In an FIR digital filter, each sample in the output signal is found by multiplying...

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Electrical Engineering

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?

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This section provides an example of how you can create a filter with integer coefficients In this example a raisedcosine filter with floatingpoint coefficients is created and the filter coefficients are then converted to integers Define the Filter Coefficients To illustrate the concepts of using integers with fixedpoint filters this example will use a raisedcosine filter b rcosdesign25 125 8 sqrt The coefficients of b are normalized so that the passband gain is equal to 1 and are all smaller than 1 In order to make them integers they will need to be scaled If you wanted to scale them to use 18 bits for each coefficient the range of possible values for the coefficients becomes 2 17 2 17 1131072131071 Because the largest coefficient of b is positive it will need to be scaled as close as possible to 131071 without overflowing in order to minimize quantization error You can determine the exponent of the scale factor by executing B 18 Number of bits L floorlog22B11maxb Round towards zero to avoid overflow bsc b2L Alternatively you can use the fixedpoint numbers autoscaling tool as follows bq fib true B signed true B 18 bits L bqFractionLength It is a coincidence that B and L are both 18 in this case because of the value of the largest coefficient of b If for example the maximum value of b were 0124 L would be 20 while B the number of bits would remain 18 Build the FIR Filter First create the filter See Answer

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