Let's assume i'd like to create a digital lowpass with 5 taps. I am not using a window function but just the impulse response from my fourier integral.

i get the following coefficients: 0.5 0.86 1 0.86 0.5

What i don't understand: How does the filtering work. Assuming i have a constant signal '1' and i want to use the filter on that.

I applied the filter and what i get is

0.5 1.36 2.36 3.22 3.72 3.22 2.36 1.36 0.5

But now i am clueless how to draw this? The output is bigger then my input signal?

Let us assume that I wouldd like to create a digital lowpass with 5 taps. I am not using a window function but just the impulse response from my Fourier integral.

I get the following coefficients: $h=[0.5\, 0.86 \,1 \,0.86\, 0.5]$.

What I don't understand: how does the filtering work? Assuming that I have a constant signal $x$ with '1' and I want to use the filter on that.

I applied the filter and what I get is

$$y=[0.5 \, 1.36\, 2.36\, 3.22\, 3.72\, 3.22\, 2.36\, 1.36\, 0.5 ]\,.$$ But now i am clueless how to draw this? The output is bigger then my input signal?