### Philip Oakley (@philipoakley)

How fast do you want to track the line voltage? Is this single phase or three phase? Do you need an estimate every cycle, or half cycle, or faster (3ph)? These are...

Years ago (on a Sinclair QL IIRC) I did calcs regarding adding rms noise equal to 1/2 lsb and found that with sufficient averaging, you got at least 8 extra bits...

It is also worth reflecting on how this affects investigations of signals in noise and the apparent sharpness of the transition. In a broad band signal you can...

I'm not familiar with 'liquid'. The fftw3 does work, but the user interfaces can make implicit assumptions that don't match what you expect (true for all implementations)One...

Are you using a full complex fft, or one that assumes symmetry of the positive and negative spectrums. Many FFTs make the assumption of real valued inputs, such...

Vaguely sounds like the Lifted wavelet transforms, with the wavelet transform being seen as cascaded short ffts or FIR filters. Still sounds interesting. Definately...

In line with the other replies, try explaining the code to a video recording as if you'll be publishing the explanation of how to debug to YouTube (other platforms...

While it is true that oversampling doesn't add any more data, what it does provide is extra spaces for the smooth interpolation of the spectrum to better estimate...

Just thinking out loud here. If the matrix is split into a complex conjugate part and a residual part (which would be complex and could be off diagonal), does that...

As @krasin notes the missing signal frequencies appear in the second half of the signal. That will be because it's a chirp, so the frequency changes with time (=...

My impression is that 'gap' in the frequency band is, as you expect, caused by the undersampling of the signal. You will have a period where you have an almost fs/2...

Notice where the nulls stay aligned and ponder why is that? Also beware using the same analysis technique as used for generating the problem (i.e. digital sampling...

IIRC, I did my original calculation on a Sinclair QL to see what linearity was possible out of filtering sample noise on an ADC..A side fact is looking at the 'knee'...

With ideal Gaussian noise, with rms = 0.5 bits (of the ADC), then you can gain upto 8 extra bits by averaging a long sequence of results for a constant DC level...

Hi Adilko, It's not that it's impossible, rather it is just that you need either sneaky techniques or careful selection of the method. I don't think the laser...

Remember that "phase" is measured in metres (or millimetres, or microns) as it is 'fractions of a wavelength'.So shifting to optical frequencies, where the wavelength...

This is mathematics, not real world, isn't it? The error, if there is one ;-), is the last step where 'b' should be subtracted from both sides, resulting in the...

Do make sure that if x[0...n] = 1, that you have stability, rather than an exponential 'explosion'. That is, don't forget the effective multiplier for the x[n]...

Some quick thoughts.There are two things to consider: the amount of overdrive, i.e. just a little clipping, or large overdrive giving a trapezoid shape, or the massive...

Is there a typo here"0 2÷3 2÷3" ?Should it read"0 1÷3 2÷3", i.e. ~ "0 0.333333 0.666666" ?If not, maybe a slight expansion of the text to tease out more of the...

Also, ultimately, the transmitted signal is a purely real signal, sampled in the time domain, thus all those complex parts are mathematical artefacts with various...

Definitely start with a lower sequence rate, and lower them until you can see the sequence cleanly.Also consider doubling the 'sample/bit rate' in the sense that...

You forgot the distinctions around zero.Some number systems have no zero, such as Roman numerals (and no negative).We also have the subtle distinction between additive...

Are you simply averaging the theta values, which have roll-over, as that roll over can cause a significant non-linearity. You could average the complex phase (i.e....

Just a quick thought, without any real 'thinking' - do those two delayed signals simply amount to a small phase shift that effectively increase the size of the signal,...

Random noise can produce wildly random results (well, because..). It's a reasonable approximation but the statistics aren't always as good is hoped.You didn't say...

The maximum value is determined by the initial y[0] {aka y(1)} value copied from x[0] {x(1)}, so the randomised trial will get rather random results because the...

so, I think you have: y[n] = 0.98*y[n-1] + (x[n] - x[n-1])Assuming that y[-1] = 0, you have a 2% decay on any existing y[n-1] value, plus the difference between...

The Wikipedia 'Stability' section https://en.wikipedia.org/wiki/Infinite_impulse_res... maybe a useful place to start.Separating the variables will be part of the...

Maybe it needs A=[1 2 3 4 5 6]; A(:)and B = [1 2 3; 4 5 6]; B(:)to highlight the internal ordering. (Perhaps along with sum(A) and sum (B) just to clarify..)The...

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