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Signals and Systems

Signals and Systems - Signals and Systems Summer 2009 Dr...

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Click to edit Master subtitle style 10/6/09 Signals and Systems Summer 2009 Dr. Jean Andrian
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10/6/09 Reading assignment: Signals and Systems by Haykin and Van Veen Chapter 1, sections 1.1 to 1.8
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10/6/09
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10/6/09
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10/6/09
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10/6/09
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10/6/09
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10/6/09 Even and odd signals CT signal x(t) is said to be an even signal if x(-t)=x(t) for all t X(t) is said to be an odd signal if x(-t)=-x(t) for all t DT signal x[n] is even if x[-n]=x[n] for all n And odd if
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10/6/09 Any signal x(t) can be decomposed into a sum of even and odd components xe(t) and xo(t) such that x(t)= xe(t)+xo(t) where xe(t)= ½[x(t)+x(-t)] and xo(t)= ½[x(t)-x(-t)]
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10/6/09 A complex-valued signal is said to be conjugate symmetric if x(t)= x*(-t) x(t)= a(t) + j b(t) x*(t)= a(t) – j b(t) x*(-t)= a(-t)+ j b(-t) True if a(t)=a(-t) and b(-t)=-b(t) that is the real part is even and the imaginary part is odd
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10/6/09 Periodic signals A CT periodic signal x(t) is a function of time that satisfies the condition x(t)= x(t + T) for all t, T>0 and is the smallest number such that the condition is satisfied. T is called the period and f = 1/T is called the fundamental frequency of the signal. The frequency is measured in hertz (Hz). The angular frequency is measured in radians per second, and is defined by ω = 2π f = 2 /T π
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10/6/09 Periodic signals (cont.) A DT periodic signal x[n] is such that x[n] = x[n + N] for integers n, where N is the smallest positive integer. N is called the fundamental period of the DT signal x[n]. The fundamental angular frequency or, simply, the fundamental frequency of x[n] is defined by Ω = 2π/N, which is measured in radians.
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