The Sampling Theorem - An Intuitive Approach
Scott Kurtz from DSPSoundWare.com has put together a video presentation that aims to help DSPers gain a better intuitive understanding of the Sampling Theorem. Feel free to have a look and share your thoughts by commenting this blog post.
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Comment by ●February 1, 2015
Hi,
I like this video. The notion of showing the red phasor smoothly rotating and the green dot periodically sampling the red phasor's position is a great idea. And I like that the video shows the green 1000 Hz samples being 180 degrees out of phase with the green 7000 Hz samples.
My only cautionary comment is that the green Frequency Domain display may confuse, or mislead, a beginner in DSP. At the time stamp of 11:20 the video shows the spectrum of an analog 7000 Hz tone sampled at 8000 samples/second. And the Freq Domain display shows spectral components whose frequencies are higher than the 8000 Hz sample rate. Performing the FFT of the green discrete time samples can never produce spectral values greater than 8000 Hz. So the green Freq Domain display is not the FFT of the green Time Domain #1 samples. Another thing that might puzzle DSP beginners is "In the green Freq Domain display, why does the 1000 Hz and 7000 Hz spectral components show spectral leakage but the 9000 Hz spectral component (a perfectly thin vertical line) shows no spectral leakage?" The green Freq Domain display is the FFT of something, but it's not the FFT of the green Time Domain #1 samples.
Forgive me for being "picky." In any case, I like this video animation.
[-Rick-]
I like this video. The notion of showing the red phasor smoothly rotating and the green dot periodically sampling the red phasor's position is a great idea. And I like that the video shows the green 1000 Hz samples being 180 degrees out of phase with the green 7000 Hz samples.
My only cautionary comment is that the green Frequency Domain display may confuse, or mislead, a beginner in DSP. At the time stamp of 11:20 the video shows the spectrum of an analog 7000 Hz tone sampled at 8000 samples/second. And the Freq Domain display shows spectral components whose frequencies are higher than the 8000 Hz sample rate. Performing the FFT of the green discrete time samples can never produce spectral values greater than 8000 Hz. So the green Freq Domain display is not the FFT of the green Time Domain #1 samples. Another thing that might puzzle DSP beginners is "In the green Freq Domain display, why does the 1000 Hz and 7000 Hz spectral components show spectral leakage but the 9000 Hz spectral component (a perfectly thin vertical line) shows no spectral leakage?" The green Freq Domain display is the FFT of something, but it's not the FFT of the green Time Domain #1 samples.
Forgive me for being "picky." In any case, I like this video animation.
[-Rick-]
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