It sure looks to me like your Analog Discovery has everything you need. Download the latest version of Waveforms. On the scope view, note that you can set the mode to record. Note that in the Config tab you can set the recording sample rate and the duration. On the far right, you can set 'Position' for the view so you can look around in any area of the captured waveform.
One of the neat new gadgets in the latest Waveforms is the Spectrum Analyzer.
I suppose I could use the AD to generate a 10 kHz modulated signal and then run it back into the Scope to see how this all plays. So, here it is... A 10 kHz carrier with a 100 Hz modulation. I sampled at 1 MHz and took 2,000,000 samples (2 seconds). I'm not sure what is happening with the FFT but it is what it is. I just wanted to verify that the scope will record.
I added a Spectrum Analyzer capture as well.
I'm pretty sure if you play around with the AD and the latest Waveforms, you will get where you want to be.
ETA: I am using version 1 of the Analog Discovery.
ETA: I replaced the images with ones that don't have Channel 2 cluttering up the display.