Question

For each of the following signals, determine whether or not it is bounded. For the bounded signals, find a bound, Bx​.

(a) x(k)= [1+sin(5πk)] μᵏ
(b) x(k)= k(.5)ᵏ μᵏ
(c) x(k)= [1+(.5)k(1+k) sin(10k)​] μᵏ
(d) x(k)= [1+(−1)ᵏ] cos(10k) μᵏ

Answer 1

The question involves determining if given signals are bounded and finding the associated bounds for those that are, which involves understanding functions like sine and exponential functions along with step-functions. However, without additional definitions or domain specifications, a precise analysis cannot be provided.

Step-by-step explanation:

The given question requires analyzing different signals to determine whether they are bounded, and for those that are, to find a bound Bx. The signals in question vary with respect to the parameter k, and they utilize mathematical operations such as sine functions, exponents, and step-functions (represented by μ), to describe their behavior. A bounded signal is one that does not grow towards infinity, and a bound Bx can be thought of as a value that the signal does not exceed in magnitude. However, without further information, such as the definition of the step-function μ or the domain of k, it is challenging to provide a complete analysis for each case (a) to (d).