Dc valueDefinition:the dc value of w(t) is given by its time average,(w(t))Wde= (w(t) =lim1/T r/2J T/2w(t)dtorWdc= <w(t)) =1/(t,-t,)/ w(t)dtPower: Definition:the instantaneous power is given by:p(t) = v(t)i(t)and the average power is : P=<p(t)>=<v(t)i(t)>i(t)+circuitv(t)
• Definition:the dc value of w(t) is given by its time average, 〈w(t)〉. Wdc=〈w(t)〉=lim1/T - T/2∫ T/2w(t)dt or Wdc=〈w(t)〉=1/(t2 -t1 )∫ w(t)dt Power • Definition:the instantaneous power is given by: p(t) = v(t)i(t) and the average power is : P=<p(t)>=<v(t)i(t)> Dc value + v(t) - i(t) circuit
Rms Value and Normalized Power Definition:the root mean square (rms) value of w(t)isgiven by:Wrms=[<w?(t)>j1/2Theorem:if a load (R) is resistive,the average power is:P= <v2(t)>/R=<i(t)>R= V2rms/R=I 2rmsR: Definition:if R-1Q,the average power is called normalizedpower.Then i(t)= v(t) = w(t) and P=<w2(t)>Energy and Power Waveforms:: Definition:w(t) is a power waveform if and only if thenormalized power P is finite and nonzero(O<P<oo).Definition:the total normalized energy is given by
• Definition:the root mean square (rms) value of w(t)is given by: Wrms=[<w2 (t)>]1/2 • Theorem:if a load (R) is resistive,the average power is: P= <v2 (t)>/R= <i2 (t)>R= V2 rms/R=I 2 rmsR • Definition:if R=1Ω,the average power is called normalized power. Then i(t) = v(t) = w(t) and P= <w2 (t)> Energy and Power Waveforms: • Definition:w(t) is a power waveform if and only if the normalized power P is finite and nonzero(0<P<∞). • Definition:the total normalized energy is given by: Rms Value and Normalized Power
T/21w?(t)dtE = limT→8 TT3Definition:w(t) is an energy waveform if and only if thetotal normalized energy is finite and nonzero (O<E<oo),Waveform: power signal or energy signalAveragePower=0Energy finitePower finiteEnergy=00Physically realizable waveform:Energy waveformPeriodic waveform:Power waveformDecibel. Definition:the decibel gain of a circuit is given bydB=10log(average power out/average power in)=10log(Pout/Pin)
• Definition:w(t) is an energy waveform if and only if the total normalized energy is finite and nonzero (0<E<∞). Waveform: power signal or energy signal Energy finite Average Power=0 Power finite Energy=∞ Physically realizable waveform:Energy waveform Periodic waveform:Power waveform Decibel • Definition:the decibel gain of a circuit is given by dB=10log(average power out/average power in) =10log(Pout/Pin) − → = / 2 2 2 ( ) 1 lim T T T w t dt T E
For normalized power case(R=1),we have:dB=20log(Vrms out /Vrms in)= 20log(Irms out /Irms in)
For normalized power case(R=1Ω),we have: dB=20log(Vrms out /Vrms in)= 20log(Irms out /Irms in)
Fourier Transform and Spectraw(t),voltage or current,time function+analysis in time-domain. Their fluctuation as a function of time is animportant characteristic to analyze the signal'scomportment when they present in the transmissionchannel or other communication's units.-Frequencyanalysis of signal. → Tool to realize the frequencydomain analysis of signal -Fourier TransformationDefinition:The Fourier Transform (FT) of w(t) is :W(f)=F[w(t)]= -..Jw(t)exp[-j2元ft]dtf :frequency (unit:Hz if t is in sec)In general,W(f) is called a two-sided spectrum of w(t)Some properties: W(f) is a complex functionso W(f)-X(f)+jY(f)=/ W(f) / exp[jo(f))
w(t),voltage or current,time function analysis in time domain. Their fluctuation as a function of time is an important characteristic to analyze the signal’s comportment when they present in the transmission channel or other communication’s units. Frequency analysis of signal. Tool to realize the frequency domain analysis of signal Fourier Transformation • Definition:The Fourier Transform (FT) of w(t) is : W(f)=F[w(t)]= -∞∫ ∞w(t)exp[-j2πft]dt f :frequency (unit:Hz if t is in sec) In general,W(f) is called a two-sided spectrum of w(t) Some properties: W(f) is a complex function so W(f)=X(f)+jY(f)=│W(f)│exp[jθ(f)] Fourier Transform and Spectra