§2.2. Basic operations Example-Consider the two following sequences of length 5 defined for o<n<4 an}=346-90} {b|}={2-145-3} New sequences generated from the above two sequences by applying the basic operations are as follows
§2.2.1 Basic Operations • Example - Consider the two following sequences of length 5 defined for 0≤n≤4 : {a[n]}={3 4 6 –9 0} {b[n]}={2 –1 4 5 –3} • New sequences generated from the above two sequences by applying the basic operations are as follows:
82. 2. 1 Basic operations cn}={an],b|}={6-424-45 dn}={an+bl}={5310-4-3} em}=(3/2){an}={4.69-13.50} As pointed out by the above example operations on two or more sequences can be carried out if all sequences involved are of same length and defined for the same range of the time index n
§2.2.1 Basic operations {c[n]}={a[n].b[n]}={6 –4 24 –45 0} {d[n]}={a[n]+b[n]}={5 3 10 –4 -3} {e[n]}=(3/2){a[n]}={4.5 6 9 –13.5 0} • As pointed out by the above example, operations on two or more sequences can be carried out if all sequences involved are of same length and defined for the same range of the time index n
82. 2.1 Basic operations However if the sequences are not of same length in some situations this problem can be circumvented by appending zero-valued samples to the sequence(s)of smaller lengths to make all sequences have the same range of the time index Example- Consider the sequence of length3 defined for0≤n≤2:{叫}={-2,1,3}
§2.2.1 Basic operations • However if the sequences are not of same length, in some situations, this problem can be circumvented by appending zero-valued samples to the sequence(s) of smaller lengths to make all sequences have the same range of the time index • Example - Consider the sequence of length 3 defined for 0≤n≤ 2: {f[n]}={-2, 1, -3}
§2.2. Basic operations We cannot add the length -3 sequence to the length-5 sequence fan defined earlier We therefore first append fnt with 2 zero-valued samples resulting in a length-5 sequence fen[=f-2 1-30 ·Then gn}={am}+{fin={153-90
§2.2.1 Basic Operations • We cannot add the length-3 sequence to the length-5 sequence {a[n]} defined earlier • We therefore first append {f[n[} with 2 zero-valued samples resulting in a length-5 sequence {fe [n[}={-2 1 –3 0 0} • Then {g[n]}={a[n]}+{f[n]}={1 5 3 –9 0}
§2.2. Basic operations Example -1-1xn-2]-1xn-3 [n yIn] yn=1x+Q2x{n-|+3-2+x|-3]
§2.2.1 Basic Operations • Example - y[n]=α1 x[n]+ α2 x[n-1]+ α3 [n-2]+ α4 x[n-3]