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I've heard about shaping the symbol with a rect filter at the transmitter, but why? Isn't this just implicit from the fact that it's going to be transmitted as a symbol truncated to the symbol period regardless? Or is that simply what they're referring to by shaping it with a rect filter i.e. isolating the symbol to that window. Am I right in thinking it's just the default. Also does the receiver extend the signal as if it were infinite when performing the fourier transform and therefore the rect pulse shaping at the receiver is simply the receiver not doing that?

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  • $\begingroup$ I can think of a couple of possibilities, but it depends on the presentation -- can you link to an example, or post a picture of a relevant page? $\endgroup$ – TimWescott Aug 31 '20 at 21:39
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In most waveforms for data communication we do NOT want to transmit a rect for each pulse given the excessive bandwidth required (since a rect is a Sinc function in frequency which is relatively very wide-band). This is the motivation for pulse shaping (such as the commonly implemented root-raised cosine pulse shape): to limit the transmitted spectrum and improve the overall spectral efficiency of the waveform.

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  • $\begingroup$ Yeah but if you don't do pulse shaping isn't the default result just a rect or does the receiver perform the FT on the waveform as if the period repeated infinitely in the time domain $\endgroup$ – Lewis Kelsey Aug 30 '20 at 0:40
  • $\begingroup$ Not necessarily—— the input to the pulse shaping filter is impulses. And the receiver doesn’t necessarily perform a FT $\endgroup$ – Dan Boschen Aug 30 '20 at 0:41
  • $\begingroup$ researchgate.net/profile/Thinh_Pham2/publication/262563009/… isn't the original OFDM symbol implicitly in the shape of a rect pulse filter. I.e. using one would do nothing..? That's what I hope is the case otherwise I'm stuck $\endgroup$ – Lewis Kelsey Aug 30 '20 at 0:59
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    $\begingroup$ @LewisKelsey yes you are correct; for OFDM doing nothing prior to the FT in the receiver is equivalent to a rectangular window. $\endgroup$ – Dan Boschen Aug 30 '20 at 12:52
  • $\begingroup$ Great that was basically the question I was asking $\endgroup$ – Lewis Kelsey Aug 30 '20 at 14:02
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This has been resolved. It was due to a misunderstanding of what a pulse filter was. It's used on the ZOH output of the DAC to convolve it, which is a multiplication in the frequency domain, i.e. it's a frequency domain filter of a certain shape to remove excess images by shaping the overall freuency domain. This is filtering, whereas what I was referring to was windowing of an OFDM symbol, which is by default a rect shape and is a convolution of the frequency domain with orthogonal sincs at the subcarriers

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  • $\begingroup$ the Zero-order hold (ZOH) is a model of what happens when a DAC outputs a piecewise-constant output signal. compared to a train of impulses (which are brick-wall filtered to recover the original), the output of a DAC can be modeled as this train of impulses passed through a ZOH filter, which, like any LTI filter, is multiplication in the frequency domain. $\endgroup$ – robert bristow-johnson Oct 21 '20 at 22:44
  • $\begingroup$ @robertbristow-johnson the ZOH output is a multiplication with a sinc in the frequency domain and then this is truncated with a rect in the reconstruction filter after it, that's my understanding $\endgroup$ – Lewis Kelsey Oct 22 '20 at 3:15
  • $\begingroup$ it is a multiplication with a sinc in the frequency domain, but unless there is an additional "reconstruction filter" there is no additional truncation. so what comes out of the DAC is a piecewise constant function and that does have images that could stand to be removed with a reconstruction (or anti-imaging) filter. but that latter filter is not always there. $\endgroup$ – robert bristow-johnson Oct 22 '20 at 4:56
  • $\begingroup$ yes that's what my conception of what happens was $\endgroup$ – Lewis Kelsey Oct 22 '20 at 4:57

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