Determine the value of Einfinity and Pinfinity for each of t

Determine the value of E_infinity and P_infinity for each of the following signals: x(t) = e^j(2t+pi/8)_u(t) x(t) = e^j2t cos(2t) x[n] = (0.4+j0.3)^n u[n] x[n] = e^6 pi n cos[pi/2(2n+1)]

Solution

Fossil-based fuels (oil, coal, and natural gas) currently provide about 85% of all the energy use both in US and worldwide. We all know that these resources are being constantly depleted and can\'t be replaced within any practical time span. People often wonder how long exactly would they last? The remaining amount of a particular resource is often characterized by so-called Reserves-to-Production ratio (R/P). In plain language, R/P basically gives us the length of time the reserves would last if their usage continue at the current rate. Here are estimated world total R/P ratios for the main conventional fuels: oil - 46 years, natural gas - 58 years, coal - 118 years. Of course, the usage is constantly changing and once in a while new deposits are found. That\'s why the above numbers are corrected every year.
Aside from being finite, energy production from fossil fuels results in by-products of combustion, or emissions. These emissions affect our environment and may be causing the climate change. In contrast, renewable energy (RE) resources, as the name implies, are constantly replenished naturally and will never be exhausted. Their use generally has a much lower environmental impact than that of conventional fuels. That is why the technologies that utilize them are often called \"green\". In addition, RE can boost US energy security by reducing our dependence on the imports. All these factors, coupled with the government incentives and mandates, result in growing interest in using alternative sources of energy.