Are Stationary Random Processes Always Ergodic?

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Iain Explains Signals, Systems, and Digital Comms

Күн бұрын

Explains the how Stationarity is related to Ergodicity in random processes, using an example and diagrams.
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Пікірлер: 17

@stephensu4371 Жыл бұрын

gday iain

@Yilin-wk8gl 10 ай бұрын

Hi professor, I wonder if you do some research on the random field? And could you give me some suggestions on learning the 2D random field, like some textbooks or whatever?

@iain_explains 10 ай бұрын

Thanks for the topic suggestion. I'll add it to my "to do" list.

@leonardocai7394 10 ай бұрын

random vibration ( Wirsching, Paez, Ortiz) has a some chapters related to random variables, and random process in time and frecuency, statistical properties of random processes.

@DamaKubu 4 ай бұрын

I like your simple intuitive explanation, but there are at least two types of stationarity. What you mean here is refering to stationary in wide sense? That is the mean and variance of distribution not changing.

@iain_explains 4 ай бұрын

Here are my videos on that: "What is a Stationary Random Process?" kzfaq.info/get/bejne/m9KGZ6WQkp2dn6M.html and "What does Wide Sense Stationary (WSS) mean?" kzfaq.info/get/bejne/l62oeqyKp96qoH0.html

@ashutoshsingh-et7vm Жыл бұрын

Hello, sir I have one doubt when I use FFT by folding and found total energy in frequency and time domain, respectively it's coming twice, but it should be the same, I guess. Can you tell me why this is happening?

@iain_explains Жыл бұрын

Sorry, what do you mean by "FFT by folding"?

@ashutoshsingh-et7vm Жыл бұрын

@@iain_explains when i am folding negative frequency on positive frequency

@iain_explains Жыл бұрын

Sorry, what? Why would you do that?

@ashutoshsingh-et7vm Жыл бұрын

@@iain_explains Sir i means to say when we find power in frequency domain and power in time domain they must be equal but when we calculate power in frequency domain why we use vrms^2 while calculating power in frequency domain

@ashutoshsingh-et7vm Жыл бұрын

% Parameters Fs = 1000; % Sampling frequency (Hz) duration = 1; % Signal duration (seconds) f = 250; % Frequency of the sine wave (Hz) % Generate the time axis t = 0:1/Fs:duration-1/Fs; % Generate the sine wave x = sin(2*pi*f*t); % Compute the FFT of the signal X = fft(x); % Frequency axis for plotting freq = (0:length(X)-1)*Fs/length(X); % Compute the amplitude spectrum amp_spectrum = abs(X); e=2*amp_spectrum(1:length(freq)/2); % Plot signal versus time subplot(2, 1, 1); plot(t, x); xlabel('Time (s)'); ylabel('Signal'); title('Signal versus Time'); % Plot FFT amplitude versus frequency (folded) subplot(2, 1, 2); plot(freq(1:length(freq)/2), amp_spectrum(1:length(freq)/2)); % Plot only half of the spectrum xlabel('Frequency (Hz)'); ylabel('Amplitude'); title('Folded FFT Amplitude versus Frequency'); % Adjust plot layout sgtitle('Signal Analysis'); % Compute the sum of squared magnitudes in the time domain time_domain_power = sum(abs(x).^2); % Compute the sum of squared magnitudes in the frequency domain frequency_domain_power = sum(2*abs(e/2).^2)/length(X); % Compare the two powers disp(['Time domain power: ', num2str(time_domain_power)]); disp(['Frequency domain power: ', num2str(frequency_domain_power)]); so in this code while calculating frequency domain power I am using rms value then only power is coming same

@Hassan_MM. 7 ай бұрын

Stationarity : Their Marginal or Joint prob.functions are time independent Ergodicity : Their probability function is Time independent. Specifically, pattern or type of their Randomness doesn't change over Time Is it so ❗️

@gingarrison104 Ай бұрын

Hi professor, I want to know why the Topic of "random" is important for telecommunications

@iain_explains Ай бұрын

Here are some videos you might like to watch, that discuss examples of randomness in communication systems: "What is Gaussian Noise?" kzfaq.info/get/bejne/jK-mjNufzdHappc.html , "What is Rayleigh Fading?" kzfaq.info/get/bejne/Y6x_obxzv52-loU.html , "How is Data Sent? An Overview of Digital Communications" kzfaq.info/get/bejne/g6eUl8V3y6nXeaM.html