Timeline for Understanding noise removal method using wavelets
Current License: CC BY-SA 4.0
9 events
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| Nov 3, 2020 at 17:05 | comment | added | Sm1 | I am into estimation and looking into noise removal methods for chaotic systems. But very less information is present in books and other areas on signal processing for these types of systems. I have posted a new question stackoverflow.com/questions/64666503/… Would be grateful if you could take a look and provide an answer if possible. | |
| Nov 3, 2020 at 16:36 | comment | added | Fat32 | @Sm1 You can eithe romit $Fs$ (by setting it to whatever you want, such as 1) or you can associate a sampling period $T_s$ with the system and then define $F_s$ and $F_n$ as such. If you set $T_s = 1$ seconds, then your $F_s = 1$ Hz and $F_n = 0.5$Hertz. What's your subject matter of study ? | |
| Nov 3, 2020 at 15:59 | vote | accept | Sm1 | ||
| Nov 3, 2020 at 15:58 | comment | added | Sm1 | Thank you once again. So, in the case of discrete chaotic systems such as this one, $T_s$ appears to be. Thus, $F_s =1$ and Nyquist frequency = 0.5. Is my understanding correct? | |
| Nov 3, 2020 at 12:42 | comment | added | Fat32 | The factor $U$ can be any integer > 2. Larger the better but not too large! Say less than 100. But this's not a method of denoising. I used it to disintegrate high freq noise and the signal spectrums, by forcing signal spectrum to low freqs (with the help of interpolation). Then the added white noise was easier to recognise. Whether this is a valid act, depends on your actual noise characteristics. If your signal and noise spectrum were overlapping (as in the original case) then what I have done here will simply be cheating, and not a legitimate denoising of the actual data+noise case... | |
| Nov 3, 2020 at 12:33 | comment | added | Fat32 | Nevertheless, you can assign a sampling frequency to the observed data (eventhough it's not sampled), considering the time between two consecuitve observations : the period $T_s$ between two sequence values $x_n$ and $x_{n+1}$. This period may represent your sampling period, then your sampling frequency will be $F_s = 1/T_s$ and your Nyquist frequency will be $F_n = F_s/2$ Hz. | |
| Nov 3, 2020 at 12:29 | comment | added | Fat32 | Your recursion is an example of chaotic(?) nonlinear system that's extremely sensitive on intial conditions. I don't think so it does have an analytic expression for a Fourier transform. Furthermore, it does not represent a sampled continuous waveform, instead by nature a discrete type of data, (eventhough you used CWT [cont wavelet transform] on it), hence does not have a Nyquist Frequency. For plotting such discrete-natured data, Nyquist frequency is simply omitted and you focus on discrete-time frequencies in radian per sample (or cycles per sample) notation. | |
| Nov 3, 2020 at 3:52 | comment | added | Sm1 |
Thank you for answering. I never thought of interpolation aspect, this is new to me. Thank you for sharing this knowledge. Could you please clarify these points?(a) What is your intuition behind selecting the interpolation value, U?. (b) can you please mention what is the sampling and nyquist frequency for this kind of signal? This information is required to plot the scalogram image (Questions 2 &3).
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| Nov 3, 2020 at 1:27 | history | answered | Fat32 | CC BY-SA 4.0 |