Hi!

I played around with sideband modulation using the hilbert~ object and was wondering about the sideband attanuation performance. Here is my patch:

In the picture below you see my modulated output in the first pane and the demodulated output in the second pane. Testsignal is a 440Hz sine shifted by 2000Hz.

what I dont understand is why is there only 40 dB attenuation between the 2 Sidebands?
Is this because the hilbert~ isnt perfect 90° over the frequency range?

I tried to implement hilberto~ from this blog https://www.katjaas.nl/hilbert/hilbert.html on the very end you see the Max patch
but its output was not more, but at least, decent glitches... : I dont get what I did wrong here.

any input is appreciated,
Seb

I think the feedback coefficients in your hilberto~ implementation should have opposite signs (all positive). And yes, the second sideband seems to be a product of the imperfect orthogonality. With a perfect 90° phase relationship it should completely disappear. That's why it's called "single sideband modulation", I guess.

@seblleb Approx a week ago I posted about a way to implement the Hilbert transform that I learned from that same @katjav page you linked to, so I naively tried it with your patch. I'm not sure what the result is supposed to be and I don't know how you are plotting those spectra, but I'm hoping my little monkey+typewriter effort gives you evidence about your problem and moves you to explain in more detail the theory behind what you're doing and what you're expecting to get. Links to explanations also acceptable, I just wanna learn.
hilberto~ test.pd

PS I know that the FFT Hilbert subpatches introduce latency and so maybe there are supposed to be delays inserted, but I don't understand what's going on so I'm not gonna spritz perfume on what might be a stinky pile

@manuels said:

I think the feedback coefficients in your hilberto~ implementation should have opposite signs (all positive).

as far as i can see, he got them perfectly right.

And yes, the second sideband seems to be a product of the imperfect orthogonality.

though that polyphase setup is close to perfect (in practice it is like 20 times better than using only 2 filters for the hilbert transform)

to my understanding what he sees is a result of the phase response of this hilbert transform. it kind of only happens when the test tone is a sine or harmonic.

not sure if it is releated to the beating phaenomenon, which is the other "problem" with frequency shifters.

Thanks for the replies!
@jameslo I am using sonic visualiser to plot the spectra and measure stuff. its very pretty. also for waterfall diagrams
here you see the analog concepts we implement completely from discrete components: [ https://sound-au.com/project204.htm](link url)
the math behind single side band is quite easy. In pd I wanted to do a simulation of it just to see how it interacts with other stuff I build.

@manuels and @Obineg so I tried with opposite signs which was fun waveshaping weardness, but no 90° phase shift.

then I tried to replace the hilbert~ object with a phasor~ and two cos~ but with 90° phase shift as it is used for the modulator and it worked "clean" regarding the sideband.
I have only seen Harmonics from over driving somewhere. thats also a thing that confuses me. When modulating like this the signal clearly shouldn't go below 2 so multiplying by 0.5 should attenuate enough to get a linear response.

could you further explain what you mean by: it kind of only happens with sine or harmonic? If there is no input signal I have the 2* f_modulator bleeding at -40dB.

also I thought about the one sample delay i made with rzero_rev~ 0, it translates to y[n] = x[n-1] and means a onw sample delay. am I right with that or do I miss sth?

this is how olli~ looks here:

olli~.pd
olli~-help.pd
EDIT
uses Cyclone's [delay~ 1 1]
Vanilla would be [rzero_rev~ 0]

@manuels and @Obineg so I tried with opposite signs which was fun waveshaping weardness, but no 90° phase shift.

Hm, strange ... Did you make sure you only changed the signs of the feedback coefficients (first two arguments of biquad~)? I tried that, and it kind of seems to work: hilberto-test.pd

The reason for the opposite signs, as I understand it, is that in Pd the difference equation only uses additions. (Not sure if this is just a matter of taste or maybe a more efficient implementation.)
The topic is also discussed here: https://cycling74.com/forums/converting-pure-data-biquad-coefficients

my mistake sry.
thanks a lot! now it works with the positive feedback coeefficients.
with 440Hz Testtone and 2000Hz carrier I now get -60dB attenuation when demodulated.

yes, it is not only the order which is different.