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| Anthocyanina:
--- Quote from: loop123 on April 02, 2024, 09:41:47 pm --- --- Quote from: gf on April 02, 2024, 01:49:01 pm --- --- Quote from: loop123 on April 02, 2024, 01:14:32 pm ---Ok. I'm familiar with 48kSA/s since my Audacity uses that audio sample rate too. Let's say the audio sample rate is 2000kSA/s instead of just 48kSA/s then you can already see the jagged edge noise in the 900Hz, right? --- End quote --- No, it is not a matter of the sample rate (48kSa/s is more than enough for this signal), and it's not a matter of sampling. It is a matter of filtering. Feeding an analog white noise signal though a corresponding analog filter would have the same effect. Btw, it's not difficult to do the same simulation in Audaity, too. I'm not familiar with this program, still I was able to find all the tools within a couple of minutes. Create one track and fill it with a sine wave. Create a 2nd track and fill it with white noise. Create a 3rd track by mixing the two tracks. Apply lowpass filter to the 3rd track. Done. See attachment. --- End quote --- Ok I tried Audacity generator and mixing. I first created white noise in 1st track. then apply 1000kHz filter to the white noise. In the first screenshot I added a 50Hz sine wave in 2nd track and mix in 3rd track. There is noise. (Attachment Link) In the following image I added a 900Hz sine wave in 2nd track with the same white noise 1000kHz filtered in first track and mix in 3rd track. The jagged edge is not seen. (Attachment Link) If the above methods are correct. Can we just say that in the 900Hz. There is simply less noise per sine wave compared to the 50Hz in first image that is why there is no jagged edge in the 3rd track? --- End quote --- there is the same amount/magnitude/presence of noise, it just looks different. you can do an FFT to confirm that, then increase the noise amplitude, and do another FFT and see how the noise floor rises equally on both 50 hz and 900 hz if the applied noise is the same |
| loop123:
--- Quote from: Anthocyanina on April 02, 2024, 09:53:27 pm --- --- Quote from: loop123 on April 02, 2024, 09:41:47 pm --- --- Quote from: gf on April 02, 2024, 01:49:01 pm --- --- Quote from: loop123 on April 02, 2024, 01:14:32 pm ---Ok. I'm familiar with 48kSA/s since my Audacity uses that audio sample rate too. Let's say the audio sample rate is 2000kSA/s instead of just 48kSA/s then you can already see the jagged edge noise in the 900Hz, right? --- End quote --- No, it is not a matter of the sample rate (48kSa/s is more than enough for this signal), and it's not a matter of sampling. It is a matter of filtering. Feeding an analog white noise signal though a corresponding analog filter would have the same effect. Btw, it's not difficult to do the same simulation in Audaity, too. I'm not familiar with this program, still I was able to find all the tools within a couple of minutes. Create one track and fill it with a sine wave. Create a 2nd track and fill it with white noise. Create a 3rd track by mixing the two tracks. Apply lowpass filter to the 3rd track. Done. See attachment. --- End quote --- Ok I tried Audacity generator and mixing. I first created white noise in 1st track. then apply 1000kHz filter to the white noise. In the first screenshot I added a 50Hz sine wave in 2nd track and mix in 3rd track. There is noise. (Attachment Link) In the following image I added a 900Hz sine wave in 2nd track with the same white noise 1000kHz filtered in first track and mix in 3rd track. The jagged edge is not seen. (Attachment Link) If the above methods are correct. Can we just say that in the 900Hz. There is simply less noise per sine wave compared to the 50Hz in first image that is why there is no jagged edge in the 3rd track? --- End quote --- there is the same amount/magnitude/presence of noise, it just looks different. you can do an FFT to confirm that, then increase the noise amplitude, and do another FFT and see how the noise floor rises equally on both 50 hz and 900 hz if the applied noise is the same --- End quote --- There is the same amount of noise given the same time. But one 900Hz sine wave can form superposition with the noise at smaller scale that is why the 900Hz sine wave has no jagged edge. Is this simple interpretation correct? If wrong. Then is it like the quantum vacuum where no matter how smaller scale you try to sample it, the noise is the same because the quantum vacuum is random and lorentz invariant and background independent? |
| radiolistener:
--- Quote from: loop123 on April 02, 2024, 10:47:17 pm ---Then is it like the quantum vacuum where no matter how smaller scale you try to sample it, the noise is the same because the quantum vacuum is random and lorentz invariant and background independent? --- End quote --- :-DD :-DD :-DD Are you kidding? :popcorn: |
| Anthocyanina:
--- Quote from: loop123 on April 02, 2024, 10:47:17 pm --- --- Quote from: Anthocyanina on April 02, 2024, 09:53:27 pm --- --- Quote from: loop123 on April 02, 2024, 09:41:47 pm --- --- Quote from: gf on April 02, 2024, 01:49:01 pm --- --- Quote from: loop123 on April 02, 2024, 01:14:32 pm ---Ok. I'm familiar with 48kSA/s since my Audacity uses that audio sample rate too. Let's say the audio sample rate is 2000kSA/s instead of just 48kSA/s then you can already see the jagged edge noise in the 900Hz, right? --- End quote --- No, it is not a matter of the sample rate (48kSa/s is more than enough for this signal), and it's not a matter of sampling. It is a matter of filtering. Feeding an analog white noise signal though a corresponding analog filter would have the same effect. Btw, it's not difficult to do the same simulation in Audaity, too. I'm not familiar with this program, still I was able to find all the tools within a couple of minutes. Create one track and fill it with a sine wave. Create a 2nd track and fill it with white noise. Create a 3rd track by mixing the two tracks. Apply lowpass filter to the 3rd track. Done. See attachment. --- End quote --- Ok I tried Audacity generator and mixing. I first created white noise in 1st track. then apply 1000kHz filter to the white noise. In the first screenshot I added a 50Hz sine wave in 2nd track and mix in 3rd track. There is noise. (Attachment Link) In the following image I added a 900Hz sine wave in 2nd track with the same white noise 1000kHz filtered in first track and mix in 3rd track. The jagged edge is not seen. (Attachment Link) If the above methods are correct. Can we just say that in the 900Hz. There is simply less noise per sine wave compared to the 50Hz in first image that is why there is no jagged edge in the 3rd track? --- End quote --- there is the same amount/magnitude/presence of noise, it just looks different. you can do an FFT to confirm that, then increase the noise amplitude, and do another FFT and see how the noise floor rises equally on both 50 hz and 900 hz if the applied noise is the same --- End quote --- There is the same amount of noise given the same time. But one 900Hz sine wave can form superposition with the noise at smaller scale that is why the 900Hz sine wave has no jagged edge. Is this simple interpretation correct? If wrong. Then is it like the quantum vacuum where no matter how smaller scale you try to sample it, the noise is the same because the quantum vacuum is random and lorentz invariant and background independent? --- End quote --- if your noise contains every frequency between 1 and 1000hz, your low frequency signal has what you call jagged edges because the signal's period is too long compared to most of the noise, so the higher frequency noise will look "jagged" because, let's say the 1khz component of the noise, it goes up and down in a much shorter time than your 50hz signal. at 900hz, the period of the signal is much shorter than that of most of the components of the noise, and very close to that of the higher frequency components of the noise, so as your signal goes up and down, the higher frequency noise goes up and down at about the same rate, so there is a visually different effect if you observe the captured waveform, and the lower frequency noise is also there, but its period is so much longer that it is barely "visible" if you observe a single, or a few periods of your high frequency signal. do this in audacity, generate a 50hz signal, without noise, and generate a 900hz signal, also without noise, then add them. if you zoom out, you will see the 50hz signal with the 900hz making it look fuzzy, but if you zoom in, you will see the 900hz signal slowly being offset from the center at a rate of 50hz. both signals are equally present in that sum output, it just looks different depending on how zoomed in or out you look at it. |
| loop123:
--- Quote from: Anthocyanina on April 03, 2024, 12:07:57 am --- if your noise contains every frequency between 1 and 1000hz, your low frequency signal has what you call jagged edges because the signal's period is too long compared to most of the noise, so the higher frequency noise will look "jagged" because, let's say the 1khz component of the noise, it goes up and down in a much shorter time than your 50hz signal. at 900hz, the period of the signal is much shorter than that of most of the components of the noise, and very close to that of the higher frequency components of the noise, so as your signal goes up and down, the higher frequency noise goes up and down at about the same rate, so there is a visually different effect if you observe the captured waveform, and the lower frequency noise is also there, but its period is so much longer that it is barely "visible" if you observe a single, or a few periods of your high frequency signal. do this in audacity, generate a 50hz signal, without noise, and generate a 900hz signal, also without noise, then add them. if you zoom out, you will see the 50hz signal with the 900hz making it look fuzzy, but if you zoom in, you will see the 900hz signal slowly being offset from the center at a rate of 50hz. both signals are equally present in that sum output, it just looks different depending on how zoomed in or out you look at it. --- End quote --- Thanks guys. The appearances and explanations of the noises at 50Hz and 900Hz are very clear now. There is another topic that I've been thinking for over a month. Can you share any software that can demonstrate the power of digital filter especially oversampling that can apply lowpass or bandpass filter with brick wall frequency response. My BMA-200 that uses the AMP01 has 2 order Butterworth filter with -12dB/octave response while my gtec USBamp has no amplifier but only ADC that directly maps the microvolt signal at +- 250mV. I'd like to know if it's oversampling (ability to do moving averages) capability can make me see signal that I can't with the BMA (between 1 to 2400Hz), and worth spending $3000 just to get the software to run it. Here is the spec of the USBamp. Pls share sofware to demonstrate the power of oversampling via digital filter. How much can it beat 2 order Butterworth filter with its almost brick wall response? Member "gf" told me not make another thread so I post this question here. Remember that a 2nd order Butterworth filter with less vertical low-pass edge only adds about 7.5% noise compared to the digital brick-wall filter. So does digital filter oversampling only remove the noise above the cut-off or can it also make the noise less below the cutoff? Please share software so I can try to see the process. Thanks. https://www.gtec.at/product/gusbamp-research/ " Each of the 16 analog to digital converters operates at 2.4576 MHz. Oversampling 64 times yields the internal sampling rate of 38,400 Hz (per channel and for all channels!). In addition, a powerful floating point Digital Signal Processor performs oversampling and real-time filtering of the biosignal data (between 0 Hz – 2,400 Hz). Therefore, a typical sampling frequency of 256 Hz yields an oversampling rate of 9,600. This results in a very high signal to noise ratio, which is especially critical when recording evoked potentials (EP) in the EEG or identifying small amplitude changes in high-resolution ECG recordings. You are measuring far below the noise-range of conventional amplifiers." |
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