# 4.4 - 4.4 Mathematical Representation of Signals Consider...

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53 4.4 Mathematical Representation of Signals Consider the following waveform: () cos ( ) et E t ω φ =+ e(t) Δ t t = . t =−Δ Note the sign convention where a negative phase difference is a positive time difference. (Things that come later have phase < 0) Here's a different way of showing the same thing. At any fixed point in time: φ E R i Phasor.

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54 Properties of phasors The phase angle φ is the angle between E and the Real axis. The amplitude at time t is the projection of E onto R. Oscillatory motion appears as counter-clockwise rotation at a constant angular frequency, ω . The usual variation in amplitude is seen as the variation in E r , the projected length of the vector of fixed length |E| onto R. When = 0, E r = |E| When = 90 o or π /2, E r = 0 When = 180 o or π , E r = -|E| An alternative to: ( ) () cos et A t =+ is: A t = ∠+ If the convention is adopted to draw the diagram at t =0, then we can write, eA = . must be remembered. Sometimes you will find, A = E , but we will keep this bold notation for standard complex variables. Finally, you may well encounter
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4.4 - 4.4 Mathematical Representation of Signals Consider...

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