Great video! Nice explanation for window the data, comprehension about formula that is used and it is just so easy to understand your point of view. Congrats, you are a good professor.
Given that wavelets exhibit localization in time and frequency and wavelet analysis allows for efficient multi-scale analysis, wavelet analysis is superior for financial data where there exists higher order non-stationarity and multi-scale dynamics. Conditional on the data, I use either wavelet packet denoising or wavelet NN-ARFIMA hybridization.
In short, wavelet analysis works by analyzing the time series/signal at varying frequencies at varying resolutions.For high frequencies, there is strong time resolution and poor frequency resolution. For low frequencies, there is strong frequency resolution and poor time resolution. Unlike Fourier that uses long forms, wavelets are highly localized. Unlike Fourier, it allows one to see the non-stationarity in the process. Heres a good simple introduction I found by searching one second on google georgemdallas.wordpress.com/2014/05/14/wavelets-4-dummies-signal-processing-fourier-transforms-and-heisenberg/
***** There exists more advanced tools such as Hilbert Huang transform (R package hht). Its ability to handle nonlinear and non-stationary process is unmatched. It, also, has the sharpest time-frequency representations. These are extremely computationally intensive!!! It took me hours to run a HH spec on my personal laptop.
This has been implemented in Matlab as spectrogram() function. How do we determine the optimal window size? How does overlap affect the frequency-time resolution? Thank you.
L is the number of data points being analyzed in each segment of data, 812 in this example. So we are finding the frequency characteristics for segments of length 812. N is the length of the DFT used to analyze the L=812 data points in each segment. So each segment of L=812 data samples are effectively padded with zeros to length N=2048. N only controls the number of frequencies at which we evaluate the DFT (N frequencies). This concept is discussed in several of the earlier videos in The Discrete Fourier Transform and Applications playlist.
Hi Mr. Van Veen could you please help me with this question? Develop a sliding DFT algorithm and compute sliding DFT for x(n) = [0,1,2,3,4,5]. if sliding window length-4.
Can we "hack" the "no free lunch here" problem by getting lets say 128 samples and pad them with zeros up to 2048 and then take FFT? Wouldn't it give us bigger resolution and better "dynamics"?
Now I understand, the L - length is the problem here. You explained that in the video and in answer to Derza Arsad question. After watching this video again, it gets clear :)
1:36 "Rather than sliding the window through a fixed data record, it turns out that it's easier, to fix the window, and slide the data past the window."
Great video! Nice explanation for window the data, comprehension about formula that is used and it is just so easy to understand your point of view. Congrats, you are a good professor.
Excellent Explanation. Thanks from Colombia
This was very helpful, thank you!
Wait, I think the explanation at 2:25 is a bit wrong, it should extract the value from X[n] up through X[n+L-1]. CMIIW btw
Arent you the man who co-authored Simon Haykin's signal and systems book ?
Wonderful lecture! Thank you very much Sir.
Even though I am a wavelet guy, I can still appreciate short time fourier transform.
wavelet is just an optimization for computation complexity , wavelet is for engineers :)
Given that wavelets exhibit localization in time and frequency and wavelet analysis allows for efficient multi-scale analysis, wavelet analysis is superior for financial data where there exists higher order non-stationarity and multi-scale dynamics. Conditional on the data, I use either wavelet packet denoising or wavelet NN-ARFIMA hybridization.
***** Do you use matlab or R code? How good are you at mathematics?
In short, wavelet analysis works by analyzing the time series/signal at varying frequencies at varying resolutions.For high frequencies, there is strong time resolution and poor frequency resolution. For low frequencies, there is strong frequency resolution and poor time resolution. Unlike Fourier that uses long forms, wavelets are highly localized. Unlike Fourier, it allows one to see the non-stationarity in the process.
Heres a good simple introduction I found by searching one second on google
georgemdallas.wordpress.com/2014/05/14/wavelets-4-dummies-signal-processing-fourier-transforms-and-heisenberg/
***** There exists more advanced tools such as Hilbert Huang transform (R package hht). Its ability to handle nonlinear and non-stationary process is unmatched. It, also, has the sharpest time-frequency representations. These are extremely computationally intensive!!! It took me hours to run a HH spec on my personal laptop.
This has been implemented in Matlab as spectrogram() function.
How do we determine the optimal window size?
How does overlap affect the frequency-time resolution?
Thank you.
Good Explanation Thank you!
Great Explanation, thanks!
what is the different between L and N in the saxophone riff section? doesnt N suppose to have the same number as sampling rate?
L is the number of data points being analyzed in each segment of data, 812 in this example. So we are finding the frequency characteristics for segments of length 812.
N is the length of the DFT used to analyze the L=812 data points in each segment. So each segment of L=812 data samples are effectively padded with zeros to length N=2048. N only controls the number of frequencies at which we evaluate the DFT (N frequencies). This concept is discussed in several of the earlier videos in The Discrete Fourier Transform and Applications playlist.
Great explanation thank you
Hi Mr. Van Veen
could you please help me with this question?
Develop a sliding DFT algorithm and compute sliding DFT for x(n) = [0,1,2,3,4,5]. if sliding window length-4.
I am looking for a relation between length of a window and bandwidth of the filter. Any clues/hints?
Can we get information for the phase of specific frequency? Thanks!
WOW now I see it clearer! One question just to know, in the formula could it be x[n-m] instead of x[n+m] to advance the signal x forward? thank u.
a typo in the title, "Spect(r)ogram"
very good. Thank you for that
Can we "hack" the "no free lunch here" problem by getting lets say 128 samples and pad them with zeros up to 2048 and then take FFT? Wouldn't it give us bigger resolution and better "dynamics"?
Now I understand, the L - length is the problem here. You explained that in the video and in answer to Derza Arsad question. After watching this video again, it gets clear :)
amazing!!!!! thank you
thank you so much!
what is the different n and m? may i have your email, sir?
excellent
great!
thanks :)
1:36 "Rather than sliding the window through a fixed data record, it turns out that it's easier, to fix the window, and slide the data past the window."
fs = 44.1 kHz
wow