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Analog raised cosine filter ?

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I was wondering if there is a way to implement an analog Pulse shaping raised cosine filter ?
I looked in the internet, but only found digital implementations.


Hi Geogi, in principle I don't see why not, I found this on ebay, http://www.ebay.co.uk/itm/3-X-1MHZ-RAISED-COSINE-FILTER-/111992476524

Well, technically you wouldn't, because all-pole analog filters have polynomial transfer functions.  Cosine is a transcendental function, so has no equal in finite polynomials (i.e., filters without infinite numbers of L and C).  The best you can do is an approximation.

The roll-off region (say 0 to 6dB insertion loss) should be pretty easy to reproduce, but the asymptotes cannot simply go to zero; you're left with a residual level in the cutoff band.

An approximation could be specified by the sharpness of the cosine (beta in these https://en.wikipedia.org/wiki/Raised-cosine_filter formulas) and desired stopband attenuation (i.e., it doesn't go to zero in the "otherwise" region, but is at least some amount of attenuation there).

To match the most desirable property (periodic zeroes in the impulse response), you'd probably want to use a different approach, though.  I don't know enough about real analysis to do that (but who cares, anyway; just have a computer solve it).

That said, at least if your cutoff frequency is conveniently high: you can use a transmission line, cut so that its impedance varies as a function of length, to implement the impulse response.  The total length of the line corresponds to the length of the impulse response, and needs to be N/2 times the wavelength for N zeroes.  Actual stopband performance will depend on how precisely cut the transmission line is, and its losses.  (It's not impossible to get infinite attenuation in the stopband, but you need the reflected wave to cancel perfectly with the incident wave, which isn't going to happen for much frequency range, because transmission line losses rise as ~sqrt(f).)

Probably, SAW filters implement this pretty regularly, at more modest frequencies.  But as those are rather special purpose items, you'd probably never see it, except for a few you might randomly wander across, made for a special frequency.



--- Quote from: Georgi on May 20, 2016, 06:25:06 am ---Hi,
I was wondering if there is a way to implement an analog Pulse shaping raised cosine filter ?
I looked in the internet, but only found digital implementations.


--- End quote ---


A lot depends on what you are trying to do. Are you trying to shape a generated pulse or filter a received pulse? As mentioned above, you can only do it just so well and then things fall apart. For the pulse generation side, there are a few odd non-linear things you can throw into the mix.


For pulse shaping I would use a network of series resistors with capacitors to ground forming an RC low pass filter. I use one of these for shaping the keying waveform in a CW transmitter, a rising square wave pulse going in produces a beautiful rising raised cosine at the output. Values depend on your required rise time and are computed using the formula risetime= 1/(2 PI R C)


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