Hi guys i have to find the fourier transform of the convolution: $$ sinc(t/2T)*\sum\limits_{n-\infty}^{+\infty} (-1)^{n}\delta(t - nT) $$

i was thinking of express the summatory as : $$\sum\limits_{n-\infty}^{+\infty} (-1)^{n}\delta(t - nT) = \mathrm{III}_{2T}(t) -\mathrm{III}_{T}(t-1)$$ so we have:

$$ sinc(t/2T)*[\mathrm{III}_{2T}(t) -\mathrm{III}_{T}(t-1)]$$

So the convolution in the fourier domain became a product: $$ rect(f2T)\mathrm{III}_{1/2T}(t)-2rect(f2T)\mathrm{III}_{1/T}(t)e^{ipif} $$

Well is this a good result and how i can find the energy from this formula ?

  • $\begingroup$ Please define your symbols, What is $III$ ? Also in your last formula you seem to mix frequency and time domain functions. $\endgroup$ – Hilmar Dec 3 '20 at 20:51
  • $\begingroup$ Hi , III is the delta comb ,where i mix them ? $\endgroup$ – Giovanni Cerciello Dec 3 '20 at 21:15
  • $\begingroup$ You appear to do a Fourrier transform in going from equation 3 to equation 4. However the variable of the $III$ function is still $t$ $\endgroup$ – Hilmar Dec 4 '20 at 17:46

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