Which design usually begins with specifying the desired output?

Functional design is a design approach that focuses on the functionality and performance of a system, rather than its structure or appearance. Functional design usually begins with specifying the desired output, such as the goals, objectives, and requirements of the system, and then derives the input, processes, and data needed to achieve the output. Functional design can be applied to various types of systems, such as software, hardware, or business processes. Functional design is often contrasted with other design approaches, such as organizational design, object-oriented design, and structured design, which have different emphases and methods. References:

System Analysis & Design - System Design1

Process models in design and development2

B. Engineering Design3