Image text transcribed for accessibility: Fourier series and compression. Many applications in electrical engineering. such as image compression, video streaming, etc., require n signal to be compressed using a lossy compression scheme. In this problem, we explore how much a signal is corrupted by discarding some of its Fourier series coefficients. If we can discard some coefficients without changing the signal drastically, we can store (or transmit) fewer coefficients to represent the signal. Supposes we are given the Fourier coefficients of a signal that w wish to compress: Ck = a-|k|, where a > 1 and k = .... -1, 0, 1,.... Assume that the signal has period 2pi. The signal can be expressed as the Fourier series Compute the energy in one period of this signal (the power of this signal). Hint: you can use Parseval's theorem: Also recall the following geometric series properties: We want to store the signal using just the Fourier series coefficients. Since there are an infinite number of coefficients, we cannot store them all. Instead, we keep only the coefficients Ck where -N k N, and discard all the coefficients for |k| > N (we assume they are zero). How much energy is in one period of this "compressed" signal? If a = 1.2 and we only keep the 21 coefficients for -10 k 10, what percentage of the energy of the original signal is captured in the compressed signal?