Let sampling frequency of the given signal be 1024 samples/sec. I performed DWT decomposition using db wavelet for 5 levels, so I will get 5 levels of detailed coefficients and one approximation level coefficients. My query is, how can we calculate frequency range of the levels (5 detailed levels) of the coefficients ?
The frequency band corresponding to this sampling frequency is from -512 to 512. Let's as usual neglect the negative part for real signals.
The first level trend contains 0..256, the detail 512..256. The second level trend then contains the frequencies 0..128, the second level details 256..128. Etc.
The reversal of the frequencies is only useful for packet transforms, decomposing the first level details will contain in the trend component the frequencies 512..384, the details the frequencies 256..384.
There will be a rather substantial overlap in the frequency ranges, the Daubechies wavelets are not constructed for maximal band separation, but for maximal number of vanishing moments. See Rioul/Duhamel: "A Remez-like algorithm for wavelet filter construction" (from memory) for an algorithm constructing filter banks with better separation. Some wavelet packages have a "remez" command to compute such wavelet filters.
The frequency band corresponding to this sampling frequency is from -512 to 512. Let's as usual neglect the negative part for real signals.
The first level trend contains 0..256, the detail 512..256. The second level trend then contains the frequencies 0..128, the second level details 256..128. Etc.
The reversal of the frequencies is only useful for packet transforms, decomposing the first level details will contain in the trend component the frequencies 512..384, the details the frequencies 256..384.
There will be a rather substantial overlap in the frequency ranges, the Daubechies wavelets are not constructed for maximal band separation, but for maximal number of vanishing moments. See Rioul/Duhamel: "A Remez-like algorithm for wavelet filter construction" (from memory) for an algorithm constructing filter banks with better separation. Some wavelet packages have a "remez" command to compute such wavelet filters.
using DWT, as the number of levels increases the frequency resolution increases and the time resolution decreases. If you start with a signal containing the frequencies from 0 to 1000 Hz, after the first level decomposition, the approximation channel will contain half the frequencies (0 to 500) and the details channel will contain the frequencies from 500 to 1000, Downsampling by a factor of 2 will be done according to the Nyquist rule. At the second level, the approximations are decomposed into approximation and details a gain using the same above procedure. You can read Robi Polikar tutorial for more information, it is very interesting
First detail level - frequency band: [512, 1024] Hz,
Second detail level - frequency band: [256, 512] Hz,
Third detail level- frequency band: [128, 256] Hz,
Fourth detail level - frequency band: [64, 128] Hz,
Fifth detail level - frequency band: [32, 64] Hz,
Fifth approximation level - frequency band: [0,32] Hz.
Dr. Isar, doesn't the first detail level band you suggested violate the nyquist frequency criterion?
Hi,
My EEG Data has 250 Hz Sampling frequency, And I want to extract signals of all bands from given main signal. Please tell me that in how many levels should I decompose my Signal for Fs=250?
Hi,
Using MATLAB software, the maximum number of levels Jmax with which a signal can be decomposed, can be determined using the following equation :
Jmax= fix(log2[(N/Nw)-1])
N is the length of the signal, Nw gives the length of the decomposition filter associated with the chosen mother wavelet and fix is to round the value in the brackets to its nearest integer.
Best regards,
@ Prof.Kemari, how do you determine the length of decomposition filter associated with chosen mother wavelet ?
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