I hope you are able to get it functioning, but I have no idea what it is used for.
A correlator is a multipurpose instrument that looks for matches (correlation) between two input signals, which may include the same input signal offset by time. The correlator will dig out signals from under the noise floor. OK so at this point I am confident what I have said is meaningless, so let me show you an example.
A common requirement for power supply design (or any closed loop control system) is to measure the frequency response and display this as a Bode plot.
The ideal Bode plot measures amplitude (y-axis) vs frequency (x-axis) from 0Hz to ∞Hz. The Bode plot works in the frequency domain.
The Bode plot is the result of applying a unity function as and input, (often a constant amplitude input signal, amplitude = 1) to a control system and measuring the output signal. When you apply a unity function as an input to a control loop, you get the frequency response of that control loop, the Bode plot. One of the ways of achieving that is to use a AWG to sweep from a very low frequency to a very high frequency and view the output (Bode plot) on a standard DSO. That method is described in this link
https://siglentna.com/application-note/power-supply-loop-response-bodeii/ using a Siglent AWG and DSO. It works but is sensitive to noise and can't be used on a live system where there are significant control loop demand signals ie. real life. The amplitude of the signal could be increased above the noise, but often the large signal response of a closed loop control system is different to the small signal response. Things like slew rate limiting, amplitude limits etc.
Another input signal with a value of "1" across the entire frequency spectrum is the impulse function. This is a single pulse with infinite amplitude and a pulse width approaching zero. An impulse is a unity function. When graphed in the time domain (like you would see on an oscilloscope), the area (energy) under the pulse = 1. An ideal impulse is made up of frequencies from 0Hz to ∞Hz. One of the ways to approximate a impulse is to apply an electrostatic discharge as the input signal. Usually not a practical solution.
The beautiful thing about the impulse function is that when you transform an impulse from the time domain (oscilloscope) to the frequency domain ( spectrum analyser), the signal has infinite bandwidth and near zero amplitude. The total area (energy) under the signal = "1". It looks like white noise and it is practical to produce such a signal. Note that viewing an ideal impulse would require a spectrum analyser with no noise floor. In practice a true impulse will be buried in noise.
So now we know that applying a white noise input signal to a control loop will provide the Bode plot as an output. That would be useful if the output signal was visible above the noise floor of the instrument. The amplitude of the white noise could be increased but that would produce similar results to the Siglent method with the same issues and limitations.
OK so what if the white noise input signal was sequentially applied, say 100 times. If you summed the 100 control loop output signals, it would be like multiplying the input signal 100x. In addition, if you sum true noise present in the control loop, the unwanted noise will be attenuated 100x. That would give a signal to noise ratio gain of 100x100=10,000 (40dB) to lift the wanted output signal (Bode plot) out from beneath the noise floor. What is needed is an instrument that can read two input signals many times and sum the similarity (correlate) to attenuate the system noise and amplify the wanted white noise signal. That is what the HP 3721A does.
It would be really convenient if the wanted white noise signal was replayed but true white noise is always random and is never repeated. Fortunately pseudo white noise can be replayed and repeated any number of times. The pseudo noise generator would need to be interfaced so the HP 3721A knows when the replay is started, and clocked to keep in sync. That noise generator is the HP3722A pseudo noise generator.
If the noise generating bit sequence is very long, then the generated noise will include very low frequency components. Much too low for any typical spectrum analyser to view. HP created the HP 3720A with a bandwidth of 0.005 Hz to 250 kHz using the internal HP 3721A clock to sync.
So in this example, a control loop can be stimulated with a very low amplitude signal to produce a small-signal Bode plot that is resistant to true system noise when the HP 3721A and HP 3722A are combined. The output can be viewed on the HP 3720A spectrum display. The 3 instruments were made for each other and when combined, they can do some seemingly magic things. They are especially good at separating known signals and lifting them from under the noise floor.
So ~40 years ago I learned the Siglent method, using noise and not an AWG, for defining the frequency response of a control system. I didn't know there was an instrument called a correlator. I have never seen a working HP 3721A and until a couple of weeks ago, I didn't know this instrument existed, so I am looking forward to seeing what it can do in practice. In the absence of a HP 3722A noise generator, I am already planning to build an equivalent pseudo noise source. As a side note, adding basic correlation functionality to a Siglent DSO is probably just a factory software modification away. No need for glass bit memory.
When I saw this HP 3721A listed, I was just curious. It was HP, big, heavy, the seller was close and it was cheap. It wasn't until I started doing some research I figured out what it was capable of, especially when connected to the noise generator, spectrum display, and an early HP computer. If you want to measure the frequency response of a suspension bridge or, retrieve sonar/radar return signals from far below the noise floor, these instruments will do the job. This is an instrument I never new I needed until learned about it. Unfortunately I don't think I will ever have the opportunity to obtain the 3 instruments and an original HP computer in one place to see them working together.
This is an example of one application where a correlator, and no other instrument, would excel in providing the desired output. There is a whole lot I don't yet know about applications for this correlator.