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Programming Questions 1 Convolutions Define the following signals I=(3, 4, 1.2.5, 6, 7, 8, 2, 4] h = [1 4:1) s) Calculate the convolution between these two signals, r*h, in time domain (don't use any libraries or built in functions besides addition and multiplication). Note that the convolution of two signals of length N and M should be of size (N+M - 1). b) Describe in words what this convolution does. c) Convolutions are (N) when computed in the time domain for two 1D signals of length N. Le, the physical resources (eg., time) that are needed to convolve two 1D signals of the same length are proportional to the square of the signal length. However, with a constant filter like h, we can modify the process to make it (N). Show how to do a convolution with s filter like h where all the elements are the same in O(N) time. d) Show the time difference from the technique discussed in c) by replicating and h 100 times to make then 100 times the original length, and time how long the convolution takes with the regular technique vs the more efficient one. Programming Questions 1 Convolutions Define the following signals I=(3, 4, 1.2.5, 6, 7, 8, 2, 4] h = [1 4:1) s) Calculate the convolution between these two signals, r*h, in time domain (don't use any libraries or built in functions besides addition and multiplication). Note that the convolution of two signals of length N and M should be of size (N+M - 1). b) Describe in words what this convolution does. c) Convolutions are (N) when computed in the time domain for two 1D signals of length N. Le, the physical resources (eg., time) that are needed to convolve two 1D signals of the same length are proportional to the square of the signal length. However, with a constant filter like h, we can modify the process to make it (N). Show how to do a convolution with s filter like h where all the elements are the same in O(N) time. d) Show the time difference from the technique discussed in c) by replicating and h 100 times to make then 100 times the original length, and time how long the convolution takes with the regular technique vs the more efficient one