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## Simulation in Digital Communication

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**Simulation in**Digital Communication**chapter # 6**Digital Transmission Through Bandlimited Channels**6.2 - The power Spectrum of a Digital PAM Signal**A digtal PAM signal at the input to a communication channl reciprocal of the symbol rate pulse waveform scale factor (where 2d is the “Euclidean distance”)**to determine the spectral characteristics of**the random process V(t), we must evaluate the power spectrum. 1)mean value 2)autocorrelation function**The power spectrum of V(t) is the Fourier**transform of the average autocorrelation function. The power spectrum of amplitude sequence an**Problem 6.1**Answer ip_06_01 Determine the power spectrum of V(t) when {an} is an uncorrelated sequence and g(t) is the following rectangular pulse.**Problem 6.2**Answer ip_06_02 Suppose the autocorrelation function of the sequence {an} is and g(t) is the rectangular pulse.shown at the previous problem. Evaluate Sv(f) in this case.**SOLUTION**The power spectrum of the PAM signal was given by from and using also the data we can replace...**6.3 - Characterization of bandlimited channels and channels**distortion We can characterize many communication channels as bandlimited linear filters, described by their frequency response phase response Amplitude response**we can also express it as an**envelope delay (group delay) :**nondistorting (ideal) channel**Amplitude response -constant phase response - linear function of frequncy (envelope delay -constant) distorting channel Amplitude distortion - Amplitude response isn’tconstant delaydistortion- envelope delayisn’tconstant)**Effect of channel distortion**channel input channel output equalizer**Average amplitude and delay characteristics**of a medium-range telephone channel,**Impulse response of the average channel**with amplitude and delay shown before**Problem 6.3**Answer ip_06_03 T.B.D**Impulse response**Frequency response of linear phase FIR filter**Problem 6.4**Window method if the desired channel response is C(f) for |f|<W and C(f)=0 for |f|>W then Impulse response for example: if channel is ideal, then C(f)=1, |f|<W and hence**Answer**ip_06_04 Let us design an FIR filter with: W=2000 Hz and Fs =1/Ts=10KHZ. (this digital filter may be implemented by sampling h(t) at t=nTs, where Ts is the sampling interval and n = 0,+/-1,+/-2,...)**Problem 6.5**The impulse response of a two-path(multipath) radio channel can expressed as: random processes the delay between 2 paths**Answer**ip_06_05 simulate such a channel on the computer