Data Transmission Exercises

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Data Transmission Exercises Prof. Dr. J. Habermann FH Giessen-Friedberg, University of Applied Sciences

Lecture 1:1. Classify the following signals into the categories energy signals power signals neither energy nor power signals.

Calculate, if possible, signal energy or signal power 1. x1 (t ) = e t cos(t ) 2. x 2 (t ) = sgn(t ) 3. x3 (t ) = A cos(2f 1t ) + B cos(2f 2 t ) 2. Determine if the following signals are energy or power signals. Calculate energy or power spectral density and the signal energy or signal power: 1. x(t ) = sin c(t ) = 2. x(t ) =

sin(t ) t

n =

(t 2n)

3. White Gaussian noise with zero mean and a power spectral density of N0/2 is transmitted over a low pass filter with bandwidth B. Calculate the autocorrelation function of the output process Y(t). 4. The output process of a LTI system is stationary if the input process is stationary. Is the opposite also true, i.e., can it be assumed that the input process is stationary if the output process is stationary ? 5. Calculate the power spectral density for the following processes: 1. X (t ) = A cos(2f 0 t + ) , where A is a constant and is a random variable. is uniformly distributed in [0, /4]. 2. X(t) = X + Y, where X and Y are independent . X is uniformly distributed in [-1,1], and Y is uniformly distributed in [0, 1]. Oct-10 page

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6. What is the equivalent noise bandwidth of a bandpass filter with bandwidth W ?

Oct-10 page

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Lecture 2:1. Given are the following functions n(t):

1. 2.

Show that the functions are orthonormal. Express the signal x(t) as a weighted linear combination of the above functions, if 1, x(t ) = + 1, 1, 0 t 1 1< t 3 3