how to filter without a for loop (first order filter)

Hi for a large vector (361156 points or more) I have this for loop to filter engine speed (RPM), it works fine but it is too slow

for i=1:length(RPM)
   RPMFilt(i) = RPM(i) + RPMFilt(i-1) - RPM(i) * RPMFiltConstant
end

where RPMFiltConstant = 0.98 (heavily filtered)

Too avoid the for loop, I guess that I could use the filter function y = filter(b,a,x) (only the matlab filter function, I don't have the DSP or signal processing tool boxes)

But the problem is I am not sure what I should set b and a to in order to achieve the same result as the equation above with 0.98 filter constant, can anyway explain and show how to calculate what b and a should be for different values of RPMFiltConstant between 0 and 1.

thanks

[Jan]

Your code does not run: What is RPMFilt(i-1) for i=1 ? Please post the real code, which runs and produces the wanted result.

Answer 1

[Jan]

Your code does not run: What is RPMFilt(i-1) for i=1 ? Please post the real code, which runs and produces the wanted result.

Do you pre-allocate the output?

RPM = rand(1, 361156);
RPMFiltConstant = 0.98;

tic;
RPMFilt    = zeros(size(RPM));
RPMFilt(1) = RPM(1);  % Or what else?
for i = 2:length(RPM)
  RPMFilt(i) = RPM(i) + RPMFilt(i-1) - RPM(i) * RPMFiltConstant;
end
toc

This takes 0.026 sec on my R2016b/64/Win7 system. Not so much. This is a little bit faster:

tic;
b          = 1 - RPMFiltConstant;
RPMFilt    = zeros(size(RPM));
RPMFilt(1) = RPM(1);  % Or what else?
for i = 2:length(RPM)
  RPMFilt(i) = b * RPM(i) + RPMFilt(i-1);
end
toc

And with filter:

    RPMFilt = [RPM(1), filter([0.02, 0], [1, -1], RPM(2:end), RPM(1))];

[Andrew Tilmouth]

thanks for the reply, yes I forgot to post RPMFilt(1) = RPM(1); it was further up in the code, the reason that the for loop was running slow seems to be that I was using the interp1 function inside the for loop , when I took it out it's fast like you say, thanks for your help

[Lugi Marcato]

RPMFiltConstant is equal to Tsimpling/(Tsimpling+tau)?

what is [0.02, 0], [1, -1]?

[Jan]

@Lugi: I do not knwo what Tsimpling and tau is.

[0.02, 0], [1, -1] are the filter parameters B and A, which perform the same calculations as the for loop, except for rounding errors:

RPM = rand(1, 361156);
RPMFiltConstant = 0.98;
R1    = zeros(size(RPM));
R1(1) = RPM(1);  % Or what else?
for i = 2:length(RPM)
  R1(i) = RPM(i) + R1(i-1) - RPM(i) * RPMFiltConstant;
end

R2 = [RPM(1), filter([1-RPMFiltConstant, 0], [1, -1], RPM(2:end), RPM(1))];

max(abs(R1 - R2) ./ abs(R2))  % Relative error: about 1.7763e-15