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Audio AI Researcher & Developer
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Module 2
Spectral Analysis of Audio Signals
1
Introduction to the Continuous Fourier Transform
Define the Continuous Fourier Transform and its role in decomposing signals into frequency components.
2
Deriving the Discrete Fourier Transform
Derive the Discrete Fourier Transform (DFT) as the discrete-time counterpart of the Fourier Transform.
3
DFT Implementation and Spectral Interpretation
Implement a DFT from scratch and interpret its magnitude and phase spectra outputs.
4
FFT vs. DFT: A Computational Efficiency Showdown
Explain the computational efficiency of the Fast Fourier Transform (FFT) algorithm compared to a naive DFT.
5
STFT: Derivation and Windowing Trade-offs
Derive the Short-Time Fourier Transform (STFT) and explain the trade-offs of different windowing functions.
6
Spectrogram Analysis with Python
Compute and visualize spectrograms from audio signals using Python libraries like librosa or torchaudio.
7
Mel Scale and Spectrogram Conversion
Explain the psychoacoustic basis of the mel scale and convert linear spectrograms to mel-spectrograms.
8
MFCCs from Mel-Spectrograms
Derive Mel-Frequency Cepstral Coefficients (MFCCs) from mel-spectrograms using the Discrete Cosine Transform (DCT).
Previous module
Foundations of Digital Audio
Next module
Audio Data Augmentation and Pipelines