🚀 go-pugleaf

   I am taking a course at the University called:
       Signal Processing Algorithms (ECE 416).
   I have a strong mathematical background, and understand
the mathematics behind The Fourier and Z-Transforms. For example
I know that any signal is composed of an Amplitude and a
phase, and given any digital signal the signal can be changed
by using filters or Amplifiers. (I fully understand what Amplifiers
do - eg. Amplify the Power, Voltage or Current).
   What I am confused about is: What is the purpose behind filter
design? I know they can be used in Radar.  More specifically,
I know that FIR (finite impulse response) has the following
transfer function:  H(z) =        -1         -L
                           b  + b z  + ...+b z
                            0    1          L

               Now, 1) What does it do? What are the benefits
                      over IIR? When is it used?
                    2) What is "impulse response"? I know it is h,
                       but is it just frequency??
                    3) For example they say that the impulse
                       response can be gotten by taking fourier,
                       and in FIR filters is an infinitely long
                       sequence, but what does this all mean?
                     4) I seen many diagrams saying "FIR Impulse
                       response for low-pass filter with..." and
                       Diagram shows Amplitude and Sample number,
                       but how can FIR be don to low pass "filter"?
                       2 filters?? hmmm...
                                        Thanks.