I am a self-learner of DSP by reading various books. I have accomplished basic understanding of Signals - CT and DT and a few transforms. I recently started to learn FIR / IIR Filters.
The part that I cannot understand is that they are termed as 'Filters' which for me logically means blocking / allowing from a threshold value - ex. lower values would be passed higher would be filtered or removed. So if we have a low pass filter - it would lead us to remove high values from a sequence and vice versa for high pass filters - is my understanding correct?
Like HPF (High Pass Filter):
x(n)={1,2,3,4,5,6,7,8,9}
Set threshold as >=5 so output sequence would be {5,6,7,8,9}
OK but the document states FIR / IIR about :
Finite Impulse Response (FIR) : this type of filter gives a finite number of nonzero outputs (response) to an impulse function input. It does not use feed-back.
While
Infinite Impulse Response (IIR) : this type of filter uses feed-back, so it could have an infinite number of nonzero outputs (response) to an impulse function input.
Now I cannot understand what FIR / IIR has to do with my concept of filters - allow / block high / low values. Where does the question of Feedback comes here?
Similarly for wavelets -
We call an octave a level of resolution, where each octave can be envisioned as a pair of FIR filters, at least for the one-dimensional case. One filter of the analysis (wavelet transform) pair is a lowpass filter (LPF), while the other is a highpass filter (HPF). Each filter has a down-sampler after it, to make the transform efficient. For example, a simple lowpass filter may have coefficients {1/2,1/2}, producing outputs (x[n] + x[n - 1])/2, which is clearly the average of two samples. A corresponding simple highpass filter would have coefficients {1/2,-1/2}, producing outputs (x[n] - x[n - 1])/2, half the difference of the samples.
I am not able to get the concept of how and why here equation : (x[n] + x[n - 1])/2 and (x[n] - x[n - 1])/2 is being referred?