“The Quantization process introduces an error defined as the difference between the input signal, x(t) and the output signal, yt). This error is called the Quantization Noise.”

**Quantization Noise and
Signal-to-Noise:**

“The
Quantization process introduces an error defined as the difference between the
input signal, x(t) and the output signal, yt). This error is called the
Quantization Noise.”

q(t) =
x(t) – y(t)

Quantization
noise is produced in the transmitter end of a PCM system by rounding off sample
values of an analog base-band signal to the nearest permissible representation
levels of the quantizer. As such quantization noise differs from channel noise
in that it is signal dependent.

Let “Δ‟
be the step size of a quantizer and L be the total number of quantization
levels. Quantization levels are 0, ± ., ± 2 ., ±3 . . . . . . . The
Quantization error, Q is a random variable and will have its sample values
bounded by [-(Δ/2) < q < (Δ/2)]. If is small, the quantization error can
be assumed to a uniformly distributed random variable.

Consider
a memory less quantizer that is both uniform and symmetric.

L =
Number of quantization levels

X =
Quantizer input

Y =
Quantizer output

The
output y is given by

Y=Q(x)

which is
a staircase function that befits the type of mid tread or mid riser quantizer
of interest.

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