I am a bit confused with simple discrete functions. A bit worried it may be something easy that I am missing, in which case please be kind.I would appreciate it if someone could help me.
For a simple discrete function like the following where x[n] = {-1,-2, 2, 2, 3}, the -2 being the sample 0 i.e. n=0. I have attached a picture of the function. Now if the function is delayed by 1 sample the function will look like this: y[n]=x[n-1]. The minus denoting a delay of 1 sample.
So for x[n-1], the minus denotes a lag, its not used as a subtraction. Therefore the discrete function would look as follows: y[n] = x[n-1] = {-1,-2, 2, 2, 3}, the -1 being sample =0.
When the function is reversed in time, then the sample amplitudes are flipped over with the 0 being the pivot point. The function being: y[n] = x [-n] , the series being {3,2, 2, -2, -1}, -2 being sample 0.
When there is a function which is reversed in time and also has a shifting value, then why does that arithmetic give you the correct sample number e.g.
y[n] = x [-n] , {3,2, 2, -2, -1} -2 is sample 0.
y[n]= x [-n-1] or y[n] = x[-1-n]
Sample number x[-n] substituted x[-n-1] New sample number
-3 -3-1 -4
-2 -2-1 -3
-1 -1-1 -2
0 0-1 -1
1 1-1 0
Why does a time reversed sifting of a discrete function give the correct new sample number when arithmetic is applied but the same does not happen for a function that is simply shifted.
For example y[n] = x[n-1], x[n] = {-1,-2, 2, 2, 3}, -2 is the sample 0.
Sample number x[n] substituted x[n-1] New sample number
-1 -1-1 -2, this should be the new sample 0.
And so on.
For a simple discrete function like the following where x[n] = {-1,-2, 2, 2, 3}, the -2 being the sample 0 i.e. n=0. I have attached a picture of the function. Now if the function is delayed by 1 sample the function will look like this: y[n]=x[n-1]. The minus denoting a delay of 1 sample.
So for x[n-1], the minus denotes a lag, its not used as a subtraction. Therefore the discrete function would look as follows: y[n] = x[n-1] = {-1,-2, 2, 2, 3}, the -1 being sample =0.
When the function is reversed in time, then the sample amplitudes are flipped over with the 0 being the pivot point. The function being: y[n] = x [-n] , the series being {3,2, 2, -2, -1}, -2 being sample 0.
When there is a function which is reversed in time and also has a shifting value, then why does that arithmetic give you the correct sample number e.g.
y[n] = x [-n] , {3,2, 2, -2, -1} -2 is sample 0.
y[n]= x [-n-1] or y[n] = x[-1-n]
Sample number x[-n] substituted x[-n-1] New sample number
-3 -3-1 -4
-2 -2-1 -3
-1 -1-1 -2
0 0-1 -1
1 1-1 0
Why does a time reversed sifting of a discrete function give the correct new sample number when arithmetic is applied but the same does not happen for a function that is simply shifted.
For example y[n] = x[n-1], x[n] = {-1,-2, 2, 2, 3}, -2 is the sample 0.
Sample number x[n] substituted x[n-1] New sample number
-1 -1-1 -2, this should be the new sample 0.
And so on.
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