problemsforthe10thquiz name: studentid:...
TRANSCRIPT
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.