Basic signal operations include time reversal, time scaling, time shifting, and amplitude transformations. These operations are fundamental in signal processing and analysis.

Time Reversal mirrors a continuous-time signal about the vertical axis at t=0. This is achieved by substituting t with −t. For example, if a signal x(t) is considered, the time-reversed signal is x(−t). This operation can be graphically represented, showing the mirrored signal.

Figure1

Time Scaling compresses or expands a signal in time by replacing t with at, where a is a constant. If ∣a∣>1, the signal compresses; if ∣a∣<1, it expands. A negative value of a induces both time reversal and compression or expansion. A graphical representation of this operation on a signal demonstrates these effects.

Time Shifting of a continuous-time signal is done by replacing t with tt0, where t0 is a constant. A positive t0 delays and shifts the signal to the right, while a negative t0 advances the signal and shifts it to the left. For instance, a signal x(t) shifted by t0 is represented as x(tt0).

Amplitude Transformations of a continuous-time signal are generally of the form Ax(t)+B, where A and B are constants. These transformations scale the amplitude and can also shift it vertically. Graphically, an amplitude transformation of a signal shows the effect of scaling by A and shifting by B.

These basic operations—time reversal, scaling, shifting, and amplitude transformations—are essential tools for manipulating and analyzing signals, allowing for various adjustments and modifications in signal processing applications.

Tags
Signal OperationsTime ReversalTime ScalingTime ShiftingAmplitude TransformationsSignal ProcessingContinuous time SignalGraphical RepresentationSignal ManipulationSignal Analysis

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