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Given that x[n] = [5 1 7 9 4 3], where 5 is x[0]. Find x[n-1] , 2x[n-1] and -2x[n-1]+3.

Attempting this question without any guidance from my professors unfortunately as they did not teach this bit. Searched online and also there aren't many questions like this.

From what I know,

(I) Having n-1 means you should shift right by 1, which means x[0] is now equals to 0? So x[n-1] = [0 5 1 7 9 4 3]?

ii) 2x[n-1] is simply a magnitude scaling of part one, so is it simply just 2x[n-1] = [0 10 2 14 18 8 6]?

(iii) -2x[n-1]+3. Is this simply again a magnitude scaling by -2 of part 1? Not sure how to do the +3 function though.

Any help will be appreciated here :)

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  • \$\begingroup\$ Yes to first two. Add 3 to all values, e.g. x[n]+3 = [ 8 4 10 12 7 6] \$\endgroup\$
    – Chu
    Commented Aug 8, 2021 at 9:01

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Your attempts (1) and (2) are correct.

(1) \$x[n-1]\$ : represents time shifting of \$x[n]\$ to the positive side by \$1\$ sample. So, shift each sample to the right. Hence the \$0^{th}\$ sample becomes \$0\$.

(2) \$2.x[n-1]\$ : represents amplitude scaling of the time-shifted version of \$x[n]\$ by \$2\$. So, multiply each sample by \$2\$.

(3)\$-2.x[n-1]+3\$ : represents amplitude scaling of \$x[n-1]\$ by \$-2\$, and then amplitude shifting by \$3\$, i.e., you have to simply add \$3\$ to each sample.

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