Talk:Relations between Fourier transforms and Fourier series

I believe this article is very useful, it explains the different transforms in a much more intuitive way than the article on Fourier Analysis, it would be a shame to have it deleted. To be honest the image illustrates the idea like no other text I have found thus far. Please let's make an effort to keep the article online, there must be a niche for it.189.211.23.181 (talk) 22:59, 25 November 2011 (UTC)

I'm not native English so every suggestion is accepted. For now, my (not particularly inspired) proposals are:


 * 1) Relations among the continuous, discrete and periodic Fourier transforms (maybe a bit improper)
 * 2) Relations among the continuous Fourier transform, the DTFT, the Fourier series and the DFT (are abbreviations acceptable?)
 * 3) Relations among the various Fourier transforms (too generic)

I hesitate between the first and the second. Comments are welcome :).

TheNoise 19:46, 13 July 2007 (UTC)

I'm happy with the new name ;).

I've completed the missing sections in the article and now I'm thinking of removing the math-stub status in the following days.

TheNoise 14:23, 15 July 2007 (UTC)

Already done, This article ceased to be a stub many days ago.--Cronholm144 14:42, 15 July 2007 (UTC)

Incorrect formulas on cube graph
$$x_n = \sum_{k=-\infty}^{+\infty} x[n-kN] = \bar x(nT)$$    should be     $$ \bar x[n] = \sum_{k=-\infty}^{+\infty} x[n-kN] = \frac{1}{N} \sum_{k=0}^{N-1} X_k\cdot e^{i 2\pi \frac{n}{N} k} $$

$$\bar X(f) = \frac{1}{T} \sum_{k=-\infty}^{+\infty} X\!\left(f-\frac{k}{T}\right) $$    should be     $$ \bar X(f) = \sum_{k=-\infty}^{+\infty} X\!\left(f-\frac{k}{T}\right) = \mathcal{F}\ \left \{\sum_{n=-\infty}^{+\infty} x[n]\ \delta(t-nT)\right \} $$

$$x[n] = x(nT)\,$$    should be     $$x[n] = T\cdot x(nT)\,$$

$$\bar X_k = \frac{1}{T_0} \bar X \left(\frac{k}{T_0} \right)$$    should be     $$ X_k = \bar X \left(\frac{k}{T_0} \right) = \sum_{n=0}^{N-1} \bar x[n]\cdot e^{-i 2\pi \frac{k}{N} n} $$

--Bob K (talk) 13:26, 2 December 2011 (UTC)