Homework Answers
The z-score for X = -0.5 is
The required probability is
P(X < -0.5) = P(z < -1.58) = 0.0571
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3. In most communication systems, the noise (X) is treated as an additive Gaussian noise (random2...
Perform the following using Matlab For an additive Gaussian noise: a. Generate 4000 samples with ...
using matlab
Perform the following using Matlab For an additive Gaussian noise: a. Generate 4000 samples with mean value of 3 and variance of 9. b. Plot the sample values using two different ways. c. Determine the actual mean, variance, and standard deviation. d. Determine the median, mode, and range. e. Sketch the histogram. tle- enerate and plot the probability density function (pdf) and its corresponding cumulative distribution function (cdf) ror he M For the following two signals: / and...
An 8-ary PSK (phase shift keying) signal is transmitted over an additive, zero mean, band-limited Gaussian noise channe...
An 8-ary PSK (phase shift keying) signal is transmitted over an additive, zero mean, band-limited Gaussian noise channel.The channel output is r(t)-s(t)+n(t), st<T, where s(tAcos 2rft+0) for ie 10,123,4,5,6,7) were,+8 16 8 The noise n(t) is narrowband, zero mean, bandpass Gaussian noise with power spectral density Sn (f) is shown in Figure 3, where B is the bandwidth of the noise S, (f) (Watts/Hz) 2 cf (Hz) Figure 3 T herefore, 2 2 2 0 elsewhere (i) What is the...
1. The random variable X is Gaussian with mean 3 and variance 4; that is X...
1. The random variable X is Gaussian with mean 3 and variance 4; that is X ~ N(3,4). $x() = veze sve [5] (a) Find P(-1 < X < 5), the probability that X is between -1 and 5 (inclusive). Write your answer in terms of the 0 () function. [5] (b) Find P(X2 – 3 < 6). Write your answer in terms of the 0 () function. [5] (c) We know from class that the random variable Y =...
Bit Error Probability: Consider the following model for a digital communication system: r =√Es + ...
Bit Error Probability: Consider the following model for a digital communication system: r =√Es + n where s {-1 1) with equal probability, and n is additive white Gaussian noise with zero mean and variance 1, and E is the signal to noise ratio. The receiver decides s = +1 if r > 0, and decides s = -1, if r <0. Estimate the error probability using Monte Carlo simulations by generating many samples and making as many decisions for...
3. Let Zt) be a Gaussian white noise, that is, a sequence of i.i.d. normal r.v.s...
3. Let Zt) be a Gaussian white noise, that is, a sequence of i.i.d. normal r.v.s each with mean zero and variance 1. Let Y% (a) Using R generate 300 observations of the Gaussian white noise Z. Plot the series and its acf. (b) Using R, plot 300 observations of the series Y -Z. Plot its acf. c) Analyze graphs from (a) and (b). Can you see a difference between the plots of graphs of time series Z and Y?...
2. Let y=-3x+4.For the case that X is Gaussian random variable of normal distribution given as...
2. Let y=-3x+4.For the case that X is Gaussian random variable of normal distribution given as N (0,4), find the probability density function of Y. What is the mean and variance of Y
A communication system has a Gaussian pdf with zero mean, o = 1/2 variance and a...
A communication system has a Gaussian pdf with zero mean, o = 1/2 variance and a bandwidth W = 10kHz with noise power No 10-15 W/Hz. The transmission loss power is 100dB. Calculate the transmitted power, St, to achieve the output signal to noise ratio, (Sp)... = 40 dB for each modulation scheme as listed below. Show your all calculations for each modulation scheme in detail and explain your solutions clearly. SSB b. DSB-LC with modulation index u = 1...
Question 1 The noise floor, also known as additive white Gaussian noise (AWGN), is a continuous...
Question 1 The noise floor, also known as additive white Gaussian noise (AWGN), is a continuous noise level that appears over a wide spectrum when viewed in the frequency domain. True False 10 points Question 2 When considering the impact of impulse noise, we find that it is more devastating to a digital communications link, than an analog one. Therefore, error control methods should be used on all digital links. True False 10 points Question 3 When two transmitters operate...
2. The output Y of a binary communication system is a unit-variance Gaussian (Normal) random variable...
2. The output Y of a binary communication system is a unit-variance Gaussian (Normal) random variable with mean 0 when the input X is 0, and mean 1 when the input is 1. Assume that the input is 1 with probability p. (a) Determine fr(w). : If ( c) The receiver uses the following decision rule decide that input was 1; otherwise, decide that input was 0. Show that this decision rule leads to the following threshold rule: If Y...
Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is...
Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is modeled as a WSS random process with PSD S,(f). Let Y(t) denote the random noise process at the output of the filter. A linea filsee Figure 1: The Filter. (T) Je Sinc 1. Find the frequency response, H(f), of the filter. 2. If X(t) is a white noise process with PSD No/2, find the PSD of the noise precess Y(t). 2- f 3. Is...
using matlab
Perform the following using Matlab For an additive Gaussian noise: a. Generate 4000 samples with mean value of 3 and variance of 9. b. Plot the sample values using two different ways. c. Determine the actual mean, variance, and standard deviation. d. Determine the median, mode, and range. e. Sketch the histogram. tle- enerate and plot the probability density function (pdf) and its corresponding cumulative distribution function (cdf) ror he M For the following two signals: / and...
An 8-ary PSK (phase shift keying) signal is transmitted over an additive, zero mean, band-limited Gaussian noise channel.The channel output is r(t)-s(t)+n(t), st<T, where s(tAcos 2rft+0) for ie 10,123,4,5,6,7) were,+8 16 8 The noise n(t) is narrowband, zero mean, bandpass Gaussian noise with power spectral density Sn (f) is shown in Figure 3, where B is the bandwidth of the noise S, (f) (Watts/Hz) 2 cf (Hz) Figure 3 T herefore, 2 2 2 0 elsewhere (i) What is the...
1. The random variable X is Gaussian with mean 3 and variance 4; that is X ~ N(3,4). $x() = veze sve [5] (a) Find P(-1 < X < 5), the probability that X is between -1 and 5 (inclusive). Write your answer in terms of the 0 () function. [5] (b) Find P(X2 – 3 < 6). Write your answer in terms of the 0 () function. [5] (c) We know from class that the random variable Y =...
3. Let Zt) be a Gaussian white noise, that is, a sequence of i.i.d. normal r.v.s each with mean zero and variance 1. Let Y% (a) Using R generate 300 observations of the Gaussian white noise Z. Plot the series and its acf. (b) Using R, plot 300 observations of the series Y -Z. Plot its acf. c) Analyze graphs from (a) and (b). Can you see a difference between the plots of graphs of time series Z and Y?...
2. Let y=-3x+4.For the case that X is Gaussian random variable of normal distribution given as N (0,4), find the probability density function of Y. What is the mean and variance of Y
A communication system has a Gaussian pdf with zero mean, o = 1/2 variance and a bandwidth W = 10kHz with noise power No 10-15 W/Hz. The transmission loss power is 100dB. Calculate the transmitted power, St, to achieve the output signal to noise ratio, (Sp)... = 40 dB for each modulation scheme as listed below. Show your all calculations for each modulation scheme in detail and explain your solutions clearly. SSB b. DSB-LC with modulation index u = 1...
2. The output Y of a binary communication system is a unit-variance Gaussian (Normal) random variable with mean 0 when the input X is 0, and mean 1 when the input is 1. Assume that the input is 1 with probability p. (a) Determine fr(w). : If ( c) The receiver uses the following decision rule decide that input was 1; otherwise, decide that input was 0. Show that this decision rule leads to the following threshold rule: If Y...
Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is modeled as a WSS random process with PSD S,(f). Let Y(t) denote the random noise process at the output of the filter. A linea filsee Figure 1: The Filter. (T) Je Sinc 1. Find the frequency response, H(f), of the filter. 2. If X(t) is a white noise process with PSD No/2, find the PSD of the noise precess Y(t). 2- f 3. Is...
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