Реферат: Quantization error analysis of the quadrature components of narrowband signals

.

The last expression means that the variance of the amplitude error of the signal caused by quantization errors of its quadrature components is practically equal to the variance of the quantization error of the A/D converter.

Phase error analysis of the quantized narrowband signals

The phase error _i of the distorted signal (we measure the phase error by comparing the input phase with the output phase) can be found from fig. 2. Actually, from the triangle OBE we get

hence

.(17)

Let us define the limits of the angle variation. From the triangle OBF we get

, (18)

and from the triangle OAG we get

. (19)

Transforming formula (18) considering the formula (19) we obtain

. (20)

It is obvious from formula (20) what the maximum phase error will be, provided the value of the inphase component is minimum and the quantization error is maximum, i.e. provided

. (21)

Inserting these values into formula (20), we get

. (22)

Transforming in the formula (22) the sum of angles [8] we get

. (23)

Solving the equation (23) with respect to we get

. (24)

It is clear that maximum value of the angle will be, if , hence

.(25)

We have found that maximum phase error does not exceed 53°. Therefore we can replace sin in the formula (17) by its argument (with the error less than 10 %)

. (26)

The mean of the phase error is

, (27)

where .

The variance of the phase error can be found from formulas (6) and (9)