Where is the "time and frequency" in a Discrete Wavelet Transform? - Signal Processing Stack Exchange most recent 30 from dsp.stackexchange.com 2019-07-22T21:45:32Z https://dsp.stackexchange.com/feeds/question/22963 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://dsp.stackexchange.com/q/22963 0 Where is the "time and frequency" in a Discrete Wavelet Transform? student1 https://dsp.stackexchange.com/users/8825 2015-04-24T13:24:19Z 2015-05-01T09:37:21Z <p>The DWT is motivated by the ability to see signal in time and frequency at the same time, if I understood that correctly.</p> <p>I am using the following Matlab commands for some signal x:</p> <pre><code>[A,D] = dwt(x,'db4'); </code></pre> <p>Then I plot A vs some vector t, representing 'time'. I do know the algorithm behind A and D: low (high) pass filter, then downsample by 2.</p> <p>My questions: Where is the time axis and where is the frequency axis if I all what I have are the coefficients A (approximation) and D (detail)?</p> <p>Second question: If all of this is a simple filtering and downsampling, I don't see what is new in DWT...</p> https://dsp.stackexchange.com/questions/22963/-/22964#22964 1 Answer by Antoine Bassoul for Where is the "time and frequency" in a Discrete Wavelet Transform? Antoine Bassoul https://dsp.stackexchange.com/users/13315 2015-04-24T13:59:36Z 2015-05-01T09:37:21Z <p>DWT is motivated by the ability to analyse the signal in time and frequency <strong>with an adaptative time and frequency resolution</strong>.</p> <p>Some clever algorithm allows you to perform a wavelet analysis with a recursive implementation. Matlab's DWT does that, matlab's dwt perform only one level of DWT, therefore, A is only the output of the low-pass filter while D is the output of the high-pass filter. There is no time and frequency here. It only gives you a very coarse information about the time-frequency content of the signal. Please check how to implement a DWT.</p> <p>Second question : To see the novelty, you have to compare that to short-time frequency transform. With the DWT the time-frequency resolution depend on the frequency while with the STFT it's always the same. This is a <strong>VERY DESIRABLE</strong> property : You want a short time windows for quicly mooving high frequency signals and a long window for slower low frequency signals. </p> <p>Moreover, please consider that the filtering/downsampling implementation is a very refined and efficient one. DWT is an incredible tool for analysis, denoising, feature extraction etc ...</p>