-checked rather than executed. Floating-point residuals near an ideal zero are expected. A magnitude cutoff is a reporting choice that can also remove a real small signal, so choose it according to the data scale. The tests select scalar components and do not establish a GUI array-entry workflow.

IMSUM, IMABS, INDEX.

• Function-specific Help
• Complete versioned callback
• English native-name registration
• Normalization and polar conversion
• FFT selection and output shape

The saved formula identities, local input values and typed results were reconciled. The stale SUM cache changed to 3 and the uncached SUM returned 7. Saved formulas use ORG.LIBREOFFICE.FOURIER for this operation. The examples establish only the listed development-build results; unexecuted guards and current-source behavior remain separately scoped.