Which circuit samples analog signals, processes them as numbers, then converts them back to analog?

The correct choice involves a digital signal processing circuit, which is specifically designed to handle analog signals by first converting them into digital form. This process includes sampling the analog signals at specific intervals and quantifying their amplitude into numerical data. Once the signal has been processed—whether it involves filtering, compression, or other forms of manipulation—the circuit then converts the digital data back into an analog signal for output. This conversion back to an analog format is crucial in applications like audio and video, where the output needs to be in a form that can be used by speakers or display technologies.

In contrast, other circuits mentioned, such as audio processing circuits, may perform similar functions but do not specifically encapsulate the comprehensive sampling, processing, and reconversion of digital signals. A receiver circuit typically focuses on tuning and demodulating signals rather than the detailed processing that a digital signal processing circuit entails. An amplifier circuit by itself primarily increases the amplitude of signals without engaging in the sampling and processing activities featured in digital signal processing. Thus, the digital signal processing circuit is uniquely qualified for the processes described in the question.