Signal Transformation

Question 1

Amplitude Scaling

Answer 1

When a signal x(t) is scaled by a constant c, the signal value at every time instant is multiplied by c. The transformation signal is written as cx(t). If c is negative, the signal also rotates about the horizontal axis.

Question 2

Time Reversal

Answer 2

If x(t) is the original signal, the time-reversed signal is denoted by x(-t) and it is obtained by flipping x(t) about the vertical axis

Question 3

Time Shift

Answer 3

If x(t) is the original signal, the time-shifted signal is denoted by x(t+c) or x(t-c).

X(t+c) is obtained by shifting x(t) to the left by c units.

X(t-c) is obtained by shifting x(t) to the right by c units.

Question 4

Time Scaling

Answer 4

If x(t) is the original signal, the time-scaled signal is denoted by x(ct)

4 cases

• c is positive, |c| > 1
• c is positive, |c| < 1
• c is negative, |c| > 1
• c is negative, |c| < 1

Question 5

|c| > 1

Answer 5

The transformation is called signal compression. The transform signal is obtained by compressing the time axis by c units.

Question 6

|c| < 1

Answer 6

Signal expansion

Question 7

Combination of Basic Transformations

Answer 7

C1x(C2t + C3)

C1-amplitude scaling
C2-time scaling
C3-time shift

1. Time shift
2. Time scaling
3. Amplitude scaling