First, please disconnect your PDA, and don't connect it again until you know how to manage the analog input.
Electronics: A PDA running a tone generator app ... A 3.5mm plug ... PDA, wires ... alligator clips ... jumpers that connect to the arduino's A0 and GND pins. That's literally it.
Thanks for sharing that part. It turns out to be an important detail. The PDA delivers both negative and positive voltage to its ouput. You've got it connected directly to the Arduino's analog input. The analog input isn't intended to operate with a negative input. It will read the data incorrectly, and it may sustain permanent damage from exposure to a negative voltage.
I'll recommend that you capacitively couple the PDA signal to A0, and offset it by half-scale. If you're using the FHT example that I suspect, it expects an input signal that's centered around half-scale. If you want help doing that, please say so, and we'll help.
See, you told us something about your setup, and we told you something that matters.
If you want to know more, you'll have to be forthcoming with information. We'll still insist on seeing your code, seeing the display code, knowing what kind of Arduino you're using, knowing which library you're using to do the FHT, and knowing what hardware you're using to display the graph. Because it looks very much like there's erratic performance on the communication channel between the Arduino and the display device, we'll want to know about how those two are connected, too. We'll also insist on knowing how everything else is connected. The best way to describe that is with a schematic. If you want, you can draw one by hand, photograph it, and, after you make sure that the photo is readable, attach it to your post. If you have a handy way of drawing a clearer schematic, so much the better. Unless your setup is extraordinarily neat, a photograph of the actual setup is unlikely to be helpful.
There's little point in troubleshooting more subtle aspects of this project while the analog input isn't working properly. Fix that, tell us what happened, and then we'll look at the rest.