How to get the high frequency portions of an audio using DWT?

Question

I basically want to use a digital wavelet transform to get the high frequencies of an audio signal and get the time information or really anything that can make me understand where they happen so I can compare with the data I get by reading the audio so I can perform some operations on the samples that have a high frequency.

I'm new to signal processing but I have studied a scientific paper that used DWT for that and I want to try to replicate that idea.

Yes I have studied DWT and what got me into it was the fact that you can get time information from it, as far as I understand. And I know about the coefficients but I don't know what to do with them exactly.

For all that, I'm using scipy to read a wav file and getting "data" that I suppose is the amplitude of every sample, the scipy.io.wavfile.read documentation doesn't make that clear). For the DWT itself, I'm using PyWavelets.

This is what I have right now (adapted):

from scipy.io import wavfile
import numpy as np
import pywt

sample_rate, data = wavfile.read('test.wav')

coefficientsApproximation, coefficientsDetail = pywt.dwt(data, 'db1')

coefficientsApproximation = np.array(coefficientsApproximation)
coefficientsDetail = np.array(coefficientsDetail)

The length of data is the number of samples. If I divide it by the sample rate I get the length of the audio in seconds, as expected.

The data itself is presented like this:

array([[ 19,  20],
       [ 19,  19],
       [ 20,  19],
       ...,
       [-84, -84],
       [-75, -75],
       [-74, -74]], dtype=int16)

Which is a 2D numpy array (2D because the audio is stereo, but don't focus on that cause I'm also working with mono).

coefficientsDetail is presented like this:

array([[-0.70710678],
       [ 0.        ],
       [ 0.70710678],
       ...,
       [ 0.        ],
       [ 0.        ],
       [ 0.        ]])

Which is again a 2D numpy array.

coefficientsApproximation is presented similarly:

array([[  27.57716447],
       [  26.87005769],
       [  27.57716447],
       ...,
       [-118.79393924],
       [-106.06601718],
       [-104.65180362]])

I want to use the information of WHERE are the high frequencies happening so that I can actually change the data variable based on that (e.g. change all the values related to a high frequency to 20). I tried to find a way to use the values of coefficientsDetail in order to do that but I wasn't able to do it.

Answer 1

Any highpass filter will give you high frequency time information.

A standard method for analysing and processing audio is a windowed/overlapped fft filterbank. I would suggest using that as a starting point as you will find more references and code snippets and litterature. Then, if you want to achieve something more specific, wavelets may well be the choice.