Harmonics　and　interharmonics　adversely　affect　power　grids.　The　fast　Fourier　transform　(FFT)　algorithm　is　one　of　the　most　commonly　used　methods　for　harmonic　analysis.　However,　in　practical　applications,　the　accuracy　of　harmonic　analysis　can　be　seriously　affected　by　fence　effect　and　spectral　leakage,　which　are　undesired　characteristics　inherent　to　discrete　Fourier　transforms.　Moreover,　when　non-synchronous　sampling　is　carried　out,　the　phase　measurement　is　not　accurate　enough,　and　there　is　a　large　error　in　the　identification　of　interharmonics.　In　order　to　improve　the　measurement　precision,　the　method　of　allphase　spectrum　analysis　is　used,　since　it　has　the　characteristics　of　phase　invariance　and　good　spectral　leakage　suppression.　A　novel　method　based　on　improved　Nuttall　double-window　all-phase　FFT　is　proposed　by　improving　the　window　function　and　the　spectrum　correction　method　for　achieving　higher　precision.　Through　simulation　and　experimental　verification,　the　proposed　algorithm　has　proven　to　perform　better　than　the　traditional　algorithms　both　for　the　detection　of　harmonics　and　interharmonics.　In　addition,　the　computation　burden　is　not　considerably　increased　when　compared　to　such　algorithms,　which　allows　the　on-line　use　of　the　proposed　algorithm.　©　The　Institution　of　Engineering　and　Technology　2018.