This knowledge base article explains how we can download/export the Analytics logs in NSM.
Step 1:
Login to NSM | Navigate to the inventory
Step 2: Navigate to the firewall view (The firewall you want to download the logs for) | Monitor | Analytics
Step 3: On the top right side, Click on LOG and also you can select the time frame you want the logs for (Maximum 30 days and it can be a custom date as well).
Step 4: When you click on the time frame, it should start showing up data, You can change the limit (No of entries displayed) of you want
Step 5: Click on Export > Click on OK > It will save the file in .csv format. (The maximum entries that can be exported are 8000)

NOTE: This can only be done if you have an NSM Advanced license