Question

Consider a discrete-time (dt) signal x[n] = (5−n)p5[n] where pn [n] = u[n] − u[n − n]. (a) roughly sketch x[n] showing all its non-zero samples.

Answer 1

To sketch the given signal x[n]=(5−n)p5[n], we need to find the non-zero samples. The non-zero samples are x[0]=5, x[1]=4, x[2]=3, x[3]=2, x[4]=1, and x[5]=0.

Step-by-step explanation:

To roughly sketch the given signal x[n]=(5−n)p5[n], we need to find the non-zero samples. The signal is multiplied by the signal pn[n]=u[n]−u[n−n]. The unit step function u[n] is equal to 1 for n≥0 and 0 otherwise. Let's find the non-zero samples:

For n=0, pn[0]=u[0]−u[0−n]=u[0]−u[0]=1−1=0.

For n=1, pn[1]=u[1]−u[1−1]=u[1]−u[0]=1−1=0.

For n=2, pn[2]=u[2]−u[2−1]=u[2]−u[1]=1−1=0.

By observing the pattern, we see that pn[n] is equal to 1 for n≥0 and 0 otherwise. Therefore, x[n]=(5−n)p5[n]=(5−n) for n≥0 and x[n]=0 for n<0. The non-zero samples are x[0]=5, x[1]=4, x[2]=3, x[3]=2, x[4]=1, and x[5]=0. We can now sketch the signal showing these non-zero samples.