Historically anyway, specs were purely swept instruments: little more than a radio receiver, but with tight tolerances (emphasis on amplitude and logarithm correctness, usually), and automatic wide range tuning (using a variable oscillator, most popularly a YTO (YIG tuned oscillator: like a crystal oscillator, but tuned to an electronic resonance of a yttrium iron garnet (YIG) crystal, which varies proportionally with frequency). When swept at an appropriate rate (slow enough for the bandwidth settings) and plotted on a graph, you get a spectrogram.
The average SA is little more than a computer wrapped around a very nice radio. ADC sampling measures the detector output, and DACs or switches control the signal path and frequency sweep. Only the rated bandwidth is acquired at any given time, sequentially across the entire band. Intermittent signals therefore have to be dealt with in a suitable manner (peak, average, quasi-peak, ...?).
DSAs however were oriented more towards mechanical and acoustic analysis, made possible (obviously) by the advance of digital computation. Which was slow at first (< megasamples/sec), but when you're only looking at frequencies of kHz or less, this is more than good enough.
Sampling is performed continuously, then the data converted en masse via Fourier Transform. This has several important implications:
- The bandwidth measured is, in a sense, maximal. Any given frequency bin is derived from all the information acquired during the sample period. (Whereas a spec samples only the frequencies it is tuned to at a given moment.)
- The amplitude is the peak sine component, for that frequency, for the entire sample period. It's not intermittent or modulated, it's not peak (over some time frame), or average (in the SA sense), or anything else. It is a kind of average, but because the phase and amplitude over the entire acquisition period matters, it's a true vector average -- whereas the SA will yield more of an RMS average, now because it is phase-insensitive.
- The bandwidth per bin (and usually per pixel, on a digital display) is determined by the sample rate and number of samples. For the SA, you still benefit from setting an unusually low bandwidth (= high frequency precision) for a relatively wide span, but doing the equivalent (more samples than there are pixels to display) with a DSA will result in aliasing -- the loss of information. (There are tricks to manage the losses around marginal conditions, like this. For example, sampling perhaps 3x too much data, multiplying it by a suitable function such as a Hanning window, then rescaling the FT result, perhaps with a weighing function such as antialiasing, or taking the RMS or peak value, when merging neighboring bins together -- because the window function acts to smooth the frequency display, this is now a reasonable step to take.)
Nowadays, DSAs offer as much power as DSOs, which in turn offer more power than any analog instrument of either kind did, back when digital ones were still new. And algorithms and programs have been developed to deliver the same old functionality with the new machines: such as (phase insensitive) peak or quasi-peak readouts, or narrow frequency sweeping (think: using the DSA's ADC as an SDR).
Disclaimer: I have used both analog and digital scopes, but not of SA/DSAs. So I don't know how they actually compare in terms of bandwidth and noise and tradeoffs and such. What I've seen, seems to be well in line with my intuition. So, don't worry about them, just get whatever's best these days. Or, get a vintage one if you like (but not, like, really old and crusty, they'll probably be more hassle).
The main feature, as far as total acquisition bandwidth and update rate and all that, will be: because a DSA can acquire and process a huge amount of data at once, while an SA must do it one frequency range at a time: the DSA can acquire and display the correct spectrogram (peak, average, whatever) very quickly, even when very intermittent signals are present.
A very typical use-case is a switching supply putting out noise modulated by 100/120Hz: the supply rectifier acts as a PIN diode, gating RF into the AC line; the diodes also generate noise due to reverse recovery. The resulting spectrum (on an SA) is a forest of dancing harmonics; a long averaging or "max hold" period is necessary to find the true amplitudes at all frequencies. A DSA with enough memory (and acquisition power, and processing power) to acquire >8.33ms of contiguous data, will be able to perform the same measurement in exactly one pass, period.
Tim