Pauly 24 complex number in polar form z rej r is

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Unformatted text preview: ntations easily. EE102A:Signal Processing and Linear Systems I; Win 09-10, Pauly 26 Signal Energy and Power If i(t) is the current through a resistor, then the energy dissipated in the resistor is ￿T ER = lim i2(t) R dt This is energy in Joules. T →∞ −T The signal energy for i(t) is defined as the energy dissipated in a 1 Ω resistor Ei = lim T →∞ ￿ T i2(t)dt −T The signal energy for a (possibly complex) signal x(t) is Ex = lim T →∞ ￿ T −T |x(t)|2dt. EE102A:Signal Processing and Linear Systems I; Win 09-10, Pauly 27 In most applications, this is not an actual energy (most signals aren’t actually applied to 1Ω resistor). The average of the signal energy over time is the signal power 1 Px = lim T →∞ 2T ￿ T −T |x(t)|2dt. Again, in most applications this is not an actual power. Signals are classified by whether they have finite energy or power, • An energy signal x(t) has energy 0 < Ex < ∞ • A power signal x(t) has power 0 < Px < ∞ These two types of signals will require much different treatment later. EE102A:Signal Processing and Linear Systems I; Win 09-10, Pauly 28 Properties of Energy and Power Signals An energy signal x(t) has zero power 1 = lim T →∞ 2T Px =0 ￿ T |x(t)|2 dt ￿ −T ￿￿ ￿ →Ex <∞ A power signal has infinite energy Ex = lim T →∞ ￿ T |x(t)|2 dt −T 1 = lim 2T T →∞ 2T ￿ ￿ EE102A:Signal Processing and Linear Systems I; Win 09-10, Pauly T |x(t)|2 dt = ∞. −T ￿￿ ￿ →Px >0 29 Classify these signals as power or energy signals 2 1 -2 -1 0 1 -T 2 0 t 1 t −2 −1 0 cos(2! f t ) -2T 2 1 e−t T 2T t 1 2t −2 −1 0 1 2t e−t sin(2! f t ) t A bounded periodic signal. A bounded finite duration signal. EE102A:Signal Processing and Linear Systems I; Win 09-10, Pauly 30...
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This note was uploaded on 09/28/2013 for the course EE 108b taught by Professor Mukamel during the Fall '13 term at Singapore Stanford Partnership.

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