This is of course because the dot product is a measure of how much two vectors / signals overlap. If the dot-product between our signal and a sine wave of a certain frequency results in a large amplitude this means that there is a lot of overlap between the two signals, and our signal contains this specific frequency.
Wavelet transform series#
That is, by multiplying a signal with a series of sine-waves with different frequencies we are able to determine which frequencies are present in a signal. In the previous blog-post we have seen how the Fourier Transform works. 2.1 From Fourier Transform to Wavelet Transform
Wavelet transform install#
PS: In this blog-post we will mostly use the Python package PyWavelets, so go ahead and install it with pip install pywavelets. 3.6 Comparison of the classification accuracies between DWT, Fourier Transform and Recurrent Neural Networks.3.5.3 Using the features and scikit-learn classifiers to classify two datasets.3.5.1 The idea behind Discrete Wavelet classification.3.5 Using the Discrete Wavelet Transform to classify signals.3.4 Removing (high-frequency) noise using the DWT.3.3 Deconstructing a signal using the DWT.3.2.3 Training the Convolutional Neural Network with the CWT.3.2.2 Applying the CWT on the dataset and transforming the data to the right format.3.2.1 Loading the UCI-HAR time-series dataset.3.2 Using the Continuous Wavelet Transform and a Convolutional Neural Network to classify signals.3.1 Visualizing the State-Space using the Continuous Wavelet Transform.2.5 More on the Discrete Wavelet Transform: The DWT as a filter-bank.2.4 Continuous Wavelet Transform vs Discrete Wavelet Transform.2.3 The different types of Wavelet families.2.2 How does the Wavelet Transform work?.2.1 From Fourier Transform to Wavelet Transform.The contents of this blogpost are as follows:
Wavelet transform code#
By providing Python code at every step of the way you should be able to use the Wavelet Transform in your own applications by the end of this post. In this blog-post we will see the theory behind the Wavelet Transform (without going too much into the mathematics) and also see how it can be used in practical applications. However, I believe it is also due to the fact that most books, articles and papers are way too theoretical and don’t provide enough practical information on how it should and can be used. This is partly because you should have some prior knowledge (about signal processing, Fourier Transform and Mathematics) before you can understand the mathematics behind the Wavelet Transform. A much better approach for analyzing dynamic signals is to use the Wavelet Transform instead of the Fourier Transform.Įven though the Wavelet Transform is a very powerful tool for the analysis and classification of time-series and signals, it is unfortunately not known or popular within the field of Data Science. Whether we are talking about ECG signals, the stock market, equipment or sensor data, etc, etc, in real life problems start to get interesting when we are dealing with dynamic systems. That’s too bad, since most of the signals we see in real life are non-stationary in nature. The more non-stationary/dynamic a signal is, the worse the results will be. That is, the frequencies present in the signal are not time-dependent if a signal contains a frequency of x this frequency should be present equally anywhere in the signal. The general rule is that this approach of using the Fourier Transform will work very well when the frequency spectrum is stationary. In that blog post we were able to classify the Human Activity Recognition dataset with a ~91 % accuracy. This simple approach works surprisingly well for many classification problems. The location (frequency-value) and height (amplitude) of the peaks in the frequency spectrum then can be used as input for Classifiers like Random Forest or Gradient Boosting. The larger and sharper a peak is, the more prevalent a frequency is in a signal. The peaks in the frequency spectrum indicate the most occurring frequencies in the signal. In a previous blog-post we have seen how we can use Signal Processing techniques for the classification of time-series and signals.Ī very short summary of that post is: We can use the Fourier Transform to transform a signal from its time-domain to its frequency domain.
0 kommentar(er)
