SQNR = \\(10 log_{10}⁡\\frac{P_x}{P_n}=20 log_{10} \\frac{⁡σ_x}{σ_e}\\)

The effect of the additive noise eq (n) on the desired signal can be quantified by evaluating the signal-to-quantization noise (power) ratio (SQNR), which can be expressed on a logarithmic scale (in decibels or dB).

The signal-to-quantization noise (power) ratio (SQNR), which can be expressed on a logarithmic scale (in decibels or dB) :

In the mathematical model for the quantization error eq (n). To carry out the analysis, the following are the assumptions made about the statistical properties of eq (n).

In the statistical approach, we assume that the quantization error is random in nature. We model this error as noise that is added to the original (unquantized) signal. If the input analog signal is within the range of the quantizer, the quantization error eq (n) is bounded in magnitude

In the equation SQNR = \\(10 log_{10}⁡ \\frac{P_x}{P_n}\\), then the terms \\(P_x=\\sigma^2=E[x^2 (n)]\\) and \\(P_n=\\sigma_e^2=E[e_q^2 (n)]\\).

In the statistical approach, we assume that the quantization error is random in nature. We model this error as noise that is added to the original (unquantized) signal. If the input analog signal falls outside the range of the quantizer (clipping), eq (n) becomes unbounded and results in overload noise.

\\(P_n=\\sigma_e^2=\\int_{-\\Delta/2}^{\\Delta/2} e^2 p(e)de=1/\\Delta \\int_{\\frac{-\\Delta}{2}}^{\\frac{\\Delta}{2}} e^2 de = \\frac{\\Delta^2}{12}\\).

In the equation SQNR = \\(10 log_{10}⁡\\frac{P_x}{P_n}\\) then the terms Px is the signal power and Pn is the power of the quantization noise

The effect of the additive noise eq (n) on the desired signal can be quantified by evaluating the signal-to-quantization noise (power) ratio (SQNR).