Spectral leakage bias in harmonic distortion measurements

Spectral leakage bias in harmonic distortion measurements occurs when a finite record spreads a strong component into bins interpreted as distinct harmonics. A waveform can have zero physical total harmonic distortion while a naive FFT-bin ratio reports otherwise. Confining a sinusoid to a finite interval creates spectral sidelobes; the pinned primary guide derives this leakage from the finite-time Fourier transform.^[ref]

For an exact discrete calculation, take $x_m=A\cos (2\pi \nu m/N+\varphi )$, where $\nu$ is the number of cycles in the record. With the unscaled forward discrete Fourier transform, a finite geometric sum giveswherewhenever the denominator is nonzero, with the finite-sum limit elsewhere. Integer-cycle coherent sampling makes the unwanted integer bins cancel; a noninteger cycle count generally does not. The negative-frequency contribution also matters because the input is real.

For an original pure-tone example, let $A=1$, $\varphi =0$, $N=128$ and $\nu =5.3$. Its true higher-harmonic amplitudes are zero. Yet choosing the nearest bins $5$, $11$, and $16$ for the fundamental, second and third harmonic givesA naive result would be about $6.58\%$ distortion from this undistorted sinusoid. This is an exactly specified record calculation, not an instrument's measured distortion floor.

A window reduces some sidelobes at the cost of a broader main lobe and a changed amplitude normalization. Its coherent gain of a window must be treated consistently, and one cannot assume that one selected bin captures a noncoherent tone's full amplitude. Zero padding samples the same finite-record spectrum more densely; it does not restore missing observation time or remove leakage.

A measurement can instead synchronize the source and acquisition for an integer number of cycles, fit a justified sinusoidal model, or use a validated window/band-integration method. The finite-record phasor extraction with coherent sampling gives a particularly transparent exact case. Calibrated receiver response and actual harmonic coverage remain necessary, as in the primary Anritsu apparatus.^[ref] Power spectral density and squared-amplitude spectrum outputs also have different units; an arbitrary square root of a density bin is not a calibrated harmonic amplitude.^[ref]