  The Multi-frequency Angular Power Spectrum (MAPS) is an alternative to
spherically-averaged power spectra, and computes local fluctuations in the
angular power spectrum without need for line-of-sight spectral transform. To
test different approaches to MAPS and treatment of the foreground
contamination, and compare with the spherically-averaged power spectrum, and
the single-frequency angular power spectrum. We apply the MAPS to 110~hours of
data in $z=6.2-7.5$ obtained for the Murchison Widefield Array Epoch of
Reionisation experiment to compute the statistical power of 21~cm brightness
temperature fluctuations. In the presence of bright foregrounds, a filter is
applied to remove large-scale modes prior to MAPS application, significantly
reducing MAPS power due to systematics. The MAPS shows a contrast of
10$^2$--10$^3$ to a simulated 21~cm cosmological signal for spectral
separations of 0--4~MHz after application of the filter, reflecting results for
the spherically-averaged power spectrum. The single-frequency angular power
spectrum is also computed. At $z=7.5$ and $l=200$, we find an angular power of
53~mK$^2$, exceeding a simulated cosmological signal power by a factor of one
thousand. Residual spectral structure, inherent to the calibrated data, and not
spectral leakage from large-scale modes, is the dominant source of systematic
power bias. The single-frequency angular power spectrum yields slightly poorer
results compared with the spherically-averaged power spectrum, having applied a
spectral filter to reduce foregrounds. Exploration of other filters may improve
this result, along with consideration of wider bandwidths.
