Problems for the 10th Quiz

Name: Student ID: Score:

1. (a) (30%) Suppose {m[n], n = 0, . . . , 7} = {0, 1, 2, 1, 0,−1,−2,−1}.With step size ∆ = 2 and

eq[n] =

{∆, e[n] ≥ 0

−∆, e[n] < 0

complete the following table based on the figure above.

n 0 1 2 3 4 5 6 7m[n] 0 1 2 1 0 −1e[n] 0 1 1 0 −2 −1eq[n] 0 2 2 2 −2 −2

(b) (30%) Of the slope overload distortion and the granular noise,which one will occur if ∆ = 1?

Solution.

(a) Following e[n] = e[n− 1] + (m[n]− eq[n− 1])

n 0 1 2 3 4 5 6 7m[n] 0 1 2 1 0 −1 −2 −1e[n] 0 1 1 0 −2 −1 −1 0eq[n] 0 2 2 2 −2 −2 −2 2

(b) Since ∆ = 1 < maxn |m[n]| = 2, slope overload distortion willoccur.

Note: This is the equivalent block diagram for the delta-sigmamodulation. Hence, the integration of m[n] (i.e., i[n]) needs to be

traced, it requires ∆Ts

≥ |i[n]−i[n−1]|Ts

= |m[n]|Ts

to prevent the slopeoverload distortion.

2. (40%) What are the two main limitations of AQF in comparison withAQB?

Solution. Although AQF is in principle a more accurate estimator, ithas two main limitations in comparison with AQB; i.e., it requires

• an additional buffer to store unquantized samples for the learn-ing period (hence a processing delay due to buffering and otheroperations for AQF is necessary);

• an explicit transmission of level information ∆[n] to the receiver(as the receiver, even without noise, only has the quantized sam-ples).

The above limitations can be relaxed by using AQB.