Sampling and recovering a Sawtooth wave

[Cliste]

Hey guys, I've been working extensively on a report for the last few hours. I've managed 28 pages but I'm stuck on something.

For a 33kHz sampling of a sawtooth wave, what would the recovered wave look like? I'd imagine it would be recovered through a low pass filter?

Also, why is the wave different than the original? I'll hazard a guess that it's something to do with the bandwidth and Nyquist rate?

I'm not sure on this, although I've been struggling with the report, I'll only go online as a last resort to find the information.

I'll be very greatful for some replies,

Thank you :)

Edit: Sorry wrong part of the forum. It's late here 03:04am... getting sleepy :(.

 

[marcusl]

By sawtooth, do you mean a ramp followed by a vertical segment of -infinite slope? If so, then

Question 1) the signal has frequency components up to infinity, and by definition is not bandlimited. The act of sampling will cause aliasing, which will distort the reconstructed waveform. The aliasing, and hence the reconstructed waveform appearance, depends on the sampling frequency and on the waveform repetition frequency (which you do not mention).

Question 2) Reconstruction is not by lowpass filtering but by convolution with the "sinc function", as worked out by Shannon and independently by Whittaker, Kotelnikov and others. (Reconstruction is commonly credited also to Nyquist, but he did not contribute to this part of sampling theory). Wikipedia has a good article on this point (see Sampling Theorem). For the reconstruction process, see the wiki article "Whittaker-Shannon Interpolation."

 

[phinds]

As to why the recovered wave would be different, you need to study the Fourier transform of a sawtooth wave. What you will see is that it is the sum of an infinite series of sine waves, as are all waves of all shapes that involve instantaneous change of direction or amplitude. When you sample it at anything less than an infinite sampling rate, you are of necessity throwing out all of the series' terms beyond your sampling rate, so the resulting wave HAS to be different.

LATER: I see Marcus was putting in a more complete answer while I was typing.

 

[Cliste]

Excellent, I'm going to take all that into consideration and work my around it.

It's 04:18 now, time to sleep now I think :P.

Thanks a lot, much appreciated.

:)