The HP8910a (baseband) and HP89440 (with paired 2.65 GHz downconverter) were designed as very fast, FFT based spectrum analyzer / measuring receiver for complex I/Q digital modulation, like modern GSM / CDMA cell phone signals, digital TV, etc. It's a big fast ADC digitizer front end, and lots of DSP math to analyze and process the signals and results.
As a scalar spectrum analyzer, it's quite good. A little slower on broad sweeps, but very capable. I've measured oscillator phase noise with it. But as a vector signal analyzer, it really shines. It was quite ahead of it's time, back when it came out. There was a whole writeup in the HP Journal Dec. 1993 about its design.
Any oscilloscope can show you amplitude vs. time. For analog demodulation, this thing can show you AM, FM, or PM vs time. One button measurements of PLL synthesizer lock time. Or for digital modulation, it can display modulation symbols and decode the data. It can display and measure the modulation impairments: transmit distortion, receiver error vector magnitude, etc. I tracked down a lot of EVM problems back in the day.
Or you can use the two input channels and display correlation. I've hunted down unusual ripple in an amplifier output by checking how much the ripple correlated to suspected "culprit signals" nearby on the PCB.
It has a source (which can be a swept sine wave, additive white Gaussian noise, or can be loaded with your own arbitrary signal).
One time I was stumped by how to measure the baseband IF filter selectivity for a RF receiver chipset that integrated the entire IF filter inside the chip. Normally I would be able to sweep an RF input signal across the receiver frequency, and measure how signal strength was present at the output, as I swept across the band. But this chip also had an AGC automatic gain control amplifier integrated, which I couldn't disable, that would vary the gain as the test signal swept through the desired frequency, thus messing up my measurement. The VSA came to the rescue. I would up driving the input with AWGN noise, so the AGC detector always saw a constant level, and didn't vary the gain. Then probed the input with CH1 and the output with CH2 and set it up to calculate and display the CH2/CH1 transfer function. Gain and phase! A perfect solution.
(Something to think about: How to measure gain and phase transfer function with a sinewave is easy. Measure amplitude and phase shift at output on an oscope, right? Look at zero crossings for phase, etc. But... how to measure gain and phase when both signals are noise?) What's the phase shift of one messy noisy waveform vs. another messy noisy waveform? Not just one frequency, but a bazillion, all superimposed on each other. Now do it again, with significant time delays due to propagation or filter group delay effects... Hard for my brain to visualize the math in that case. But the 89410 had no problem. There is a whole lot of sophisticated FFT and digital signal processing in that instrument, that is quite frankly, beyond me.
It's great a very low frequencies. I even measured low frequency (sub 1 Hz) power supply R-C filter imperfections with this thing. Like ESR and dielectric absorption effects on supply filter rejection. It's a great DC coupled, millihertz vector network analyzer, where traditional RF VNA's fail because their direction couplers roll off, and directional bridges also fail to work.
I played with one of these at Motorola when they first came out in in the early1990s. No other engineers in the lab were as fascinated with all the possibilities as I was. Years later, I worked at Agilent, and worked a few cubes down from one of the HP program managers who worked on the design. He enjoyed hearing me talk about all the ways I used it for tough measurement problems.
I have watched them on Ebay for all these years, and now have one of my own. Fully loaded, it was $72K. 28 years later, you can buy one for a couple percent of the original list price.
I'm still learning new things to do with it. Just a really cool instrument.