Are oversampling and downsampling the same thing?

Question

According the books I have on DSP,

• is oversampling, sampling a signal at a much higher samplingrate then normally required, so to reduce the sample-rate (and increase the resolution of the signal) afterwards
• is downsampling (decimation), lowering the samplerate of a signal, e.g. to reduce the CPU-requirements of signal-processing blocks later down the chain

So can I conclude that these two techniques are basically the same?

And does this mean that -as a concequence- downsampling will also increase the signal-resolution, just as with oversampling?

Or am I missing something?

Kristoff

Answer 1

OK. it looks like I got things mixed up.

The book on DSP I have mentions oversampling and that it is / can be followed by downsampling/decimation, ... and therefor I (wrongly) assumed that "oversampling" included both steps.

Mystery solved. Thanks for the correction.

Kristoff

Answer 2

With oversampling, you start with a very high sample rate, leading to you having more samples of your signal. By having a lot of samples, you have increased your computational load to a given system.

With downsampling, you start with a high sampling rate, and perform decimation (always preceded by an anti-aliasing filter to prevent aliasing when one decimates a signal). By doing this, you reduce the computational load, but decrease the effective Nyquist rate, which means you can physically observe “less” frequencies

So with all of that noted, you’ll see that they are not the same at all. Downsampling does not increase the signal resolution (in your words), it actually will decrease it.

Answer 3

Oversampling is followed by digital low-pass filtering and then by decimation/downsampling.

Oversampling does not change the information content of the signal at its final sample rate. So why does one do it?

In short: aliasing. Two sine signals with frequencies differing by a multiple of the sampling frequency are indistinguishable after sampling.

So one needs to remove higher frequencies before reducing a signal to a given sample rate.

If I want to sample at 48kHz, the highest representable frequency is 24kHz since 25kHz would be indistinguishable from -23kHz (23kHz but inverted). If my analog cutoff frequency is 20kHz, I just have 4kHz to attenuate my input signal's higher frequencies. That means an awfully steep filter and that means a lot of noise.

So trick #1: I postprocess my signal digitally, removing all frequencies between 20kHz and 24kHz. This digital gap between 20kHz and -20kHz (28kHz) is 8kHz wide, so I now have 8kHz for attenuating in the analog domain before sampling: frequencies between 24kHz and 28kHz will wrap back into the -24kHz to -20kHz domain, but I clean that out digitally. And digital filtering can be a lot steeper without introducing noise.

So let's oversample: use 96kHz to start with. Then we have the whole range from 20kHz to 76kHz for digital attenuation, and our analog prefiltering just needs to go to zero between 20kHz and 76kHz. That's a whole lot less steep, and thus a whole lot less noisy.

Basically oversampling is a temporary measure that shifts a major part of the work for antialiasing filtering from the analog domain into the digital domain.

You then do digital lowpass filtering and then you decimate to the sample frequency you'd have wanted from the start but that would have resulted in steep and thus noisy analog filters.

Oversampling filters do not tend to be all that long after all, but the same kind of complexity in the analog domain would be pretty disastrous.