In an FIR digital filter, each sample in the output signal is found by multiplying M samples from the input signal by M predetermined coefficients, and adding the products. The characteristics of these filters (high-pass, low-pass, etc.) are determined by the coefficients used. For this problem, assume M = 5000, and that single precision floating point math is used. a. How many math operations (the number of multiplications plus the number of additions) need to be conducted to calculate each point in the output signal? b. If the output signal has an average amplitude of about one-hundred, what is the expected error on an individual output sample? Assume that the round-off errors combine by addition. Give your answer both as an absolute number, and as a fraction of the number being represented. c. Repeat (b) for the case that the round-off errors combine randomly. Explain in detail?
