How to create a random and smooth varying rpm profile?

Hi,

I am trying to create an rpm profile with rpm- varying between 1190 rm to 1210 rpm . Could someone help me on how to create it.

clear all
close all

fs= 10000;        % sampling frequency
dt = 1/fs; 
T = 1; % total time
t = 0:dt:T; % time vector


rpm = 1200*ones(length(t),1)+ randn(length(t),1);

figure()
plot(t,rpm); xlabel('s'); ylabel('rpm')

I tried above by adding random noise and it did not work. I am trying to create the below type of rpm profile.

Answer 1

[DGM]

Filter the rpm signal. Depending on what toolboxes you have, there are a lot of tools you could use. I'm just going to use a very rudimentary approach without anything special.

fs= 10000; % sampling frequency
dt = 1/fs; 
T = 1; % total time
t = 0:dt:T; % time vector

% a random vector
rpm = randn(length(t),1);

% filter the vector
ft = 0.05; % this scales the filter width
R = floor((ceil((ft*fs*5-1)/2)*2+1)/2); % this is always even
x = -R:R; % so this is always of odd length
fk = exp(-(x/(1.414*ft*fs)).^2); % a 1-D gaussian
rpm = conv(rpm,fk,'same'); % apply LPF

% scale/translate the vector
rpmrange = [1190 1210];
rpmrange0 = [min(rpm) max(rpm)];
rpm = (rpm-rpmrange0(1))/range(rpmrange0); % normalize
rpm = rpm*range(rpmrange) + rpmrange(1); % rescale

% show it
plot(t,rpm); xlabel('s'); ylabel('rpm')

[Kalasagarreddi Kottakota]

Hi, Thanks for your response. Can I ask you the following?

1. May I know those tool boxes?
2. What is R in your script?

[DGM]

The Signal Processing Toolbox is probably the most relevant here.

https://www.mathworks.com/help/signal/ug/filtering-data-with-signal-processing-toolbox.html

In the script, R is the half-width of the filter kernel. R is a function of fs*ft, which is what I used as the std deviation of the gaussian. The goal there is simply to create a filter that's wide enough to include a fair amount of the tails on the gaussian. In this case, the scaling factor was 5. A factor less than 5 would truncate more of the tails. The rest of the calculation of R is just to make sure that the result is an even integer.

FK doesn't have to be a gaussian. That's just what I chose to use. It could be a box or any other window function. Since the output of the filter gets scaled anyway, any normalization of the filter kernel doesn't have any effect. Notice that I didn't sum-normalize the gaussian.