After attending school in Farmville, his parents moved him to Phenix High School in Hampton, Virginia for better opportunities. After graduating high school, he attended Hampton University on a pre-medical track before being drafted into the U.S. Army in the Korean War, where he received a Purple Heart after being wounded there. Later, he attended Temple University to study physics. Initially, West was excluded from study groups due to his race but was soon invited after he was able to solve even the most complex group problems on his own.

As a graduate student, he interned with Bell Laboratories where he began designing work on the Electret microphone. He completed bachelor's and master's coursework in physics at Temple University by 1957 but did not officially graduate because he returned to Bell Laboratories to continue his work on the microphone in November of that year.

In 2001, West retired from Lucent Technologies after a distinguished 40-year career at Bell Laboratories where he received the organization's highest honor, being named a Bell Laboratories Fellow. West then joined the faculty of the Whiting School at Johns Hopkins University where he is a professor in the Department of Electrical and Computer Engineering. In 2007, West received an honorary doctorate from NJIT.

He has four children with his wife Marlene.

Along with Gerhard Sessler, West invented the foil electret microphone in 1962 while developing instruments for human hearing research. Compared to the previous condenser microphones, the electret microphone has higher capacitance and does not require a DC bias. West and Sessler optimized the mechanical and surface parameters of the system. Nearly 90 percent of the microphones produced annually are based on the principles of the foil-electret and are used in everyday items such as telephones, camcorders, hearing aids, baby monitors, and audio recording devices among others.

West measured the acoustics of Philharmonic Hall in New York City.

In a study published in 2005, West teamed with Ilene Busch-Vishniac and studied the acoustic environment of hospitals showing that hospitals are in general too loud and that the noise levels affect staff and patients.

At Johns Hopkins, he has worked on a device to detect pneumonia in lungs of young children. His research at Johns Hopkins also includes efforts to improve teleconferencing technology by transmitting stereophonic sound over the Internet and new transducers.