>> well Peter, here again is where you overreach. assuming, without loss >> of generality that the sampling period is 1, the continuous-time signals >> >> x(t) = 1/cos(theta) * cos(pi*t + theta) >> >> are all aliases for the signal described above (and incorrectly as >> "contain[ing] no aliasing"). > >Well, strictly speaking, that is true. But I assumed the signal to be >bandlimited to 0..SR/2. In that case, you can perfectly reconstruct >it, as you have no other alias between 0..SR/2.
That class of signals is band limited to SR/2. The aliasing is in the amplitude/phase offset, not the frequency. There are an infinite number of combinations of amplitude/phase of a nyquist-frequency sinusoid that will all result in the same sampled sequence. So you can't invert the sampling. You can construct a DAC that will output some well-behaved nyquist frequency sinusoid when presented with the input ..., 1, -1, 1, -1, 1, ..., but you can't guarantee that it will resemble an analog sinusoid that was sampled to produce such a digital sequence. You don't have enough info to disambiguate the phase and amplitude. E On Tue, Aug 18, 2015 at 1:51 PM, Peter S <peter.schoffhau...@gmail.com> wrote: > On 18/08/2015, robert bristow-johnson <r...@audioimagination.com> wrote: > > On 8/18/15 4:28 PM, Peter S wrote: > >> > >> 1, -1, 1, -1, 1, -1 ... is a proper bandlimited signal, > >> and contains no aliasing. That's the maximal allowed frequency without > >> any aliasing. > > > > well Peter, here again is where you overreach. assuming, without loss > > of generality that the sampling period is 1, the continuous-time signals > > > > x(t) = 1/cos(theta) * cos(pi*t + theta) > > > > are all aliases for the signal described above (and incorrectly as > > "contain[ing] no aliasing"). > > Well, strictly speaking, that is true. But I assumed the signal to be > bandlimited to 0..SR/2. In that case, you can perfectly reconstruct > it, as you have no other alias between 0..SR/2. > > -P > _______________________________________________ > music-dsp mailing list > music-dsp@music.columbia.edu > https://lists.columbia.edu/mailman/listinfo/music-dsp >
_______________________________________________ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
