How to implement a FIR approximation of the analytic signal

HI all

For a simulation I am making in a real discrete time application I need to modulate a signal. (MATLAB)

For this I will be using the analytical signal of my input.

Due to it being real time I do not want to implement it as the fft approach with hilbert(x).

I would like to use a FIR to approximate the analytical signal by a convolution with the FIR.

I have tried using online examples (FIR Analytical example), but the imaginary part, although looking similar to the hilbert created one, makes distorted signals.

Have been struggling alot just properly creating the filter's FIR and applying it for a good Analytic Signal approximation of the known values up till that point.

Any help with making these FIR and applying them correctly would be welcome.

Thank you guys in advance.

BR

Answer 1

[Star Strider]

I am not certain what you want to do or what the problem is with the hilbert function.

If you have calculated the spectrum (using fft) and want to approximate that shape or something similar to it with the FIR filter passband, I would use the envelope function (or the absolute value of the hilbert result), and then use the firls function (also consider firpm) on the envelope result to approximate the spectrum. in the FIR filter.

[Wannes Van Ransbeeck]

The idea would be that I need to modulate the analytic representation of the discrete signal.

Problem is that I do not have the full signal immedeately, say only x(1:i) at some point.

The hilbert function will not be possible because I am lacking the rest of the information on the signal and making an fft of the limited signal will give a huge inaccuracy. Therefore I thought that if I have a FIR I can apply sequentially and convolve with the signal known until that point I can get a good approximation with the limited information known at that point. Using Hilbert(x) or fft directly on my signal is therefor out of the question. Just looking for a way to get an FIR filter that I can convolve with my known input and get the approximate analytical signal out.

BR

[Star Strider]

I do not understand what ‘analytic’ means in this context. Are you intending to fit it to a specific model function with the objective of estimating parameters of the model?

Also, it is not possible to filter a point (a single value at a specific time), only vectors, and only those of sufficient length for the filter to work.

The various filter functions (specifically filtfilt that I definitely recommend for all digital filters) implements the convolution.

[Wannes Van Ransbeeck]

Sorry for my bad formualtion. With analytic I mean this, being a representation of a real valued signal that allows performing modulation operation.

The intend is not to fit it to any model function at all. I have to simualte a system in which feedback will be present. To control the feedback I have to implemet a phase modulation in the loop which allows reducing instabilities. This phase modulation has to be implemented in real time so an fft can simply not be taken of the signal since the full content of the input signal is not known. The sufficient length part I do understand, thanks for that information. Still, in real-life examples making an FIR filter that allows approximating the analytical signal is still the way to go as I found in papers. I think I found a way to correctly implement it though. The signals does not sound as distorted as before, solution ended up being just increasing the order of my filter.

I was wondering though is there a way to overcome built in caps on filter order? If my filter order becomes to big (16000-ish)the whole filterdesign algorithm fails on me.

BR

[Star Strider]

I am still lost. (Note that the Wikipedia llink also draws the signal envelope.)

If you want to identify a system that corresponds to your signal, the System Identification Toolbox has a number of functions to do just that. The easiest way to determine the number of poles and zeros your system requires is to plot the imaginary component of the single-sided Fourier transform of the signal the system creates. The peaks and valleys (actually values) correspond to the pole frrequencies, and the zero-crossings coorrespond to the frequencies of the zeros. (Be aware also of the possibility that your system could have poles or zeros at infinity, as well as at d-c.)

[Wannes Van Ransbeeck]

I will keep this in mind thank you very much :).

[Star Strider]

As always, my pleasure!