Demo, CTFT to DTFT, sampling
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From: Nasser M. Abbasi on 26 Mar 2010 19:20 Hello; I wrote this basic demo to help me learn about DSP for a class (digital filtering) at my school that I am taking now, which illustrates sampling a signal, then it generates the CTFT (cont. time Fourier transform) and then the DTFT (discrete time Fourier transform) from the samples. Both the magnitude and the phase are plotted. One can adjust the sampling frequency, signal duration, and delay time. This is a limited duration signal, so the CTFT is not bounded and I do not use any prefilter/anti aliasing filter. The signal is a simple 2 harmonics (2 cosines), each with different frequencies and amplitudes which can be adjusted. I probably could have selected a more interesting signal? but I think too late to change it now. One can choose the method of signal reconstruction from sampling, either use sinc, or staircase, or spline (just for fun). The idea of the demo is to show what happens when one samples a signal and generates the DTFT and compare it to the CTFT, i.e. the DTFT is scaled, and periodic. Also it shows some different methods of signal reconstruction. I know there are many DSP gurus here. so if you try it, and find something I can improve, or something I am doing wrong, please let me know. It is the first demo below http://12000.org/my_notes/mma_demos/index.htm Just download the file, from the link next to the screen shot there, and then double click on it. But this runs using Mathematica player, which is all free, but you need to have the player installed first (unless you already have Mathematica 7 ofcourse, then you do not need the player). The player can be downloaded from http://www.wolfram.com/products/player/ Again, if you try it, and find a problem, like is it slow? or other such things, please let me know. thanks, --Nasser
From: Foots on 27 Mar 2010 10:26
"Nasser M. Abbasi" <nma(a)12000.org> wrote in message news:hojff8$2ov$1(a)speranza.aioe.org... > Hello; > > I wrote this basic demo to help me learn about DSP for a class (digital > filtering) at my school that I am taking now, which illustrates sampling a > signal, then it generates the CTFT (cont. time Fourier transform) and then > the DTFT (discrete time Fourier transform) from the samples. Both the > magnitude and the phase are plotted. > > One can adjust the sampling frequency, signal duration, and delay time. > This is a limited duration signal, so the CTFT is not bounded and I do not > use any prefilter/anti aliasing filter. > > The signal is a simple 2 harmonics (2 cosines), each with different > frequencies and amplitudes which can be adjusted. I probably could have > selected a more interesting signal? but I think too late to change it now. > > One can choose the method of signal reconstruction from sampling, either > use sinc, or staircase, or spline (just for fun). > > The idea of the demo is to show what happens when one samples a signal and > generates the DTFT and compare it to the CTFT, i.e. the DTFT is scaled, > and periodic. Also it shows some different methods of signal > reconstruction. > > I know there are many DSP gurus here. so if you try it, and find something > I can improve, or something I am doing wrong, please let me know. It is > the first demo below > > http://12000.org/my_notes/mma_demos/index.htm > > Just download the file, from the link next to the screen shot there, and > then double click on it. > > But this runs using Mathematica player, which is all free, but you need to > have the player installed first (unless you already have Mathematica 7 > ofcourse, then you do not need the player). > > The player can be downloaded from http://www.wolfram.com/products/player/ It might be a good idea to put a link to the player on the web page. |