<HTML><FONT FACE=arial,helvetica><FONT SIZE=2>In a message dated 2/28/2002 9:34:42 PM Eastern Standard Time, jhaible@debitel.net writes:
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<BR><BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">the harmonic contents of the window function will directly reflect
<BR>the amount of artefacts in the gated sine signal.
<BR>So a triangle (or trapezoid) will produce less "click" than a rectangle, and
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<BR>a raised cosine would be even smoother.
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<BR>JH.
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<BR>An example of this in application concerns continuous wave radio transmission (CW, morse code). The shape of the keyed pulse is important because sharp edges on either the leading or tail edge of a sine carrier wave pulse will create spurious emissions and harmonics off the carrier frequency (ie, interference on other frequencies). In radio, the oscillator pulse envelope edges should be shaped away from having sharp corners to prevent the generation of key clicks and harmonics. If the oscillator output is well rounded, but the amplification of the pulse is not linear, then the envelope shape might still be altered to sharper attack and decay. Driving audio modulation of a carrier to clipping is similar, and creates what is called 'splatter' in radio lingo. I think the same sine function math is involved (fuzz?).
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<BR>A similar form of distortion results if an amplifier is pulsed into a momentary parasitic oscillation by a sharp envelope. Then, clicks form in groups on both sides of the sine carrier at multiples related to the parasitic oscillation. There's a "gibbs function" (?) that might describe the ringing at the edge of a sharp transition, but I can't remember the details.
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<BR>If you have a shortwave receiver (switchable between AM mode and SSB) you can listen to morse code and hear differences in how different transmitted signal pulses are shaped. Ranging from woody thumps (mellow), to sharp clicks and pops (harsh).
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<BR>-Karl.</FONT></HTML>