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Transcranial focused ultrasound (tFUS) is a therapeutic modality which is gaining widespread acceptance as a modality for treating neurological disorders and diseases, such as temporal lobe epilepsy (TLE). Advances in material science have enabled the production of dual-mode ultrasound arrays (DMUAs), which use the same transducers to operate in ultrasound imaging and therapy modes, making them good candidates for tFUS. The broadband capabilities which make DMUAs possible also allow for broadband ultrasound imaging and therapy to be performed. A type of signal processing common in wireless applications called orthogonal frequency-division multiplexing (OFDM) has several characteristics which make it an ideal type of signal for use in broadband tFUS applications. The work in this thesis centers around exploring the characteristics of OFDM ultrasound signals, then applying the OFDM to ultrasound interrogation, imaging, and therapy. In the field of ultrasound interrogation, a novel application of temporally extended broadband OFDM signals enables the rapid, highly resolved spectral characterization of the temporal bone of the skull. The extended duration of this broadband signal was found to increase the signal-to-noise (SNR) of broadband measurements due to an increase in the overall energy of the signal. It was also found that the lack of a consistent characteristic for determining the time of arrival (ToA) of the individual frequencies in broadband Gaussian pulses can easily lead to the introduction of a linear error in the estimation of phase, which may be a common error in the field of ultrasound interrogation in general. These observations were used to characterize the spectral-spatio-thermal acoustical characteristics of the temporal bone of a human skull, taking high spectral resolution measurements while the skull was heated over a range of 20$\degree$C. It was discovered that changes in the transmission as the skull was heated were greatly dependent on the location of the skull, with some locations exhibiting a high sensitivity to heating, changing the transmission by as much as 25\%, while others exhibit a low sensitivity, having a change of less than 2\%. A simulation is performed to show that the changes in transmission in the temporal lobe, which is of interest in the treatment of TLE, depend on the rate of change of the speed of sound of bone per $\degree$C. Additionally, for the first time, a large area of the temporal bone is scanned to perform a highly resolved spectral characterization of complex ultrasound reflection and transmission coefficients. For the first time, the cyclic nature of these signals was measured over a large area, examining how they evolve not only with frequency, but spatially as well. Next, a step was taken to investigate the use of OFDM signals for use in practical ultrasound imaging and therapy applications. They are used in a DMUA capable of performing tFUS to produce broadband pressure fields feasibly useful in HIFU applications. OFDM signals are then used in conjunction with the angular spectrum method to rapidly characterize the entire three-dimensional pressure field generated by each subcarrier of the the OFDM signal from a single two-dimensional hydrophone scan. It was found that the spatial distribution of the pressure fields predicted by the OFDM signals matched the pressure fields generated by transmitting individual subcarriers. This is a novel approach to perform rapid, spectrally dense characterizations of the broadband pressure fields generated by an ultrasound transducer capable of performing tFUS. Further uses of OFDM signals are investigated in their applications to common algorithms used in ultrasound therapy. The independent control of individual subcarriers within OFDM signals are used to generalize algorithms which were previously limited to narrowband applications. The first algorithm to be generalized is multifocusing. Multifocusing is performed using the subcarriers of the OFDM signal to generate three distinct foci, each with unique spectral characteristics. A hydrophone scan validates that only certain frequencies contributed to the generation of certain foci, while being excluded from the formation of others. Thus, it is possible to easily modulate the therapy applied to multiple targets in broadband tFUS applications. A second algorithm, previously limited to narrowband applications, is adaptive refocusing. Previous spectral characterization of the pressure field generated by the DMUA showed that each frequency of the transducer came to a focus at a different location after propagating through a Sprague-Dewey rat skull. Each of the subcarriers was successfully refocused using a hydrophone, leading to overlapping subcarrier focal volumes, causing an increase in the pressure at the target location, as well as an increase in intensity of the focal volume. It is also shown that refocusing causes a loss in the overall signal intensity; this can be easily fixed by a simple reoptimization of the transmitted signal by varying the global phase offset between the refocused subcarriers. Finally, the angular spectrum method is generalized to the broadband hybrid angular spectrum method, capable of propagating broadband ultrasound pressure waves through a complex medium. This was used to predict the pressure field behind a Sprague-Dewey rat skull using a simple model generated only by B-mode ultrasound images. This field was then used to predict the shift in the centroids of the focal volumes of each subcarrier induced by the refractive effects of the skull. Geometric beamsteering is then implemented to correct for these shifts, redirecting the focal volume of the transducer back to the target location.