Hi, Karl,
I think you can use MC56F84789 to develop the application, the on-chip ADC of MC56F84789 supports hardware triggering mode, you can use PIT module to trigger ADC via crossbar. The ADC conversion can reach up to 2MHz for single channel, the ADC channel can be configured as single-end or differential, in differential mode, the input voltage is from -3.3V to +3.3V. The MC56F84789 uses DSP56800EX core, the core is suitable for the FFT. we provide FFT api function.
The on-chip Flash is 256KB, the on-chip RAM is 32KB, I think the RAM is enough to do 2048 points FFT.
This is the link of MC56F84789:
MC56F84xxx|Digital Signal Controllers|NXP
The Tools is CodeWarrior for mcu ver10.x
Another option is KV5x/KV4x, it integrates the same ADC as MC56F84789, but it can extend external SRAM.
Kinetis® V Series: Real-time Motor Control & Power Conversion MCUs based on Arm® Cortex®-M0+/M4/M7|N...
You can also use LPC54xxx, the ADC also supports hardware triggering, and can reach up to 5MSPS, but it only supports single-ended mode rather than differential mode, in the case, you have do the differential to single-ended conversion via OP AMP.. It can also extend external SDRAM and SRAM.
LPC54000|Power Efficient 32-bit Microcontrollers (MCUs)|Cortex®-M4 Core|NXP
The i.mxrt10xx is also option:
Hope it can help you
BR
Xiangjun rong