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Square to Raised Cosine Waveform without Filtering

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KerimF

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If one searched the expression ‘Raised Cosine’, he would likely find that it is related to special filters, called Raised Cosine ones. These filters smooth the fast rise and fall edges of a squarewave signal to remove its higher harmonies.

Once, I needed this transformation. I solved it, to a good approximation, without adding a raised cosine filter.

In case a member may be interested in this too, I attached below, ‘RaisedCosine_01.zip’ which is a basic circuit of it.

For instance, I simply got its main idea from an old analogue generator IC, XR-2206, which generates square, triangular and sine waves (<400 KHz).

RaisedCosine_01.png
 

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  • RaisedCosine_01.zip
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Well, it's not "without filtering". There's a picture of an op amp lineup
and that particular op amp is pretty slew rate, drive and bandwidth
limited. A whole mess of poles. You might look at what 10X and 1/10
the square fundamental frequency look like.

Raised cosine is fancy math-mouth for "what you get when you put a
digital signal through a few poles" - not the other way around. Who
cares in RF land about whether the sine or cosine is raised? Nobody,
other than that they have to DC-block it now. But radio guys don't want
to hear about bit rate and volts P-P, so parts makers humor them and
tell the same thing in dBm and GHz but now we have to pretend that
the signal is a radio signal so, yeah, throw some math jargon at the
degraded square wave too.
 

Well, it's not "without filtering". There's a picture of an op amp lineup
and that particular op amp is pretty slew rate, drive and bandwidth
limited. A whole mess of poles. You might look at what 10X and 1/10
the square fundamental frequency look like.

Raised cosine is fancy math-mouth for "what you get when you put a
digital signal through a few poles" - not the other way around. Who
cares in RF land about whether the sine or cosine is raised? Nobody,
other than that they have to DC-block it now. But radio guys don't want
to hear about bit rate and volts P-P, so parts makers humor them and
tell the same thing in dBm and GHz but now we have to pretend that
the signal is a radio signal so, yeah, throw some math jargon at the
degraded square wave too.

Sorry, I couldn't get your remark well on how it relates what I presented here to RF.

This hardware is just for relatively low frequencies and doesn't use the concept of the raised cosine filters likely made for the digital RF transmissions.

A comparison between the spectrum of the squarewave and the generated raised cosine waveform (above) (by using the LTspice FFT, for example) shows how the amplitudes of the harmonics are reduced to a great extent (just by shaping properly the rise and fall edges with 2 back-to-back diodes).
 

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