A discrete time signal $x[n]$ is defined in terms of unit impulse function as follows:

$$x[n]= 1-\sum_{r=3}^\infty \delta[n-1-r]$$

If $x[n]$ is expressed in terms of the unit step function as $x[n]=u[an-b]$ then find the values of $a$ and $b$. I have tried to solve but not able to solve it further. Please check this image:

I have tried to solve

Please correct my grammar if there is any mistake.


1 Answer 1


Your result is correct, but it can be rewritten in an even simpler form, as suggested in the problem statement: $x[n]=u[an+b]$

If you draw the signal then you'll see that it is just a reversed and shifted unit step. From that drawing it should be easy to derive the constants $a$ and $b$.


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