how does the frequency change when you take the details coefficients of the wavelet transform?

Hello,

I am using the wavelet decomposition to get the details coefficients of my signal.

From my understanding, if I had a signal of 100Hz, cd1 would give the frequencies between 50-100Hz and throw away all the other frequencies.

Yet, when I plot a scalogram of cd1, the low frequencies from 0-50 Hz are still there.

What am I missing here?

Cheers.

Answer 1

[Anurag Ojha]

Hey Lucrezia,

As per my understanding, you are using wavelet decomposition to get the details coefficients of the signal and are getting unexpected result on plotting scalogram of cd1.

In the case of "cd1," it refers to the detail coefficients at the first level of the wavelet decomposition. These detail coefficients will contain the high-frequency components of the original signal but will not necessarily be limited to the frequency range between 50-100Hz in the case of a 100Hz signal.

Here's why you might still see low frequencies (0-50Hz) present in the scalogram of cd1:

• Wavelet Transform Resolution: The wavelet transform has limited frequency resolution at each level. While the detail coefficients will capture high-frequency details, they are not perfect bandpass filters. Some low-frequency components may still be present, especially if they are close to the high-frequency cutoff of the wavelet used.
• Overlapping Frequency Bands: The different wavelet scales may have overlapping frequency bands. The detail coefficients at a certain level will not only contain the frequencies of the original signal that are in the range you mentioned (50-100Hz), but also some frequencies close to the lower cutoff of that wavelet.
• Boundary Effects: Wavelet decomposition introduces boundary effects that can affect the details coefficients near the edges of the signal. These boundary effects may contribute to the presence of low-frequency components in the detail coefficients.