In-phase ("dispersion"), 90° out-of-phase ("absorption"), and "absolute-value" (square root of the sum of the squares of the "absorption" and "dispersion") ion cyclotron resonance (i.c.r.) spectra of CH3+ and CH4+ have been obtained by broad-band frequency-swept r.f. irradiation of an ionized methane sample, followed by broad-band detection, digitization of the transient i.c.r. response, Fourier transformation using a digital computer (1), and application of a linear phase correction across the F.t.-i.c.r. spectrum. The "absorption" spectrum is the same as would be obtained by conventional marginal-oscillator field-sweep i.c.r. detection and provides a means for identifying spurious "foldover" peaks; the "dispersion" response is not observable with a marginal oscillator detector. The principal advantages of the new "absolute-value" display are (1) the signal-to-noise ratio is significantly better than for the conventional "absorption" mode, at the expense of a slight broadening of the i.c.r. spectral line shape; and (2) "absolute-value" display will very likely be the method of choice in frequency-sweep F.t.-i.c.r. spectroscopy (2), in order to circumvent the complicated non-linear phase corrections which may otherwise be required to obtain an "absorption" mode display.