How to Compare Two Audio Files in MATLAB

Comparing audio files in MATLAB involves analyzing their similarity using techniques like cross-correlation and convolution. These methods, often implemented using Fast Fourier Transforms (FFTs), provide insights into the relationship between audio signals. This article explores how to effectively compare two audio files in MATLAB using these techniques.

Utilizing Cross-Correlation for Audio Comparison

Cross-correlation measures the similarity between two signals as a function of their relative time delay. A high cross-correlation value at a specific time lag indicates a strong similarity between the signals at that offset. In MATLAB, cross-correlation can be efficiently computed using FFTs:

1. Zero-Padding: Extend both audio signals with zeros to a length of at least N = length(signal1) + length(signal2) – 1. This prevents circular convolution effects introduced by the FFT.

2. FFT Transformation: Compute the FFT of both zero-padded signals using the fft function.

3. Element-wise Multiplication: Multiply the resulting FFTs element-wise.

4. Inverse FFT: Perform an inverse FFT on the product using the ifft function. The resulting signal represents the cross-correlation function.

% Example: Cross-correlation of two audio signals
signal1 = audioread('audio1.wav');
signal2 = audioread('audio2.wav');

N = length(signal1) + length(signal2) - 1;
signal1_padded = [signal1; zeros(N - length(signal1), 1)];
signal2_padded = [signal2; zeros(N - length(signal2), 1)];

correlation = ifft(fft(signal1_padded) .* fft(signal2_padded));

[~, peak_index] = max(abs(correlation));
time_lag = peak_index - 1; % Time lag at maximum correlation

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Distinguishing Cross-Correlation from Convolution

While closely related, cross-correlation differs from convolution. Convolution involves flipping one signal before performing the cross-correlation. To obtain cross-correlation using FFTs, either time-reverse one signal before the FFT or take the complex conjugate of one signal’s FFT:

• Time Reversal: corr(a, b) = ifft(fft(a_padded) .* fft(flip(b_padded)))
• Complex Conjugate: corr(a, b) = ifft(fft(a_padded) .* conj(fft(b_padded)))

For autocorrelation (comparing a signal with itself), the complex conjugate method is more efficient, requiring only one FFT calculation.

Optimizing Performance and Accuracy

• Real FFTs: If the signals are real-valued, utilize rfft and irfft (real FFT and inverse real FFT) for improved efficiency.

• Optimized FFT Lengths: Pad signals to lengths optimized for your FFT implementation (e.g., powers of 2 for many hardware implementations). This can significantly speed up computation.

• Peak Interpolation: Refine the estimated time lag by using parabolic/quadratic interpolation on the correlation peak. This enhances accuracy beyond the sample resolution.

Conclusion

Cross-correlation implemented via FFTs offers an efficient method for comparing audio files in MATLAB. By understanding the underlying principles and employing optimization techniques, you can accurately determine the similarity and time alignment between audio signals. This approach proves valuable in various applications, including audio alignment, speech recognition, and music information retrieval.