Talk:Upsampling

Bandwidth versus sampling rate

Something seems wrong here. The page says

"Upsampling is the process of increasing the sampling rate of a signal. This is usually done to increase the bandwidth of a signal."

I think the second sentence is not correct. Ideally, upsampling should not increase bandwidth, only sample rate.

Quoting further:

"The upsampling factor (commonly denoted by L) is usually an integer or a rational fraction greater than unity. This factor multiplies the sampling rate or, equivalently, divides the sampling period. For example, if compact disc audio was upsampled by a factor of 5/4 then the resulting sampling rate goes from 44,100 Hz to 55,125 Hz, ... The range of valid frequencies (i.e., those that satisfy the Nyquist-Shannon sampling theorem) has gone from 22,050 Hz to 27,562.5 (an increase in 5,512.5 Hz."

While it is true that at the 55,125 Hz sampling rate, frequencies up to 27,562 Hz could be represented, producing such frequency content is not the purpose of the upsampling process. In fact, any frequencies that are above 22,050 Hz after the upsampling must be undesirable artifacts, as they were not represented in the original (lower sample rate) signal - and the purpose of the low-pass filter is to eliminate any such increase in bandwidth. After applying the low-pass interpolation filter, the bandwidth of the original signal and the bandwidth of the upsampled signal should be approximately the same if the filter has done a good job. Thus the purpose of upsampling is not to increase the bandwidth of the signal. --- SudoMonas

Note, please sign your posts with ~~~~

Certainly upsampling by 16 will increase your bandwidth by 16, but your original signal won't fill the extra bandwidth. Regardless, increasing your sampling rate gives you more bandwidth. Cburnett 05:34, 9 Mar 2005 (UTC)

This seems to be a matter of confusion over the meaning of the term bandwidth. To me, bandwidth is the width of the band of frequencies that is necessary to represent the content of the signal in a frequency-based analysis (e.g., a Fourier transform), not the number of bits used to represent the signal in the time (or space) domain. After the low-pass interpolation filtering, the frequency content of an upsampled signal should not have been substantially altered. (Thanks for the signing tip - I was wondering how that was done.) SudoMonas 06:37, 9 Mar 2005 (UTC)

The frequency content of the signal has not changed, but the bandwidth increases. For example, if my original signal is 1 khz and the sampling rate is 2 khz and I upsample by 16 (so sampling rate is now 32 khz). After filtering, the signal still has a frequency content of 1 khz but the bandwidth of the signal is now 16 khz. I could, for example, add in a 10 khz sine wave and be perfectly ok. Or I could add in another single if it's less than 16 khz.

Ultimately, it would appear you're not divorcing the bandwidth of the signal from that of frequency content of the signal. Cburnett 07:09, 9 Mar 2005 (UTC)

I removed "This is usually done to increase the bandwidth of a signal, which provides room for adding more information. Upsampling by itself does not add information."

Bandwidth can refer to both "the actual width of the frequency information carried by a signal", and "the width of frequency information which can be carried by a certain sample/data rate".

if the first definition is used, upsampling does NOT increasing the bandwith. if the latter definition is used, it's not possible to upsample without increasing the bandwith.

So it's incorrect either way. (even without "This is usually done to", I don't see how the context "upsampling" would totally "rule out" the first definition)

Upsampling in practice add some degree of aliasing, which perhaps could be considered "information"?

Also, I don't understand the "Unlike in downsampling which uses a low-pass filter as an anti-aliasing filter, upsampling uses an interpolation filter, which also is a low-pass filter."

Both upsampling and downsampling refer to the sinc filter, which "strips high-frequency data from a signal", Could it be better explained what the difference is between "using sinc as an interpolation filter" and "using sinc as an anti-aliasing filter", I just find it highly confusing.

(was I too bold removing?) teadrinker 14:44, 31 March 2006 (UTC)

The filter is the same, only the purpose is different. With upsampling, there is no problem with aliasing. Mirror Vax 15:36, 31 March 2006 (UTC)

Additional text to upsampling

Towards the end of the section on 'Upsampling by integer factor', I would think that the following text might be useful

--- start text--

When zeros are inserted into the signal for upsampling, the spectrum of the upsampled sequence will have aliases at integer multiples of the original sampling frequency. These aliases can be removed to a reasonable extent by a finite impulse response low pass filter. The presence of zeros in the sequence which is passed through the filter can be used to reduce the complexity of the filter implementation. The original filter can be split to $L$ subfilters and the output of each of these subfilters is sequentially tapped to obtain the filtered output sequence .

---stop text----

What say?

Beetelbug 14:54, 12 May 2007 (UTC)

an interesting point of understanding upsampling

Maybe we can understand upsampling like this: First the sampling rate is Fs, and we want to upsampling the rate to positive infinite. (also it seems the situation is going to change from Digital world to Analog world~. ) Note that when the signal is presented by the rate of Fs, in fact the signal is periodic in spectrum whose period is Fs, the reason we can't see it is just because the sampling rate Fs gives no ability to handle. So when the sampling rate comes to really big, there will be a lot of signals repeated on the spectrum with period of Fs. Now abviously we need a interpolation filter after the upsampling process.

Terrence007 (talk) 03:47, 6 November 2011 (UTC)

interesting. Dicklyon (talk) 03:55, 6 November 2011 (UTC)

Fig 2 should be broken down into 4 different subfigures, and the table should just be in wikiformat

I edited Fig 2's caption quite a bit, trying to put it in order and making sure everything was defined in it, and settled on the following:

Fig 2: The first triangle of the first graph represents the Fourier transform X(f) of a continuous function x(t). The entirety of the first graph depicts the discrete-time Fourier transform of a sequence x[n] formed by sampling the continuous function x(t) at a low-rate of 1/T. The second graph depicts the transform of a sequence formed by separating all low-rate samples by two zeros. It is identical to the first graph, except the frequency axis uses the symbol L to represent the upsampling factor of 3. The dotted outline represents a lowpass filter with bandwidth 0.5/T. The third graph depicts the desired 3x upsampled sequence resulting from filtering the zero-inserted sequence. The bottom table expresses the maximum filter bandwidth in various frequency units used by filter design tools.

But it is a bit long. I think that entire figure best be split into a series of subfigures as separate rows with caption inbetween the frequency axis are aligned, like:

[subfigure of X(f), just one triangle] caption: The triangle of the first graph represents the Fourier transform X(f) of a *band-limited* continuous function x(t).

[subfigure of discrete-time Fourier transform of X(f)] caption: The entirety of the first second graph depicts the discrete-time Fourier transform of a sequence x[n] formed by sampling the continuous function x(t) at a low-rate of 1/T.

[subfigure of zero-inserted transform] caption: Transform of a sequence formed by separating all low-rate samples by two zeros. It is identical to the first graph, except the frequency axis uses the symbol L to represent the upsampling factor of 3.

[subfigure of low-pass filter as dotted outline] caption: The dotted outline represents a digital lowpass filter with bandwidth 0.5/T.

[subfigure of the result] caption: The final graph depicts the desired 3x upsampled sequence resulting from filtering the zero-inserted sequence.

The final table I think can better just be put in the main article rather than inside a caption. Em3rgent0rdr (talk) 04:22, 25 August 2022 (UTC)

Those are good ideas. I hope you don't mind that I took the liberty of a couple of minor edits. The reason for inserting the word digital is to clarify why its DTFT is periodic. Perhaps that should be stated more explicitly.

--Bob K (talk) 13:02, 27 August 2022 (UTC)