I used to work on analog computers during my time at Goddard Space Flight Center, when on Apollo. Had to wire analog computer patch panels which was how they were programmed, 768 point to point possible connections, how they were wired defined the simulation of the day.
Later, an engineer named Horst Schlingloff and I built a digital to analog computer interface so the newer analog computer would not need to have that point to point wire patch panel, now the digital computer ran the settings on the analog, which had a new control panel with motor driven pots that did the actual settings, so the programmer did the program on the digital computer, ran the card compiler, a few thousand punched cards is now the program to have a simulation run on the analog.

We had a huge connection speed of 50 kilobits per second after about 6 months of workðŸ™‚

Originally posted by twhitehead In what way were they 'analog' computers? Did they store or calculate numbers in an analog way? Can you explain?

Take a device and put a voltage on the input. That voltage is a real number, if the voltage varies in time then you have a function. The output may be the integral of the input, depending on the device. You can make this device with an operational amplifier. This all happens in picoseconds, unlike an integral on a digital device where the input has to copied into memory and processed by the computer. A milli-second long signal is completely processed by an analogue device by the time the signal has ended and there is no worrying about numerical stability. The advantage of a digital computer is flexibility, but if you know the device will never have to do anything different then there are real advantages with an analogue machine.

Originally posted by DeepThought Take a device and put a voltage on the input. That voltage is a real number, if the voltage varies in time then you have a function. The output may be the integral of the input, depending on the device. You can make this device with an operational amplifier. This all happens in picoseconds, unlike an integral on a digital device where the input has t ...[text shortened]... ill never have to do anything different then there are real advantages with an analogue machine.

The disadvantage is similar to the old mechanical slide rule: Limited # of digits of accuracy. They are as happy as pigs in poop if they can squeeze 5 digits accuracy out of those devices.

And in the example I quoted, where my patch panel simulated a spinning satellite with masses inside the perifery at various angles, they would have been happy with 4 digit accuracy.

Originally posted by sonhouse The disadvantage is similar to the old mechanical slide rule: Limited # of digits of accuracy. They are as happy as pigs in poop if they can squeeze 5 digits accuracy out of those devices.

And in the example I quoted, where my patch panel simulated a spinning satellite with masses inside the perifery at various angles, they would have been happy with 4 digit accuracy.

And are the digital to analogue and analogue to digital converters precise to that degree? For a digital filter using an FFT I'd expect an output with errors of the order of one part in a thousand - single precision floating point arithmetic has around 6 decimal digits of precision, a fourier transform involves of the order of N log2(N) multiply adds. Assume N is 256 (a fairly typical number) log2(256) is 8 so that is 4096 multiply adds per output. The error will be of the order of epsilon (the largest number you can add to 1.0 and get 1.0 out) times 4096 which comes to something of the order of 1/2 a percent. Obviously with double precision that goes right down, but with single precision arithmetic an analogue filter is at least as good precisionwise.

Originally posted by DeepThought And are the digital to analogue and analogue to digital converters precise to that degree? For a digital filter using an FFT I'd expect an output with errors of the order of one part in a thousand - single precision floating point arithmetic has around 6 decimal digits of precision, a fourier transform involves of the order of N log2(N) multiply adds. ...[text shortened]... down, but with single precision arithmetic an analogue filter is at least as good precisionwise.

Sure, you are talking 21st century converters. Back in 1970, things were a bit rougher. One part in a thousand is still only 3 digit accuracy.