What is the digital signal processing term for noise subtraction circuitry?

Adaptive filtering and autocorrelation.

See Wikipedia's article on Adaptive filter and the article on Matched filter. Also, see the article on Active noise control.

See Wikipedia's article on Autocorrelation

Also, see the ScienceDirect site for the article on Adaptive Filter Design and the article on Noise Cancellation

And, review the Etd OhioLink Edu site for the pdf document DESIGN AND IMPLEMENTATION OF AN ADAPTIVE NOISE CANCELING SYSTEM IN WAVELET TRANSFORM DOMA

For autocorrelation, please see the ScienceDirect site for the article Autocorrelation

And, see the I Open Shell USC Edu site for the pdf article on Autocorrelation of electronic wave-functions: a new approach for describing the evolution of electronic structure in the course of dynamics

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What is the purpose of de-emphasis in the receiver audio stage?

When coupled with the transmitter pre-emphasis, flat audio and noise reduction is received.

Deemphasis reduces unwanted frequencies, such as noise. When a transmitter sends a signal it is pre-emphasized. The receiver, then, deemphasizes undesirable frequencies, to reduce the amount of noise accompanying the desired sound. A low pass filter may be used to reduce unwanted frequencies.

See Wikipedia's article Emphasis (telecommunications)

Also, see the site DAEnotes for the article Pre-Emphasis And De-Emphasis

And, see the Repeater Builder site for the article Explanation of "Pre Emphasis, & De Emphasis" By Kevin K. Custer W3KKC.

Please see the site Total Phase for the article on What is Signal De-Emphasis and When is it Used?

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What makes a Digital Coded Squelch work?

Digital codes.

See Wikipedia's article on Squelch, and also the article on Continuous Tone-Coded Squelch System

Also, see the Repeater Builder site for the article on A Historical and Technical Overview of Tone Squelch Systems

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What causes a squelch circuit to function?

Presence of noise.

See Wikipedia's article on Squelch, and also the article on Continuous Tone-Coded Squelch System

Also, see the Repeater Builder site for the article on A Historical and Technical Overview of Tone Squelch Systems

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What makes a CTCSS squelch work?

Tones.

From wp2ahg:

CTCSS is Continuous Tone-Coded Squelch System

Tones control the squelch circuit.

You enter a tone frequency into the receiver, and the receiver will not break squelch unless it hears that sub-audible tone.

CTCSS squelch works by adding to the voice a lower frequency tone. Using different tones for other users on the same channel, CTCSS will use the tone information to mute other users.

See Wikipedia's article on Squelch, and also the article on Continuous Tone-Coded Squelch System and the article about the Squelch

Also, see the Repeater Builder site for the article on A Historical and Technical Overview of Tone Squelch Systems

And, please see the Radio Industries site for the article What Is CTCSS?

View the YouTube video from the Rohde Schwarz channel called Understanding CTCSS and DCS at 9:01 minutes.

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What radio circuit samples analog signals, records and processes them as numbers, then converts them back to analog signals?

The digital signal processing circuit.

From kj6prf:

The digital signal processing circuit samples an analog waveform (a waveform that can take on any value) to convert it to

a digital waveform (a waveform that can only take a certain set of values, like 0 or 1).

It then uses this information to do some math, then it converts its result back into an analog signal.

The advantage of using such a circuit is that filters and other designs can be reprogrammed, meet tighter specifications, and be easier to grasp conceptually than a traditional analog circuit.

See Wikipedia's article Digital signal processor, and also the article Digital signal processing

Also, see the Analog site for the article A Beginner's Guide to Digital Signal Processing (DSP)
and also the article called
DSP 101 Part 1: An Introductory Course in DSP System Design

And, view the pdf presentation from the Web CECS PDX Edu site called Design and Design and Implementation of Implementation of Signal Processing Signal Processing Systems: Systems: An Introduction An Introduction

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