![Preparation: 1. If we were to sample a periodic signal at a randomly chosen point in its period, the value of the sample would be a random variable. The distribution of this random variable is termed the amplitude distribution of the periodic signal. Derive and plot the amplitude distribution of the sinusoid, triangular, and square wave signals (specify both the density function and the distribution function) 2. calculate and plot the autocorrelation function of a sinusoid and of a 50% duty cycle square wave. 3. Calculate the cross-correlation function between a sinusoid and square wave signal, both of which have the save fundamental frequency noting that the cross-correlation of two sinusoids of different frequency is always zero.] of it and compare it to the autocorrelation function a white noise process. find it easier to compute this by making use of the Fourier series of the square wave, 4. Explain what is meant by the term bandlimited white noise. Find the autocorrelation fu](http://img.homeworklib.com/questions/f4901090-3505-11eb-8428-57077746165b.png?x-oss-process=image/resize,w_560)
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Preparation: 1. If we were to sample a periodic signal at a...
Program from problem 1: (Using MATLAB) % Sampling frequency and sampling period fs = 10000; ts...
Program from problem 1: (Using MATLAB)
% Sampling frequency and sampling period
fs = 10000;
ts = 1/fs;
% Number of samples, assume 1000 samples
l = 1000;
t = 0:1:l-1;
t = t.*ts; % Convert the sample index into time for generation and
plotting of signal
% Frequency and amplitude of the sensor
f1 = 110;
a1 = 1.0;
% Frequency and amplitude of the power grid noise
f2 = 60;
a2 = 0.7;
% Generating the sinusoidal waves...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fund...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
LMS project Using the notes discussed in class: Implementing the LMS Algorithm First generate some signals clear all c...
LMS project Using the notes discussed in class: Implementing the LMS Algorithm First generate some signals clear all close al1: Generate signals for testing the LMS Algorithm 1000 Fs Sampling frequency Sample time 1/Fs 10000: = L Length of signal S Time vector (0:L-1) *T ; Sum of a 50 Hz sinusoid and a 120 Hz sinusoid 0.7 sin (2*pi*50*t); inuside X d+ 10 randn (size (t)); Sinusoids 5O0000000L plus noise fiqure (1) plot (Fs*t (1:150),x (1:1500)) title('Signal Corrupted with...
Please do Part 4 and Show all work! 1. 145 points) <FM/FSK Modulation/Demodulations A periodic wave m(t) in Figure 1 below The resulting FM signal is demodulated as shown in the following figure b...
Please do Part 4 and Show all work!
1. 145 points) <FM/FSK Modulation/Demodulations A periodic wave m(t) in Figure 1 below The resulting FM signal is demodulated as shown in the following figure by using frequency discriminator. Assume no attenuation of the signal due to propagation loss (in other words assume amplifiers properly restored the amplitude of the transmitted signal at the receiver) [10 points] Find the Fourier Series (trigonometric Fourier Series) of the message signal m (t) where To...
LMS project Using the notes discussed in class: Implementing the LMS Algorithm First generate some signals...
LMS project Using the notes discussed in class: Implementing the LMS Algorithm First generate some signals clear all close al1: Generate signals for testing the LMS Algorithm 1000 Fs Sampling frequency Sample time 1/Fs 10000: = L Length of signal S Time vector (0:L-1) *T ; Sum of a 50 Hz sinusoid and a 120 Hz sinusoid 0.7 sin (2*pi*50*t); inuside X d+ 10 randn (size (t)); Sinusoids 5O0000000L plus noise fiqure (1) plot (Fs*t (1:150),x (1:1500)) title('Signal Corrupted with...
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...
Question 6: We will consider a piece-wise constant 1D signal in this part. Assume the signal...
Question 6: We will consider a piece-wise constant 1D signal in this part. Assume the signal (a function f(t)) contains S = 10 discrete sub-intervals of equal length. Each sub-interval contains 50 samples. This signal is given below in the variable signal acquired at sample locations sampling_locations (also provided below). Plot the 1D signal, create one plot with the regular plot commands and one plot with the stem command (use subplots to plot the two next to each other in...
Problem 2: Consider the following periodic signals x(t), a square wave, and yt), a saw tooth...
Problem 2: Consider the following periodic signals x(t), a square wave, and yt), a saw tooth 2T The pulses width of x(t) т, wave. Both have the same amplitude A and the same frequency - equal T. The duty-cycle of x(t) is defined as d- T. -A From tables of Fourier Series ofvarious periodic signals, the following formulas are given for your convenience x(= Ad+2Adnacos at+2Ad sna cos 2at+2Adl sun 3xdcos3at яd 2лd Зяd 24 (sin a 1 sin 2asin3ajain...
random vibrations Problem 1 Two random variables x and y have the joint probability density function where c is a...
random vibrations
Problem 1 Two random variables x and y have the joint probability density function where c is a constant. Verify that x and y are statistically independent and find the value of c for plx, y) to be correctly normalized. Check that Elx) Elyl-0 and that Elx2] and Ely') are both infinite Problem 2. Each sample function x(t) of a random process x(t) is given by: where a, a2, wh, and w are constants but 61 and 62,...
Program from problem 1: (Using MATLAB)
% Sampling frequency and sampling period
fs = 10000;
ts = 1/fs;
% Number of samples, assume 1000 samples
l = 1000;
t = 0:1:l-1;
t = t.*ts; % Convert the sample index into time for generation and
plotting of signal
% Frequency and amplitude of the sensor
f1 = 110;
a1 = 1.0;
% Frequency and amplitude of the power grid noise
f2 = 60;
a2 = 0.7;
% Generating the sinusoidal waves...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
LMS project Using the notes discussed in class: Implementing the LMS Algorithm First generate some signals clear all close al1: Generate signals for testing the LMS Algorithm 1000 Fs Sampling frequency Sample time 1/Fs 10000: = L Length of signal S Time vector (0:L-1) *T ; Sum of a 50 Hz sinusoid and a 120 Hz sinusoid 0.7 sin (2*pi*50*t); inuside X d+ 10 randn (size (t)); Sinusoids 5O0000000L plus noise fiqure (1) plot (Fs*t (1:150),x (1:1500)) title('Signal Corrupted with...
Please do Part 4 and Show all work!
1. 145 points) <FM/FSK Modulation/Demodulations A periodic wave m(t) in Figure 1 below The resulting FM signal is demodulated as shown in the following figure by using frequency discriminator. Assume no attenuation of the signal due to propagation loss (in other words assume amplifiers properly restored the amplitude of the transmitted signal at the receiver) [10 points] Find the Fourier Series (trigonometric Fourier Series) of the message signal m (t) where To...
LMS project Using the notes discussed in class: Implementing the LMS Algorithm First generate some signals clear all close al1: Generate signals for testing the LMS Algorithm 1000 Fs Sampling frequency Sample time 1/Fs 10000: = L Length of signal S Time vector (0:L-1) *T ; Sum of a 50 Hz sinusoid and a 120 Hz sinusoid 0.7 sin (2*pi*50*t); inuside X d+ 10 randn (size (t)); Sinusoids 5O0000000L plus noise fiqure (1) plot (Fs*t (1:150),x (1:1500)) title('Signal Corrupted with...
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...
Question 6: We will consider a piece-wise constant 1D signal in this part. Assume the signal (a function f(t)) contains S = 10 discrete sub-intervals of equal length. Each sub-interval contains 50 samples. This signal is given below in the variable signal acquired at sample locations sampling_locations (also provided below). Plot the 1D signal, create one plot with the regular plot commands and one plot with the stem command (use subplots to plot the two next to each other in...
Problem 2: Consider the following periodic signals x(t), a square wave, and yt), a saw tooth 2T The pulses width of x(t) т, wave. Both have the same amplitude A and the same frequency - equal T. The duty-cycle of x(t) is defined as d- T. -A From tables of Fourier Series ofvarious periodic signals, the following formulas are given for your convenience x(= Ad+2Adnacos at+2Ad sna cos 2at+2Adl sun 3xdcos3at яd 2лd Зяd 24 (sin a 1 sin 2asin3ajain...
random vibrations
Problem 1 Two random variables x and y have the joint probability density function where c is a constant. Verify that x and y are statistically independent and find the value of c for plx, y) to be correctly normalized. Check that Elx) Elyl-0 and that Elx2] and Ely') are both infinite Problem 2. Each sample function x(t) of a random process x(t) is given by: where a, a2, wh, and w are constants but 61 and 62,...
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