<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<style type="text/css" style="display:none;"> P {margin-top:0;margin-bottom:0;} </style>
</head>
<body dir="ltr">
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
If you think of the input as an array of values with the latest being pushed in the front and the oldest being dropped off the back</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
<span style="color: rgb(0, 0, 0); font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;"> v0 v1 v2 v3 v4 v5 ...</span><br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
and the function as a sum of these values scaled by some position-specific factor sum(vi * si) = a weighted average</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
then "fast attack" means the first few are multiplied by big factors and the last ones by smaller factors. As Mark said, you could use </div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
0.999**i as your factors, which is easily implemented as </div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
latest out = 0.5 * (latest inp + previous out) - fast decay, not so fast ramp up</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
or = 0.9 * latest inp + 0.1 * previous out - really fast decay, really fast ramp up,</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
but possibly what you want is something more like</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
latest out = F * (average of some of the latest N inputs) + (1-F) ( decaying average of the earlier inputs)<br>
<br>
If N is more than 2, and you are using integers, you can implement the first average by keeping the sum of the N inputs, and adding in the new one and subtracting off the one that is falling out into the decaying average</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
which you could easily do by keeping the latest N inputs in a ring buffer</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
If your h/w has slow floating point multiply, you may want to use something like integer code "out = 7*inp/8" where the multiply is a few shifts and adds, and the divide is a shift to do the scaling</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);" class="elementToProof">
</div>
</body>
</html>