Operations on Signals

A discrete-time signal can be transformed to acheive desired outcomes. The simplest example of a change in amplitude is that of an amplifier.

• An analog solution for an amplifier is a complicated electronic circuit.
• The digital solution is a simple multiplication operation performed by the arithmetic logic unit (ALU) of a processor.

On the other hand, a signal can be transformed by nature. We are interested in the inverse transformation to view the original signal. As an example of a change in frequency, a redshift in astronomy indicates an increase in the wavelength of radiation emitted by a receding star, planet or galaxy. This is because the color red has the longest wavelength in the visible spectrum due to the well-known Doppler effect.

There are two variables in a discrete-time signal:

• An independent time axis
• A dependent amplitude axis

Let’s focus on simple amplitude transformations to discrete-time signals.