Let's assume we're measuring a constant$-$level, but noisy, temperature signal from a thermocouple and want to reduce the noise variance of our measurements by $13$ dB $.$

a$)$ What is the number of delay elements needed in a nonrecursive moving average filter to achieve the desired measurement$-$noise reduction?

b$)$ What is the number of delay elements needed in a recursive moving average filter to achieve the desired measurement$-$noise reduction?

c$)$ What is the value of the $$ weighting factor in a standard exponential averager to achieve the desired measurement$-$noise reduction?

d$)$ Fill in the following table:

$\backslash$table$[[$Quantities$,$Nonrecursive,Recursive,Exponential$],[$Multiplies$,,,],[$Additions$,,,],[$Data Memory Locations,,,$]]$