PCM | Pulse Code Modulation Important Formulas

Pulse code modulation is used to convertor samples sample analog signal to digital signal.

1.      Quantization error = m(t) – m_q(t)

2.    Quantization error  ≤ S/2

3.     Step size = (V_H – V_L)/m

                 =  (V_H – V_L)/2ⁿ

Quantization noise is uniformly distributed in each quantization interval then the probability density is (-s/2 to s/2 with amplitude of 1/s)

The quantization noise power =N_o= E[Q²(t)]

 = _-∞ ⌡^∞ (Q² (t)* f_Q(Q)) dq

 =_-s/2⌡^s/2 (Q² * 1/s) dq

= (1/s )*(2*[Q³/3]^s/2)

N_o= S²/12

4.   bit rate r_b= n * f_s

5.     bandwidth = r_b* ½ = (n * f_s)1/2

6.   signal power is = (A²_m/2 )

              Here message signal m(t)= A_msinwt

7.    Signal to Noise ratio (S/N): (2A_m/2ⁿ) / (S²/12)

8.   Signal to noise ratio = 3/2 (2²ⁿ)

          10 log₁₀ (3/2 (2²ⁿ)) = 10[log₁₀ (3/2) + 2nlog₂]

        = (1.76 + 6N) DB

9.    Bandwidth = (R_b/2)(1+α)  here α is roll of factor