Question on FIR filter I've been trying to do this problem for the last few hours. Could someone show me the workings on how it is done? Not just the answer.



The figure shows the structure of a FIR filter where $A = 1.5$, $B = 0.69$ and $C = 3.0$.

If $x[n] = u[n]$, what is the value of $y[n]$ for $n = 20$?
[EDITED] From left to right, try to find the impulse response. On the bottom branch, delay the unit pulse $d$ and get $d[n-1]$. Add $Ad[n]$. Delay twice and get $d[n-3] +Ad[n-2]$. Add $Bd[n]$. Add $Cd[n-1]$. So the FIR coefficients of the impulse response $h$ will be $[1,A,C,B]$, but in the reverse order (as correctly pointed out by colleagues), because $y[n] = \sum d[k]h[n-k]$. So your system is causal, and $h[0]=B$, $h[1]=C$, $h[2]=A$, $h[3]=1$.

However, at $n=20$, you are in a stabilized region of the signal (all the known samples are equal to $1$, so even if you make a mistake as I did first, the answer will be the same, $1+A+C+B$, as stated before by other colleagues.