A field-programmable gate array (FPGA) is an integrated circuit designed to be configured by a customer or a designer after manufacturing

Power abs(fft): Mag or amplitude Laplace ->Pole, zero in S plane Z transform->Pole, zero in Z plane angle(fft): Phase /N: Normalize ()^1/2: Power e^-jwt = conj(e^jwt) Power = (fft())*conj(fft())/N Multiply: Upconvert Multiply Conj: Downconvert fftshift: -fs/2 0 fs/2 freqz:Horner method for given freq points. or no freq points specified. $\mathrm{SNR} = \frac{P_\mathrm{signal}}{P_\mathrm{noise}} = \left ( \frac{A_\mathrm{signal}_{RMS}}{A_\mathrm{noise}_{RMS} } \right )^2$ $\mathrm{SNR_{dB}} =10 \log_{10} \left ( \frac{A_\mathrm{signal}}{A_\mathrm{noise}} \right )^2 = 20 \log_{10} \left ( \frac{A_\mathrm{signal}}{A_\mathrm{noise}} \right )$ $= 10 \log_{10} \left ( \frac{P_\mathrm{signal}}{P_\mathrm{noise}} \right )$ dBm = dbw+30 $F(Noise Factor) = \frac{\mathrm{SNR}_\mathrm{in}}{\mathrm{SNR}_\mathrm{out}}= 1 + \frac{(L-1)T}{T_0}$ L: attenuation ratio at T0. T: measurement temperature. $Cascaded F = F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1 G_2} + \frac{F_n - 1}{G_1 G_2 G_3 \cdots G_{n-1}}$ $\mathrm{NF} (Noise Figure)= 10 \log(F) = 10 \log\left(\frac{\mathrm{SNR}_\mathrm{in}}{\mathrm{SNR}_\mathrm{out}}\right) = \mathrm{SNR}_\mathrm{in, dB} - \mathrm{SNR}_\mathrm{out, dB}$ N₀ (noise power spectral density) is the noise power the source will output in unit of bandwidth (one hertz). N₀ = kT = –174 dBm/Hz N_BW = BW*N₀ = N₀ + 10log(BW) N_1MHz = -174+log(1M) = -114dBm Eb/N0 (the energy per bit to noise power spectral density ratio) is SNR per bit $E_b/N_0=SNR\cdot\frac{B}{f_b}$ fb:the channel data rate (net bitrate), and B:the channel bandwidth In logarithmic scale (dB) $10\log_{10}(E_b/N_0) = \text{SNR}_{\text{dB}}} + 10\log_{10}\left(\frac{f_b}{B}\right)$ Es/N0 (energy per symbol to noise power spectral density) $\frac{E_s}{N_0} =\frac{E_b}{N_0}\log_2 M = \frac{S}{N}\frac{B}{f_s}$ M:bits per symbol $\operatorname{BER_{QPSK}} (Bit Error Rate) =\frac{1}{2}\operatorname{erfc}(\sqrt{E_b/N_0})$ BER =f(SNR) = f(CF) CF at the decoder at the receiver determines the actual BER. CF is affected by Noise gen, TC, RX and BW filters on the way.