----------------------NOISE_FLOOR_FFT_DB---------------------------------------------------------------- 
Noise_Floor_FFT_dB    Theoretical              
                      FFT Points    12Bits    14Bits    16Bits 
                      1024          101       113       125
                      2048          104       116       128
                      4096          107       119       131
                      8192          110       122       134
                      16384         113       125       137
                      32768         116       128       140
                      SNR_dB        74.0      86.0      98.1                      
-------------------------------------------------------------------------------------- 
                         FFT    
                                 _ _ _ _ _ _ _ _ _ _ _ _   OdB
                      Spurious  |                     ^
                      Free Dyn  |  | Fundamental      | SNR
                      Range     |  | at_max_signal    v
                           |__\ |--|---------------------------RMS_Noise_Level
                              / |  |     | 3rd Harmonic 
                                | _|     |   __| 5rd Harmonic
                                |/  \/\__|/\/  |_/\/ -------Average Noise Level
                                |______________________________\  (Noise Floor)
                                   ^  ^  ^  ^  ^  ^            /
                      
                      
                      Bin_width = Sample_rate/Number_Points_FFT
                      F_max =Sample_rate/2
RMS Signal            A/SQRT(2) = (FSR/2)/SQRT(2) = 2^(n-1)*q/SQRT(2) 
                      RMS Noise  = Qn        = q/SQRT(12)
                      SNR= RMS_Signal/RMS_Noise  = 2^(n-1)*SQRT(6)
                      SNR_pos_dB = 20*log(2^(n-1)*SQRT(6)) = 6.02*n + 1.76
                      NOISE_FLOOR_neg_dB = 6.02*n + 1.76 + 10*log(N/2) 
                      NOISE_FLOOR_neg_dB = 6.02*n +10*log(3*N/(PI*ENBW)) 
                      THD_neg_dB= 20*log(SQRT(sum_of_Harm_squared) )
                      Note: HAR (-dB)  
                      SINAD_pos_dB = -20*log(  SQRT( SNR^2+THD^2 )  )
                      SINAD = Singal to noise ratio and distortion
ENOB                  (SNR+Distortion-1.76+20*log(Amp_FS/Amp_Actual))/6.02
                      
                      ENOB= Effective number of bits
                      
                      
                      fs   = Sampling Rate (Hz) 
                      fin  = Input Signal Frequency (Hz) 
                      FSR  = Full Scale (Input) Range of 
                             Sampling A/D Converter 
                      FS   = FSRi2 = Full Scale input of 
                             Sampling A/D Converter 
                      A     = Input Signal Amplitude = FS = 
                             FSR/2= OdB 
                      n    = Numberof Bitsof Resolution 
                      q    = LSB Size 
                      LSB  = Least Significant Bit 
                      N    = Numberof FFT Points 
                      N/2  = Numberof Frequency Bins 
                             (real component) 
                      ENBW = Equivalent noise bandwidth 
                             of the window function. (For a 
                             four-term Blackman-Harris 
                             window, ENBW= 2.) 
                      
                      --------------------FFT_COS------------------------------
                      
                           ^
                          /|\             Signal = SIN(2*P()*Num/8)                 
                           S--__                                    __--
                           |    \S_                              __S
                           |       \_                          _/ 
                           |         \S                      S/      
                           |           \_                  _/   
                           |             \__            __/
                           |                S__     ___S
                           |_ _ _ _ _ _ _ _ _ _--S-- _ _ _ _ _ \
                           |                                   /                             
                      Num  Samp FFt
                       0    2    8
                       1 1.71    4
                       2    1    0
                       3  .29    0
                       4    0    0
                       5  .29    0
                       6    1    0
                       7 1.71    4     REAL MAGNITUDE
                                             ^
                                            /|\
                                             |
                                   \         |
                                    \        ^ 8 at @bin0
                                     \      /|\       
                                      \    ^ |
                                    Nyq\_ /|\|   
                                        \  | | 
                                         \ | |  
                                          \| | ^ 4 at @bin1
                                           \ |/|\ 
                                            \|_|_________________\
                                             \ |                 /
                                              \|   IMAGINARY MAGNITUDE 
                                               \  
                                                \    ^
                                              Nyq\_ /|\ 4 at @bin7  
                                                  \  |
                                                   \ |
                                                    \|
                                                     \      
                                                     _V
                                                        J_OMEGA