Test: Time Scaling Property - Electrical Engineering (EE) MCQ

Concept:

Time-shifting property: When a signal is shifted in time domain it is said to be delayed or advanced based on whether the signal is shifted to the right or left. 

For example:

Time scaling property: A signal is scaled in the time domain with the scaling factor 'a'. 

If a > 1, then the signal is contracted by a factor of 'a' along the time axis. 

if a < 1, then the signal is expanded by a factor of 'a' along the time axis. 

For example:

Analysis:

We can observe that if we scale f(t) by a factor of ½ and then shift, we will get g(t).

First scale f(t) by a factor of ½ ,

g₁(t) = f (t/2)

Shift g₁(t) by 3

In option A,

z₁[n] = x[n-3]

z₂[n] = z₁[4n] = x[4n-3]

y[n] = z₂[-n] = x[-4n-3] ≠ x[3-4n]

In option B,

z₁[n] = x[n+3]

z₂[n] =z₁[4n] = x[4n +3]

y[n] = z₂[-n] = x[-4n+3]

In option C,

v₁[n] = x[4n]

v₂[n] = v₁[-n] = x[-4n]

y[n] = v₂[n+3] = x[-4(n+3)] ≠ x[3-4n]

In option D,

v₁[n] = x[n]

x₂[n] = v₁[-n] = x[-4n]

y[n] = v₂[n-3] = x[-4(n-3)] ≠ x[3-4n]

First time shifting then compression(scaling) will be done.

We have x′(t)=

Concept:

Time-shifting property: When a signal is shifted in time domain it is said to be delayed or advanced based on whether the signal is shifted to the right or left. 

For example:

Time scaling property: A signal is scaled in the time domain with the scaling factor 'a'. 

If a > 1, then the signal is contracted by a factor of 'a' along the time axis. 

if a < 1, then the signal is expanded by a factor of 'a' along the time axis. 

For example:

Analysis:

We can observe that if we scale f(t) by a factor of ½ and then shift, we will get g(t).

First scale f(t) by a factor of 1/2 ,

g₁(t) = f (t/2)

Shift g₁(t) by 3