Finding out file extension from just a byte array

Consider a byte array stored in a column in a table in a database column. How can we identify the file extension of the byte array by inspecting the byte array itself?
Note that byte arrays could be saved many places, also within files or similar.
The extension of a file can be discovered by inspect the File header. This is the first bytes, usually the first tens or hundreds of bytes of the byte array and constitute the file header. Some extensions got multiple file headers. A best effort to identity byte contents of a column in a database.

Let's use Powershell to inspect a file on disk, a sample JPEG file (.jpg). Lets run the following little script:

format-hex .\Stavkyrkje_Røldal.jpg | Select-Object -First 16 The first few bytes are FF D8 FF