We seek to address whether solar-cycle frequency shifts of the Sun's low-l pmodes `distort' the underlying shapes of the mode peaks, when those peaks areobserved in power frequency spectra made from data spanning large fractions, ormore, of the cycle period. We present analytical descriptions of the expectedprofiles, and validate the predictions through use of artificial seismictimeseries data, in which temporal variations of the oscillator frequencies areintroduced. Our main finding is that for the Sun-like frequency shifts thedistortion of the asymmetrical Lorentzian-like profiles is very small, but alsojust detectible. Our analysis indicates that by fitting modes to the usualLorentzian-like models -- which do not allow for the distortion -- rather thannew models we derive, there is a bias in the mode height and linewidthparameters that is comparable in size to the observational uncertainties givenby multi-year datasets. Bias in the frequency parameter gives much less causefor worry, being over an order of magnitude smaller than the correspondingfrequency uncertainties. The distortion discussed in this paper may need to beconsidered when multi-year Sun-like asteroseismic datasets are analyzed onstars showing strong activity cycles.
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