Question

Consider the following signal constellation:

s0 (t)=acos(2πf ₜ), 0 ≤ t ≤ T
s1 (t)=acos(2πfₜ+ 3π ), 0 ≤ t ≤ T
s2 (t)=acos(2πf + 32π ), 0 ≤ t ≤ T
s3 (t)=acos(2πfₜ +π), 0 ≤ t ≤ T
s4 (t)=acos(2πfₜ + 34π ), 0 ≤ t ≤ T
s5 (t)=acos(2πfₜ + 35π ), 0 ≤ t ≤ T
​
Determine the dimensionality of the signal set and plot it in the signal space.

Answer 1

The dimensionality of the signal set is 5, and it can be plotted in a 3D signal space.

Step-by-step explanation:

The dimensionality of the signal set can be determined by counting the number of distinct signals in the set. In this case, there are 5 distinct signals, each corresponding to a different value of t: s0(t), s1(t), s2(t), s3(t), and s4(t). Therefore, the dimensionality of the signal set is 5.

To plot the signal set in the signal space, we can use a 3D coordinate system with the time as the z-axis. Each signal can be represented as a point in this space. For example, s0(t) can be represented as (a, 0, t) where a is the amplitude of the signal.