Hi,
I think my conclusion on your fft clk is not right. You are dividing it into 8KHz, fair enough. I wonder why not use the same 8 clk of ADC for your fft, may be it is not connected in hardware.
So generally your design looks ok in principle. You can simplify it by removing sqrt if you want. Just add squred values to get power instead of amplitude.
As such your fft result covers 0 ~ 1 i.e starts as positive from 0 ~ .5 then negative mirror image from -.5 ~ 0
0 means 0 frequency, .5 means Fs/2 = 4KHz.
so you can label your frequency axis from 0 ~ 4 then -4 to 0
You should see two lines on either side. These two should be equal if yur input is connected to real fft only. for example if your input frequency = 2Khz
then the lines should be at
+2 on your frequency axis.
I am still not sure what is your ADC actual Fs. If we assume it is 8k
while your fft clk = 18750/(1152*2) = 8.138... this is a big difference