--------------------FFT_SINE-------------------------------
                      
                      Using Excel to FFT signwaves
                      
                           ^
                          /|\             Signal = SIN(2*P()*Num/8)                
                           |      __--S--__  
                           |   __S         \S_      
                           | _/               \_           
                        _ _S/ _ _ _ _ _ _ _ _ _ \S _ _ _ _  _ _ _ _ _ _ _ \   
                           |                      \_                  _/  /
                           |                        \__            __/
                           |                           S__     ___S
                           |                              --S--
                                                       
                      Num  Samp FFt
                       0    0    0
                       1  .71  -4i
                       2    1    0
                       3  .71    0
                       4    0    0
                       5 -.71    0
                       6   -1    0
                       7 -.71    4i     REAL MAGNITUDE
                                             ^
                                            /|\
                                             |
                                   \         |
                                    \        | 
                              /______\       |       
                              \       \      |
                                       \     |   
                                     Nyq\__  | 
                                         \   |  
                                          \  |
                                           \_|____\ 
                                            \|____/_____________\
                               -4j    /______\                  /
                               @bin1  \       \   IMAGINARY MAGNITUDE 
                                               \  
                                             Nyq\__ 
                                                 \     
                                                  \ 
                                                   \______\ +4j
                                                    \     / @bin7
                                                    _V
                                                       J_OMEGA 
                      
                      
                      --------------------FFT_NYQ------------------------------
                      
                           ^
                          /|\             Signal = SIN(2*P()*Num/8)                 
                           S_        S       S       S
                           | \      / \     / \     / \
                           |  \    /   \   /   \   /   \           
                        _ _|_ _|_ _|_ _|_ _|_ _|_ _| _ \ _ _ _ \   
                           |   |   |   |   |   |   |   |   |   /
                           |   \   /   \   /   \   /   \   /            
                           |    \S/     \S/     \S/     \S/  
                           |                                 
                                                
                      Num  Samp FFt
                       0    1    0   Real    \
                       1   -1    0   Complex  |
                       2    1    0   Complex  | 8 data points in/out
                       3   -1    0   Complex  |
                       4    1    8   Real    /
                       5   -1    0
                       6    1    0
                       7   -1    4           ^   REAL MAGNITUDE
                                         ^  /|\
                                        /|\  | 
                                         |   |
                                   \     |   |
                                    \    |   |
                                     \   |   |       
                                      \  |   |
                                       \ |   |   
                                     Nyq\|   |   ^
                                         \   |  /|\
                                          \  |   | 8 at @bin4
                                           \ |   |  
                                            \|___|_________________\
                                             \   |                 /
                                              \  |   IMAGINARY MAGNITUDE 
                                               \ |
                                             Nyq\|   
                                                 \
                                                  \ 
                                                   \
                                                    \      
                                                    _V
                                                        J_OMEGA 
                      
                      

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 (See Table 1)  
NOISE_FLOOR_neg_dB    6.02*n + 1.76 + 10*log(N/2)    (See Table 1)  
                      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                  Effective number of bits
                      (SNR +Distort -1.76 +20*log(Amp_FS/Amp_Actual) )/6.02
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   
                      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 window function.  
Blackman-Harris       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 
                      
                      

Theoretical           Noise Floor_dB               (Table 1)
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
                                |/  \/\__|/\/  |_/\/ ----------- Ave Noise Level
                                |______________________________\ (Noise Floor)
                                   ^  ^  ^  ^  ^  ^            /