Hi! Embedded systems are dedicated computer systems. DSP are dedicated processor, like microcontroller which are single chip computer. All this unit can feature in an embedded system. All home theater system are not of the same features. Some has LCD, rotary switch, USB, video controller, CD controller, motor controller etc. With all these I can conclude that such are Embedded!
Can you kindly read and reference to the manufacturer of DSP processor for classification notes, examples and references.