convert time series back from zero mean and unit variance

Question

I have a rather simple question that I need some advice on. If I have a time series

t = 1:365;
raw =  10+(10-2).*rand(1,length(t)); % generate random time series
signal_1 = 10*sin(2*pi*t/12)+20; % create a signal with a period of 24
signal_2 = 10*sin(2*pi*t/32)+20; % create a signal with a period of 32

y = raw + signal_1 + signal_2; % combine the signals

and I can make the signal to have zero mean and unit variance by

y2 = (y - nanmean(y))./nanstd(y); % zero mean with unit variance

How would I convert this back to the same magnitude as the original series i.e. convert back to be the same as 'y'?

Answer 1

Record the mean and stddev before you do the transformation, so that you can reapply in the opposite direction:

mu = nanmean(y);
sd = nanstd(y);

y2 = (y - mu) / sd;

...

y3 = y2 * sd + mu;