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Using the Oxford Short Wavelength Integral Field specTrograph (SWIFT), weinvestigate radial variations of several initial mass function (IMF) dependentabsorption features in M31 and M32. We obtain high signal-to-noise spectra atsix pointings along the major axis of M31 out to ~ 700" (2.7 kpc) and a singlepointing of the central 10 pc for M32. In M31 the sodium NaI {\lambda}8190index shows a flat equivalent width profile at ~ 0.4 {\AA} through the majorityof the bulge, with a strong gradient up to 0.8 {\AA} in the central 10" (38pc); the Wing-Ford FeH {\lambda}9916 index is measured to be constant at 0.4{\AA} for all radii; and calcium triplet CaT {\lambda}8498, 8542, 8662 shows agradual increase through the bulge towards the centre. M32 displays flatprofiles for all three indices, with FeH at ~ 0.5 {\AA}, very high CaT at ~ 0.8{\AA} and low NaI at ~ 0.1 {\AA}. We analyse these data using stellarpopulation models. We find that M31 is well described on all scales by aChabrier IMF, with a gradient in sodium enhancement of [Na/Fe] ~ +0.3 dex inthe outer bulge, rising within the central 10" to perhaps [Na/Fe] ~ +1.0 dex inthe nuclear region. We find M32 is described by a Chabrier IMF and youngstellar age in line with other studies. Models show that CaT is much moresensitive to metallicity and [{\alpha}/Fe] than to IMF. We note that thecentres of M31 and M32 have very high stellar densities and yet we measureChabrier IMFs in these regions.

The initial mass functions of M31 and M32 through far red stellar absorption features