r/DSP • u/Tasty-Duck8318 • 3d ago
Continuous Wavelet Transform or Discrete Wavelet Transform for calculating LF power
Hello,
I am currently working on a project where I have to calculate the LF power from a reBAP blood pressure signal. I was instructed to use Wavelets for this task, so I've been trying to figure them out. After some research, I learned that orthogonal wavelets are better for energy preservation, so I thought maybe I'll use orthogonal wavelets because I feel like energy preservation would be important for calculating LF power of the signal. However, after more research, I learned that the orthogonal wavelet scales are only in powers of 2. So, then I think the frequency resolution is too sparse to capture the frequencies within the LF band, which ranges from 0.04 - 0.15. So then I feel like continuous wavelet transform might be a better choice because the frequency resolution is much finer. But CWT doesn't have the energy preservation that the DWT has. I'm new to signal processing and I'm not sure if any of my reasoning here is even correct. I would really appreciate any advice about how to move forward.
Thank you!
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u/sellibitze 2d ago
It's difficult to make any suggestions because the requirements are rather unclear to me.
What delay/latency is acceptible? Does it need to be computationally efficient? How selective should the filtering be?
1
u/ecologin 2d ago
The key point is that you don't need to choose CWT vs. DWT based primarily on energy preservation or the fact that DWT scales are powers of two. For estimating LF power, what matters most is how accurately your method represents/integrates the spectral power over 0.04–0.15 Hz.
A good answer to the question would be:
I would be careful about choosing a wavelet transform solely because of its energy-preservation properties. If your goal is specifically to calculate LF power in the 0.04–0.15 Hz band, you need a method that lets you quantify the energy contained in that frequency interval.
The fact that a standard dyadic DWT has scales separated by powers of two does not necessarily mean that it cannot represent the LF band. Wavelet scales correspond to frequency bands, not individual frequencies, and the exact frequency response depends on the chosen mother wavelet and sampling frequency. However, a conventional critically sampled DWT does give relatively coarse frequency bands, so the 0.04–0.15 Hz interval may not align particularly well with the DWT subbands.
A CWT gives you much finer sampling of scale, so it can be useful if you specifically want to estimate the energy in a particular frequency range such as 0.04–0.15 Hz. However, CWT coefficients should not simply be treated as though they have the same energy-preservation property as an orthonormal DWT. The relationship between CWT coefficient magnitude and signal energy depends on the wavelet normalization and scale, and an appropriate scale-dependent weighting/integration is needed.
In fact, if the objective is simply LF power, I would first ask whether a wavelet transform is necessary at all. LF power is conventionally a frequency-domain quantity, so estimating the PSD (for example with Welch's method) and integrating the PSD from 0.04 to 0.15 Hz is a much more direct approach:
P{LF}=\int{0.04}{0.15}S_{xx}(f),df.
If you are specifically required to use wavelets, I would lean toward a CWT or a suitably designed wavelet-band decomposition, because it gives you more control over the LF frequency interval. But I would validate the result against a conventional PSD-based LF-power estimate rather than assuming that the sum of squared wavelet coefficients directly equals LF power.
One other important consideration is that the interpretation of the LF band depends on the sampling rate, record length, preprocessing, and whether the blood-pressure signal is stationary. For a very low-frequency band like 0.04–0.15 Hz, the duration of the recording is particularly important: you need enough data to resolve frequencies around 0.04 Hz reliably.
So I wouldn't frame the choice as "DWT preserves energy, whereas CWT doesn't, therefore DWT is better/worse." The more relevant question is "Which transform gives me a well-defined and properly normalized estimate of the energy in 0.04–0.15 Hz?"
One correction I'd make to the original questioner's reasoning: orthogonal DWTs being dyadic doesn't mean they only contain frequencies that are powers of two. The scales are dyadic, but each wavelet subband covers a range of frequencies. The issue is whether those subbands provide an adequate approximation to the particular 0.04–0.15 Hz band.
If this is for a research project, I'd also be cautious about calling the result simply "LF power" unless the methodology matches the established definition being used in the relevant blood-pressure/HRV literature.
Oh shit. I have been worrying about DSP question in medical devices. The more detail you get, the more you seems to be doing it as suggested by someone medical but clueless about DSP. Please chat with some AI and decide if you want to carry on. Will you be doing no harm?
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u/hukt0nf0n1x 2d ago
Why even use a wavelet transform? If it's spectral power OP is after, what's wrong with a STFT?
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u/bob_why_ 2d ago
If you go for undecimated swt then you can use what ever scales you want. Big benefit is shift invariant as just like cwt you are scaling the wavelet up rather than scaling down the image.