519 A signal is quantized using 10bit PCM Find the signaltoq

5.19. A signal is quantized using 10-bit PCM. Find the signal-to-quantization noise ratio.

Solution

Signal-to-Quantization-Noise Ratio (SQNR or SN_qR) is widely used quality measure in analysing digitizing schemes such as PCM (pulse code modulation) and multimedia codecs. The SQNR reflects the relationship between the maximum nominal signal strength and the quantization error (also known as quantization noise) introduced in the analog-to-digital conversion.

The SQNR formula is derived from the general SNR (Signal-to-Noise Ratio) formula for the binary pulse-code modulated communication channel:

{\\displaystyle \\mathrm {SNR} ={\\frac {3\\times 2^{2n}}{1+4P_{e}\\times (2^{2n}-1)}}{\\frac {m_{m}(t)^{2}}{m_{p}(t)^{2}}}} alt=\"{\\mathrm {SNR}}={\\frac {3\\times 2^{{2n}}}{1+4P_{e}\\times (2^{{2n}}-1)}}{\\frac {m_{m}(t)^{2}}{m_{p}(t)^{2}}}\" class=mwe-math-fallback-image-inline aria-hidden=true v:shapes=\"_x0000_i1025\">

where

{\\displaystyle P_{e}} is the probability of received bit error

{\\displaystyle m_{p}(t)} is the peak message signal level

{\\displaystyle m_{m}(t)} is the mean message signal level

A signal is quantized using 10-bit PCM. The signal-to-quantization noise ratio will be:

(SNR)db = 6.02 n + 1.76, where n is the number of bits used for quantization