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<blockquote data-quote="Frank Koenig" data-source="post: 130311" data-attributes="member: 416">Re: Basic principles of samplingAt the risk of adding noise (dither?) to Phil&#039;s very nice explanation, I&#039;ll say a little on the subject of reconstruction, which is what happens in the digital-to-analog converter. This is more of a time domain view and does not rely directly on Fourier theory.Ideal sampling consists of multiplying a continuous waveform by a sequence of (in our case uniformly spaced) impulses. (An impulse, very roughly speaking, is a pulse of infinite amplitude, zero duration, and finite area.) This results in a sequence of impulses that are scaled in energy (area) by the amplitude of the continuous waveform&nbsp; at the time of each impulse.It turns out that there is an ideal low-pass filter, which we call the reconstruction filter, that does a perfect job of interpolating the original continuous waveform between the sample impulses, provided that there were no frequency components above the Nyquist frequency in the original waveform. This filter has a &quot;brick wall&quot;&nbsp; frequency response and hence a sin(x)/x impulse response, which is of (doubly) infinite duration and therefor physically unrealizable. In practice we approximate this filter, often by using a zero-order hold, or other interpolator, in combination with a realizable low-pass filter. (A zero-order hold replaces each impulse with a pulse whose duration is the sample interval and whose amplitude is the area of the preceding impulse.)The key here is that the reconstruction filter fills in the spaces between the samples and if Nyquist is satisfied then sufficient information exists in the samples for the filter to do this. --Frank</blockquote>

[QUOTE="Frank Koenig, post: 130311, member: 416"] Re: Basic principles of sampling At the risk of adding noise (dither?) to Phil's very nice explanation, I'll say a little on the subject of reconstruction, which is what happens in the digital-to-analog converter. This is more of a time domain view and does not rely directly on Fourier theory. Ideal sampling consists of multiplying a continuous waveform by a sequence of (in our case uniformly spaced) impulses. (An impulse, very roughly speaking, is a pulse of infinite amplitude, zero duration, and finite area.) This results in a sequence of impulses that are scaled in energy (area) by the amplitude of the continuous waveform at the time of each impulse. It turns out that there is an ideal low-pass filter, which we call the reconstruction filter, that does a perfect job of interpolating the original continuous waveform between the sample impulses, provided that there were no frequency components above the Nyquist frequency in the original waveform. This filter has a "brick wall" frequency response and hence a sin(x)/x impulse response, which is of (doubly) infinite duration and therefor physically unrealizable. In practice we approximate this filter, often by using a zero-order hold, or other interpolator, in combination with a realizable low-pass filter. (A zero-order hold replaces each impulse with a pulse whose duration is the sample interval and whose amplitude is the area of the preceding impulse.) The key here is that the reconstruction filter fills in the spaces between the samples and if Nyquist is satisfied then sufficient information exists in the samples for the filter to do this. --Frank [/QUOTE]

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