Audio Compression Using Wavelets in MATLAB

Audio compression is the process of reducing the size of an audio file while maintaining its perceived quality. One of the most common techniques used for audio compression is wavelet-based compression. In this article, we will discuss the concept of wavelet-based audio compression and how it can be implemented in MATLAB

Wavelet-Based Audio Compression:

Wavelet-based audio compression is a technique that uses a mathematical tool called wavelet transform to analyze the audio signal. The wavelet transform breaks down the audio signal into a series of sub-bands with different frequency ranges. These sub-bands can then be compressed individually, leading to better compression ratios without losing significant audio quality.

Wavelet-based audio compression works by removing the redundant or less important information from the audio signal. This is done by applying a threshold to the coefficients obtained after performing the wavelet transform. The thresholding process sets the small wavelet coefficients to zero, which reduces the amount of data that needs to be stored. The threshold is determined based on the desired compression ratio and the perceptual importance of the audio signal.

Implementation in MATLAB:

MATLAB is a popular tool used by researchers and practitioners to implement wavelet-based audio compression algorithms. The following is a step-by-step guide to implement audio compression using wavelets in MATLAB:

Step 1: Load the audio file in MATLAB using the 'audioread' function.

Step 2: Perform the wavelet transform using the 'wavedec' function. The 'wavedec' function performs a discrete wavelet transform and returns the wavelet coefficients for each sub-band.

Step 3: Apply thresholding to the wavelet coefficients to remove the less important information using the 'wthresh' function.

Step 4: Reconstruct the compressed audio signal using the 'waverec' function. The 'waverec' function performs an inverse discrete wavelet transform and reconstructs the compressed audio signal.

Step 5: Save the compressed audio signal using the 'audiowrite' function.

The following MATLAB code demonstrates the implementation of wavelet-based audio compression:

% Set the compression ratio

compression_ratio = 0.5;

% Perform the wavelet transform

wname = 'db4';

level = 5;

[c, l] = wavedec(x, level, wname);

% Determine the threshold

[thr, ~] = wthrmngr('dw2ddenoLVL', c, l, compression_ratio);

% Apply thresholding

s = wthresh(c, 'h', thr);

% Reconstruct the compressed audio signal

y = waverec(s, l, wname);

% Save the compressed audio signal

audiowrite('compressed_audio_file.wav', y, Fs);

In this code, we first load an audio file using the audioread function. We then set the compression ratio to 0.5, which means we want to reduce the size of the audio file by half. We perform a wavelet transform using the wavedec function, which decomposes the audio signal into sub-bands. We use the 'db4' wavelet and set the level to 5.

Next, we determine the threshold for the wavelet coefficients using the wthrmngr function. This function calculates the threshold based on the desired compression ratio and the wavelet coefficients.

We then apply thresholding to the wavelet coefficients using the wthresh function. This function sets the small wavelet coefficients to zero, which reduces the amount of data that needs to be stored.

Finally, we reconstruct the compressed audio signal using the waverec function and save it using the audiowrite function.

Note that this code is just an example and can be customized for specific applications by changing the wavelet function, compression ratio, and thresholding method.

Here is the full code matlab of Audio Compression Using Wavelets in MATLAB: