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What are the advantages of DSP over ASP?

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I’m assuming you are referring to “Digital Signal Processing” versus “Analog Signal Processing.”
Digital signal Processing takes place after a signal (presumably analog) is quantized and then digitized. The resulting data stream is run through digital filters to achieve a desired effect and then converted back into analog.
Analog Signal Processing uses analog filters to directly alter the signals fed into it.
Why are digital processing methods superior to analog ones?
For one thing, digital signals can be EXACTLY reproduced — something impossible for analog ones. Another advantage is that digital filters can be “undone” precisely and reversed to generate the original signal — another thing that is impossible with analog.
Lastly, since digital filters are subject to purely mathematical manipulations which would be difficult if not impossible to accomplish by stacking ever-more-convoluted analog circuits, they are preferred for complicated post-Processing tasks.

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