Comparing MFCCs and Spectrograms as Input Features

Mel Frequency Cepstral Coefficients (MFCCs) and log-mel spectrograms are both input features for speech recognition models. A practical question is which one to choose for a given model. While MFCCs were the undisputed standard for decades, the rise of deep learning has shifted the consensus. For most modern ASR systems, log-mel spectrograms are the preferred input feature. An examination of their trade-offs clarifies the reasons for this preference.

The fundamental difference lies in the final step of the MFCC calculation: the Discrete Cosine Transform (DCT). This step is designed to de-correlate the filter bank energies and compress the most significant information into the first few coefficients.

Information, Compression, and Model Architecture

The DCT in the MFCC pipeline is a form of lossy compression. It discards some of the finer-grained information about the spectral structure in exchange for a compact, de-correlated representation. This was highly advantageous for classic machine learning models like Gaussian Mixture Models (GMMs), which perform better when input features are not correlated with each other. By concentrating the most important signal information into a small number of coefficients, MFCCs provided an efficient and effective input for these earlier systems.

However, deep neural networks, particularly Convolutional Neural Networks (CNNs), operate differently. They are exceptionally good at learning relevant patterns from high-dimensional, correlated data. For a CNN, a log-mel spectrogram is analogous to a single-channel image, where the horizontal axis is time and the vertical axis is frequency.

• Log-Mel Spectrograms retain the correlation between adjacent frequency bins. A CNN can apply its convolutional filters to learn to detect shapes and patterns in this "image," such as formants (the dark bands in a spectrogram) and their movement over time. This spatial relationship between frequencies is valuable information that a CNN is designed to exploit.

• MFCCs, by applying the DCT, effectively shuffle this spectral information. The first coefficient ($c_0$) represents overall energy, the next represents the broad spectral slope, and later coefficients represent finer details. The direct "spatial" relationship between adjacent Mel filters is lost. While a neural network can still learn from MFCCs, it cannot use its convolutional structure to learn from local frequency patterns in the same intuitive way it can with a spectrogram.

The diagram below illustrates how the MFCC pipeline includes an extra DCT step that the log-mel spectrogram pipeline omits.

The critical difference is the DCT step. Log-mel spectrograms provide the direct output of the Mel filterbank, preserving local spectral structure, whereas MFCCs compress and de-correlate this output.

Dimensionality and Computational Cost

A typical MFCC feature vector might have 13, 20, or 40 dimensions. In contrast, a log-mel spectrogram commonly uses 80 or 128 Mel bins, resulting in a feature vector with 80 or 128 dimensions per time step.

In the past, the lower dimensionality of MFCCs was a significant advantage. It reduced memory requirements and computational load, which were important constraints. Today, with GPU acceleration, deep learning models can easily handle the higher dimensionality of log-mel spectrograms. The additional information contained in these larger feature vectors often leads to better model performance, justifying the increased computational cost.

Summary of Main Differences

The choice between these two feature types involves a trade-off between information retention and dimensionality. The following table summarizes the main points of comparison.

Characteristic	MFCCs	Log-Mel Spectrograms
Final Step	Discrete Cosine Transform (DCT)	Logarithm of Mel filterbank energies
Information	Compressed, de-correlated coefficients	Rich, correlated spectral structure
Dimensionality	Low (typically 13-40)	Higher (typically 64-128)
Primary Use	Legacy GMM-HMM systems, resource-constrained applications	Modern CNN, RNN, and Transformer-based models
Core Idea	Provide a compact, efficient representation for simpler models	Provide a rich, image-like representation for powerful models

Recommendation for Modern ASR

For the models we will be building in this course, such as LSTMs, Transformers, and Conformers, log-mel spectrograms are the recommended input feature. These architectures have the capacity to process high-dimensional inputs and are specifically designed to find complex, hierarchical patterns in data. By feeding them log-mel spectrograms, you allow the model to learn the most relevant acoustic features directly from a rich representation of the audio, rather than relying on the hand-engineered compression of MFCCs.

While understanding MFCCs is important for appreciating the history of ASR and for certain niche applications, log-mel spectrograms are the feature of choice for building high-performance, contemporary speech recognition systems.