# Digital Signal Processing (Discrete signals scaling, shifting etc.)

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 :)

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

(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.