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This paper describes wide-band (1 MHz-10 GHz) thermal magnetic fluctuation (TMF) noise measurements conducted on magnetoresistive devices such as giant magnetoresistive (GMR) and tunnel junction magnetoresistive (TMR) heads. The paper discusses the instrumentation, as well as the corrections necessary to separate the TMF noise from the total noise as collected. It shows that the thermal electrical noise component of this total noise is not white, but approximately follows the small-signal resistance of a saturated sensor versus frequency. The paper gives examples of noise imaging using magnetic field sweeps and electrical bias sweeps, and interprets the results. As another application example, it shows that the signal-to-noise ratio of a GMR head does not improve if one replaces the free layer by a synthetic (double) free layer with the same net moment. It presents examples of multimode TMF spectra, together with the causes of these extra resonances: spatial standing spin waves in the free layer and pinned layer resonances. It shows how one can calculate the stiffening field, damping, and free layer dimensions (magnetically active height and width) from the TMF spectra. These parameters can be obtained in a nondestructive fashion. They are difficult to measure in other ways.