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Textbook by: Carlos E. Davila. E-mail the author

# Basic Signal Operations

Module by: Carlos E. Davila. E-mail the author

Summary: Overview of basic continuous-time signal operations.

We will be considering the following basic operations on signals:

• Time shifting:
y(t)=x(t-τ)y(t)=x(t-τ)
(1)
The effect that a time shift has on the appearance of a signal is seen in Figure 1. If ττ is a positive number, the time shifted signal, x(t-τ)x(t-τ) gets shifted to the right, otherwise it gets shifted left.
• Time reversal:
y(t)=x(-t)y(t)=x(-t)
(2)
Time reversal flips the signal about t=0t=0 as seen in Figure 1.
• Addition: any two signals can be added to form a third signal,
z(t)=x(t)+y(t)z(t)=x(t)+y(t)
(3)
• Time scaling:
y(t)=x(Ωt)y(t)=x(Ωt)
(4)
Time scaling “compresses" the signal if Ω>1Ω>1 or “stretches" it if Ω<1Ω<1 (see Figure 2).
• Multiplication by a constant, αα:
y(t)=αx(t)y(t)=αx(t)
(5)
• Multiplication of two signals, their product is also a signal.
z(t)=x(t)y(t)z(t)=x(t)y(t)
(6)
Multiplication of signals has many useful applications in wireless communications.
• Differentiation:
y(t)=dx(t)dty(t)=dx(t)dt
(7)
• Integration:
y(t)=x(t)dty(t)=x(t)dt
(8)

There is another very important signal operation called convolution which we will look at in detail in Chapter 3. As we shall see, convolution is a combination of several of the above operations.

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