Artefacts when filtering a contiguous signal

Hello,

I have a signal vector vec (54 sampling points). That looks like that:

vec = [5 8 10 8 5 3 1 3 5];
vec = [vec vec vec vec vec vec];

When I filter it with a lowpassfilter, it looks like that (Fig1):

Code for the filtering is:

h = fdesign.lowpass('fp,fst,ap,ast', 0.10, 1, 1, 60);
Hd = design(h, 'equiripple');
c = filter(Hd,vec);
plot(c);

Now, I want to split the sample in zwo sections and filter them separately. As a result, I want to get the same result as in Fig1.

I tried this code:

% design filter
h = fdesign.lowpass('fp,fst,ap,ast', 0.10, 1, 1, 60);
Hd = design(h, 'equiripple');

% split signal in two sections
vec1 = vec(1:27);
vec2 = vec(28:54);

% define numerator, denominator and initial conditions for filter delay
num = Hd.Numerator;
den = 1;
zi = vec1(end-2:end);

% filter the two sections 
c1 = filter(num,den,vec1);
c2 = filter(num,den,vec2,zi);

% concatenate and plot the filtered sections 
c = [c1 c2];
plot(c);

but get artefacts in the plot:

Could someone tell me what am I doing wrong?

Best regards,

Rocketman

Answer 1

[Jan]

The final state of the filter parameters after the 1st block is not the value of the signal. Replace:

zi = vec1(end-2:end);  % Nope
c1 = filter(num, den, vec1);
c2 = filter(num, den, vec2, zi);

by

[c1, zf] = filter(num, den, vec1);
c2       = filter(num, den, vec2, zf);

There are still tiny differences in the magnitude of 1e-15 caused by rounding, because the implementations differ slightly:

c1 = filter(Hd, vec);
c2 = filter(Hd.Numerator, 1, vec)
plot(c1 - c2)

[rocketMan]

Thank you so much!!!