Shifting, scaling and reversing transform signals.
Time shift x(t-t₀), time scaling x(at), time reversal x(-t), amplitude scaling and addition are fundamental operations. Order of operations matters for combined transformations. They underlie convolution, modulation and delay lines.
x(2t) plays a recording at double speed.
Operations on signals such as shifting and scaling describe timing changes and gain changes, which are common in every processing chain.
Shifting, scaling and reversing transform signals.
Operations on signals such as shifting and scaling describe timing changes and gain changes, which are common in every processing chain.
It moves the signal along the time axis, so x(t minus t0) is the original signal delayed by t0.
It flips the signal about the vertical axis, which changes its behaviour for causal systems.
Typical applications include delaying a control signal by a fixed number of samples, reversing a recorded signal to process it backwards and scaling a sensor reading to engineering units.
Study "Basic signals" first (topic 6 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
Shift delays when t₀>0. Scaling by a>1 compresses. Precedence of shift then scale.
x(2t) plays a recording at double speed.
The next topic is "Systems", which builds directly on this one.
It is classed as Beginner in Signals, Control & Comms (topic 7 of 101). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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