Perform and interpret basic signal multiresolution analysis (MRA).

Use wavelet packets to remove harmonic interference from an electrocardiogram (ECG) signal.

Use wavelets to detect changes in the variance of a process. Changes in variance are important because they often indicate that something fundamental has changed about the data-generating mechanism.

There are a number of different variations of the wavelet transform. This example focuses on the maximal overlap discrete wavelet transform (MODWT). The MODWT is an undecimated wavelet transform over dyadic (powers of two) scales, which is frequently used with financial data. One nice feature of the MODWT for time series analysis is that it partitions the data variance by scale. To illustrate this, consider the quarterly chain-weighted U.S. real GDP data for 1974Q1 to 2012Q4. The data were transformed by first taking the natural logarithm and then calculating the year-over-year difference. Obtain the MODWT of the real GDP data down to level six with the 'db2' wavelet. Examine the variance of the data and compare that to the variances by scale obtained with the MODWT.

Measure the similarity between two signals at different scales.

この例では、ウェーブレットを使用して心電図 (ECG) 信号を解析する方法を示します。ECG 信号は往々にして非定常であり、その周波数成分は時間とともに変化します。この変化が関心の対象となるイベントです。

ウェーブレットから派生させた特徴と自己回帰モデルを使用した、心電図信号の分類。