# Transfer function coefficients and impulse response - FIR filter

I am currently working on a FIR filter (varying in time). I have the real coefficients of the filter, but I would like to know if they correspond to the coefficients from the impulse response (as $$b[k]$$) and how I could get the coefficients of the transfer function from it.

The example is that I'm trying to plot the frequency response of the filter in Matlab, but the coefficients doesn't seem the match the definition of filter(b,a,x) with a = 1 and b my coefficients.

It doesn't get me the right result (as I tested them with another FIR function but with only one tap) : I should get after the filtering, values included in $$[-20,20]$$, but with the basic function filter, I only get results in this range $$[-0.4,0.5]$$. I'm plotting the results in dB and the shape is exactly the same despite getting the wrong values.

In the definition of the filter function, it says the coefficients should be the ones used in $$H(z)$$, which I think is not the case.

I'm sorry if I'm missing a big part but I have some comprehension problem about how filters work.

• Welcome to SE.SP! Can you explain what you mean by It doesn't get me the right result  ? What were you expecting, and what did it actually give you? Please edit your question to add this information. – Peter K. May 20 '20 at 15:55
• Hey, thank you for your attention, I've edited my post and I hope it's clearer now. – ThT May 20 '20 at 16:49