Log periodics are fairly easy to design. Started my career designing them at a company called Tecom. Got pretty good at it. Have one in the attic that covers 225-400 MHz to eavesdrop on military aircraft in the area. The mechanics of putting one together is the trick, they can get heavy for lower frequencies.
A PC is not needed, we just used pocket calculators. The software being used in the vid is $$$.
Knew a guy who hand wound copper coils to break out a four channeled Russian mil system ...