Signal Processing Notebook

This project contains a Jupyter notebook, Signal_Processing.ipynb, that demonstrates core audio signal-processing techniques on a speech waveform using librosa, numpy, and matplotlib.

Notebook Overview

The notebook analyzes an audio file loaded with:

y, sr = librosa.load('./hello.wav')

Where:

• y is the audio waveform amplitude over time
• sr is the sampling rate of the audio

The notebook then extracts and visualizes several important speech/audio features.

Concepts Covered In The Code

1. Waveform / Signal Visualization

The first plot shows the raw audio signal:

plt.plot(y)

This helps us inspect how amplitude changes across time. It is the most direct time-domain representation of the sound.

2. Fourier Transform and Frequency Spectrum

The notebook computes a short-time Fourier transform using:

ft = np.abs(librosa.stft(y[:n_fft], hop_length=n_fft+1))

This is based on the Fourier Transform, which converts a signal from the time domain into the frequency domain.

Why it matters:

• It reveals which frequencies are present in the audio
• It helps identify pitch-related and timbre-related patterns
• It is the foundation for more advanced features like spectrograms, mel spectrograms, and MFCCs

The plotted spectrum shows frequency content and magnitude for a slice of the signal.

3. Spectrogram

The spectrogram is computed from the STFT:

spec = np.abs(librosa.stft(y, hop_length=512))
spec = librosa.amplitude_to_db(spec, ref=np.max)

A spectrogram shows:

• time on the x-axis
• frequency on the y-axis
• intensity/amplitude as color

Why it matters:

• It shows how frequency content changes over time
• It is one of the most common visual tools in speech and audio analysis
• It helps detect voiced regions, harmonics, and transient events

4. Mel Spectrogram

The notebook also computes a mel spectrogram:

mel_spect = librosa.feature.melspectrogram(
    y=y,
    sr=sr,
    n_fft=2048,
    hop_length=1024
)

A mel spectrogram maps frequencies onto the mel scale, which better matches human auditory perception.

Why it matters:

• Human hearing is more sensitive to lower-frequency changes than higher-frequency changes
• Mel-scaled features are widely used in speech recognition and speaker analysis
• It provides a perceptually meaningful version of the standard spectrogram

5. MFCCs (Mel-Frequency Cepstral Coefficients)

The notebook extracts 13 MFCC features:

mfccs = librosa.feature.mfcc(
    y=y,
    sr=sr,
    n_mfcc=13
)

MFCCs are compact audio features derived from the mel spectrogram and a cepstral transform.

Why they matter:

• They capture the spectral shape of speech
• They are standard features in speech recognition, speaker identification, and emotion analysis
• They reduce dimensionality while preserving useful information

The notebook includes:

• an MFCC heatmap over time
• individual plots for each of the 13 MFCC coefficients

This helps show how speech characteristics vary frame by frame.

6. Zero-Crossing Rate (ZCR)

The code computes:

zcr = librosa.feature.zero_crossing_rate(y)

Zero-crossing rate measures how often the waveform changes sign.

Why it matters:

• Noisy or unvoiced sounds often have a higher ZCR
• Voiced sounds usually have a lower ZCR
• It helps distinguish speech, music, and noise in basic audio classification tasks

7. RMS Energy

The notebook computes energy with:

rms = librosa.feature.rms(y=y)

RMS energy measures the signal strength or loudness over short frames.

Why it matters:

• It helps locate active speech regions
• It can separate silence from non-silence
• It is useful in segmentation, voice activity detection, and emphasis analysis

In the notebook, the energy plot shows how strong the signal is over time.

8. Pitch Detection

Pitch is estimated with:

f0, voiced_flag, voiced_probs = librosa.pyin(
    y,
    fmin=50,
    fmax=300
)

This estimates the fundamental frequency (f0) of the signal.

Why pitch detection matters:

• It helps analyze intonation and speaking patterns
• It is useful for speaker analysis
• It can support emotion detection
• It is also useful in singing voice analysis

The plot shows how the detected pitch changes over time in Hz.

9. Voice Activity Detection (VAD)

The notebook performs simple voice activity detection using:

intervals = librosa.effects.split(y, top_db=20)

This returns intervals where the signal is above a threshold relative to silence.

Why it matters:

• It helps isolate spoken segments
• It removes silent regions before feature extraction
• It improves efficiency in downstream speech-processing tasks

Step-By-Step Flow Of The Notebook

The notebook follows this progression:

1. Load audio with librosa.load
2. Plot the waveform in the time domain
3. Compute a Fourier-based spectrum using STFT
4. Visualize a spectrogram
5. Visualize a mel spectrogram
6. Extract and display MFCC features
7. Compute zero-crossing rate
8. Compute RMS energy
9. Detect pitch using librosa.pyin
10. Detect voiced/non-silent intervals

Libraries Used

• librosa for audio loading, transformation, and feature extraction
• numpy for numerical operations
• matplotlib for plotting

Key Learning Outcome

This notebook is a compact introduction to practical speech and audio analysis. It demonstrates both:

• time-domain analysis: waveform, zero-crossing rate, RMS energy
• frequency-domain analysis: Fourier transform, spectrum, spectrogram, mel spectrogram, MFCCs, pitch

Together, these features form the foundation of many applications in:

• speech recognition
• speaker identification
• audio classification
• music information retrieval
• voice activity detection

File In This Project

• Signal_Processing.ipynb: the main notebook containing the analysis and visualizations
• README.md: project explanation and concept summary