Nowadays, among the instrumentation park of mass spectrometry, Fourier transform mass spectrometers (FTMS), including ion cyclotron resonance (ICR) and Orbitrap FTMS, provide the highest analytical performance for accurate measurements and mass resolution. Nevertheless, molecular analysis in currently challenging research areas, such as life and environmental sciences, necessitates further improvement of these analytical characteristics. In recent decades, a regular approach to address the problem behind the analytical performance was using increased electromagnetic fields. However, per a given increase of their magnitudes, that approach is currently requiring more and more resources, hence demonstrating its limited feasibility for tomorrow. Therefore, only a qualitative breakthrough in the underlying methodology may then lead to the next series of developments enabling improved molecular analysis. The present research is dedicated to the fundamental question behind the analytical performance in FTMS. Specifically, this thesis represents an interdisciplinary study aimed at improved molecular analysis in FTMS-based applications, achieved via better comprehension of the uncertainty principle in FTMS, viz. its dependence on the measurement scheme, including ion traps, signal processing, and data analysis, as well as its influence on achievable analytical characteristics in FTMS. To start, the uncertainty principle for measurements in FTMS has been investigated, asserting a limit to the precision with which complementary physical quantities in FTMS, e.g. detection period and scale of frequency details to resolve, can be measured. Specifically, two corollaries of the uncertainty principle are considered, viz. resolution performance and performance for accurate measurements in FTMS. Importantly, the uncertainty principle shows dependence on the particular measurement scheme employed. For instance, signal detection, signal processing, and data analysis of the standard measurement scheme impose their own restrictions to the resulting uncertainty principle, thus leading to the current limitations. However, the ultimate limitations in the analytical characteristics in question are defined by the uncertainty principle limit due to physics of ion motion in the mass analyzer. Hence, with corresponding developments in data analysis methods, methods for signal processing, and designs of ion traps, novel measurement schemes have been implemented, where the quantitative form of the uncertainty principle is modified towards the ultimate limit. Finally, the implemented solutions have been evaluated in the context of FTMS-based analysis of crude oil fractions, protein identification and characterization, quantitative proteomics, and analysis of isotopic fine structures of peptides. To conclude, the achieved success of this work should considerably contribute to the currently challenging analytical applications of FTMS.