interpolate data in timeseries

Hi all,

I have a timeseries vector lets say with 7 points : v=[0.18 3.15 0.18 0.16 0.17 0.58 0.33 ];

I would like to create a new vector by interpolating data so I have extra 3 points among two values: somethng like:

v_new=[0.18 ... ... ... 3.15 ... ... 0.18... and so on ]

could you help me with that?

thanks!!

Answer 1

[dpb]

v=[0.18  3.15  0.18  0.16  0.17 0.58 0.33 ];                    % example data
% the engine
nI=3;                                                           % number points to insert
N=numel(v);                                                     % initial vector size
NN=(N-1)*nI+N;                                                  % new N for augmented v
xv=linspace(1,N,NN);                                            % uniform spacing along 1:N NN points
vv=interp1(1:N,v,xv);                                           % linear interpolation
vvv=interp1(1:N,v,xv,'pchip');                                  % or pchip interpolation

Illustrate results...

plot(v,'o-')
hold on
plot(xv,vv,'x')
plot(xv,vvv,'d-')
legend('Original','Linear','PChip')

produces

"Choose your poison" as far as what interpolant you actually want.

If you have Signal Processing TB, there's also resample you could play with.

Answer 2

[Jon]

Although you say you have a "time series" it looks like v is just an ordinary vector. Assuming you have another "t" vector to go along with this data you could do something like this:

t = [0 9 10 15 20 25 33] % made up example time vector, not necessarily evenly space
v = [0.18  3.15  0.18  0.16  0.17 0.58 0.33 ]; % your v vector
t_new = [0 2 3 9 9.5 9.8 10 11 12 15 20 21 21.2 25 29 30 33] % vector of times you want to have data for including original
v_new = interp1(t,v,t_new)

v_new =

Columns 1 through 11

0.1800    0.8400    1.1700    3.1500    1.6650    0.7740    0.1800    0.1760    0.1720    0.1600    0.1700

Columns 12 through 17

0.2520    0.2684    0.5800    0.4550    0.4237    0.3300

[Jon]

My answer shows generally how to interpolate extra points. I see @dpb gave you more precisely what you asked for, an approach to insert exactly n points between your existing points assuming the original "t" values (independent variable) is equally spaced. From your description I wasn't sure if you could assume that.

[dpb]

You can also accomplish that objective by iterating between time points...

plot(t,v,'o-')
fntv=@(t1,t2,n)linspace(t1,t2,n+2);
tv=cell2mat(arrayfun(@(i)fntv(t(i),t(i+1),nI),1:numel(t)-1,'UniformOutput',false));
vv=interp1(t,v,tv);
hold on
plot(tv,vv,'xr')

gives