I'd say great video again haha Do you know why accelerometers with higher ranges (i.e. +/- 200g) have more noise than accelerometers with lower ranges (i.e. +/-16g)? Thanks a lot!
Quoting from Gallager (p. 225): "The careful reader will observe that WGN has not really been defined. What has been said, in essence, is that if a stationary zero-mean Gaussian process has a covariance function that is very narrow relative to the variation of all functions of interest, or a spectral density that is constant within the frequency band of interest, then we can pretend that the covariance function is an impulse times N0/2, where N0/2 is the value of SW (f) within the band of interest." ... and then he goes on to say: "Engineers should view WGN within the context of an overall bandwidth and time interval of interest, where the process is effectively stationary within the time interval and has a constant spectral density over the band of interest."
You draw the unconstrained and the constrained case separately. Is it better to just concentrate on the constrained case and say what happens when W approaches infinity or Wー＞infinity? Then the sinc goes to infinite height and it’s zero crossing points shrink towards the y axis to give the delta function earlier. This seems more intuitive.
It's hard to know what to tell you, without knowing more about the question you've been asked. If the noise has a different distribution, then you'd need to integrate over that distribution when working out bit-error-rates, for example. But without knowing the actual question, I don't know what you're not understanding. Perhaps these videos might help: "How are Bit Error Rate (BER) and Symbol Error Rate (SER) Related?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-du-sExIUV-Y.html and "How are BER and SNR Related for PSK and QAM?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-vtJ6mAy3xMc.html
Great question. If the random process is "ergodic", then yes, those two quantities have the same value. Keep an eye out on the channel for an upcoming video on that topic.
So a band limited noise has more corelation with its own self as can be seen with a sinc function in time domain against a single impulse for unconstrained noise? Intuitively speaking, how will the expected value expression for correlation look like in case of bandlimited noise?
RN(0) for unconstrained and constrained are derived from single point impulse response and sinc function respectively...we see the correlation of noise increases from No/2 to NoW ...does it not signify that the noise correlation increases for a constrained noise case in contrast to unconstrained case...this is the simplest i could write to explain my statement@@iain_explains
OK, I think I see what you're saying. But you're mixing up the units. No/2 is a power spectral density (Power per unit bandwidth, measured in Watts/Hz), while NoW is a power (measured in Watts). You can't compare them directly.
@@iain_explains yes sir that is why i wanted to know why you referred to difference between their time equivalents if they are very different from each othet
Great video! Can low-pass filtered white noise be still considered gaussian noise? Could you please do a video about that? Thanks! and keep up the great work!!
Great question. Thanks for the suggestion for a new video. I've added it to my "to do" list. In summary, yes, as long as it is a linear filter. Linear filters perform convolution, which essentially involves adding delayed versions of the input to itself (according to the impulse response). The addition of two Gaussian random variables results in another Gaussian random variable. So if a linear filter has a Gaussian random process input, then the output is also a Gaussian random process.
