When a signal is analysed using Wavelet Transform as analytical tool, wavelet function and scaling functions are used as high pass filter and complementary low pass filter respectively. If we go through multi resolutional analysis in depth, we can note that at first decomposition, original signal is decomposed into low band signal and high band signal. As the high band signal is not further decomposed rather low band signal is further decomposed, we will have high scale value at high frequency band resulting poor frequency resolution.
As the low band signal is further decomposed, with smaller scaling value resulting better frequency resolution. Smaller the scaling value better the frequency resolution is. As further decomposition is done at higher level, the signal will be down sampled resulting poorer time resolution at lower frequency band.
Thus it can be stated; wavelet transform has poor frequency resolution at higher frequency and better time resolution where as it has better frequency resolution at low frequency band and poorer time resolution.
As the low band signal is further decomposed, with smaller scaling value resulting better frequency resolution. Smaller the scaling value better the frequency resolution is. As further decomposition is done at higher level, the signal will be down sampled resulting poorer time resolution at lower frequency band.
Thus it can be stated; wavelet transform has poor frequency resolution at higher frequency and better time resolution where as it has better frequency resolution at low frequency band and poorer time resolution.
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