Some essential operations for manipulating signals include shifting, scaling, and reflection. When we talk about a signal in time domain, those are called time shifting, time scaling, and time reversal (reflection).
Shifting
To shift a signal
shift to right (delay) shift to left (advance)
Shifting won’t change the size of the signal.
Scaling
The compression or expansion of a signal in time is known as time scaling. To time scale a signal by a factor of
Reflection
Reflection or time reversal can be seen as a special case of scaling with
Combined Operations
Signal operations often combine the above basic operations as
- Time-shift
by to obtain and then time-scale the shifted signal by to obtain . - Time-scale
by to obtain and then time-shift by to obtain
Related
Reference
- Linear Systems and Signals, 1.2