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Fourier analysis learning trajectories are investigated in this full paper as a joint interdisciplinary construct for a scholarly collaboration among engineering and mathematics faculty. This is a dynamic and recursive construct for aligning, developing, and sharing research based innovative practices for engineering mathematics education. Towards building more coherence and transfer of learning between engineering and mathematics courses, these trajectories offer experimental practice templates for the interdisciplinary community of practice for engineering mathematics education. Conjectured learning trajectories for Fourier analysis thinking are here articulated and experimented in three courses - Trigonometry, Linear Algebra, and Signal Processing. Informed by the interdisciplinary perspectives from the team, these trajectories help to design instruction to support the complex learning of the mathematical, and engineering foundations for the advanced mathematical concepts and practices such as Fourier Analysis for engineers. The re- sults highlight the impact of collaborative, interdisciplinary, and innovative practices within and across courses to purposefully build and refine instruction to foster coherence and transfer with learning trajectories across mathematics and engineering courses for engineering majors. This offers a transformative process towards an interdisciplinary engineering mathematics education. The valid assessment and measurement of complex learning outcomes along learning trajectories are discussed for engineering mathematics education, paving the pathway for our future research direction.