Table of Contents
What is Spectral Analysis #
Spectral analysis is a powerful technique used in various fields to study and understand the frequency components of a signal or data. It involves analyzing the frequency domain representation of a signal to extract information about its constituent frequencies, amplitudes, and phases. Spectral analysis is widely used for several reasons:

Signal Characterization: Spectral analysis helps in understanding the fundamental components of a signal, which can be useful in identifying its sources, patterns, and characteristics. For example, in physics and engineering, itâ€™s used to analyze the vibrations of mechanical systems, electromagnetic signals, and sound waves.

Frequency Identification: Spectral analysis is used to determine the frequencies present in a signal. This is especially important when dealing with signals that are complex and composed of multiple frequencies, such as music, speech, or environmental data. By identifying the frequencies, researchers can gain insights into the underlying processes or sources.

Noise Removal: Spectral analysis aids in identifying and filtering out unwanted noise or interference in a signal. In applications like audio processing or communication systems, where noise can degrade the quality of the signal, spectral analysis helps design filters to remove specific frequency components.

Quality Control and Testing: In industries such as manufacturing and electronics, spectral analysis is used to perform quality control tests on products. By analyzing the frequency response of a product or material, manufacturers can identify defects or irregularities that might not be apparent in the timedomain signal.

Diagnostic Tool: In medical fields, spectral analysis is used to analyze various biological signals, such as electrocardiograms (ECGs), electroencephalograms (EEGs), and medical imaging data. These analyses help diagnose conditions by identifying abnormal frequency patterns or changes.

Environmental Monitoring: Spectral analysis is employed to study environmental data, such as seismic signals, weather patterns, and ocean currents. By analyzing the frequency components of these signals, researchers can gain insights into natural processes and phenomena.

Communication Systems: In telecommunications, spectral analysis is used for designing modulation schemes and understanding channel characteristics. It helps determine the bandwidth required for transmitting signals and optimizing data transmission rates.

Scientific Research: In fields like astronomy and astrophysics, spectral analysis of electromagnetic radiation allows researchers to study the composition and properties of celestial objects. This information provides valuable insights into the nature of these objects and the processes occurring within them.

Machine Condition Monitoring: In industrial settings, spectral analysis is used for monitoring the health of machines and equipment. By analyzing the vibrations and frequencies emitted by machines, engineers can detect potential faults and perform maintenance before more significant issues arise.
Digital Signal Processing #
DSP (Digital Signal Processing) refers to the manipulation and analysis of signals using digital techniques. It involves processing signals in the digital domain, typically using computers or specialized hardware, to perform tasks such as filtering, noise reduction, modulation, demodulation, compression, and spectral analysis. DSP is widely used in various fields, including telecommunications, audio and video processing, medical imaging, radar systems, and more.
FFT (Fast Fourier Transform) is a specific algorithm used in DSP for efficiently calculating the Discrete Fourier Transform (DFT) of a signal. The DFT is a mathematical operation that transforms a signal from the time domain to the frequency domain, allowing you to analyze its frequency components. The FFT is a faster and more efficient way to compute the DFT, especially for large datasets, compared to the standard direct calculation of the DFT.
One of the primary applications of DSP is spectral analysis, which involves analyzing the frequency components of a signal. FFT plays a crucial role in spectral analysis by quickly calculating the frequency content of a digital signal. By applying the FFT to a timedomain signal, you obtain its frequencydomain representation, which shows the amplitudes and phases of different frequency components. This information is essential for understanding the characteristics of the signal.
A spectrogram is a visual representation of the frequency content of a signal or sound as it varies over time. It is a twodimensional representation that displays how the energy or amplitude of different frequencies in a signal changes over successive time intervals. Spectrograms are commonly used in fields such as audio processing, speech analysis, music analysis, and various scientific and engineering applications.
A good library for DSP in JavaScript is here: https://github.com/corbanbrook/dsp.js/. This provides the basic tools for DSP inclduing FFT. Here is a sample code for generating spectogram from an Audio Buffer using the FFT class from the library:
const audioBuffer = await audioContext.decodeAudioData(arrayBuffer);
const fftSize = 2048; // FFT size (powers of 2 are often used for efficiency)
const fft = new FFT(fftSize);
const channelData = audioBuffer.getChannelData(0); // Use the first audio channel
const hopSize = fftSize / 4; // Hop size for overlapping windows
const spectrogram = [];
for (let i = 0; i + fftSize <= channelData.length; i += hopSize) {
const windowData = channelData.slice(i, i + fftSize);
fft.realTransform(windowData);
const magnitudes = new Array(fftSize / 2);
for (let j = 0; j < fftSize / 2; j++) {
magnitudes[j] = Math.sqrt(windowData[2 * j] ** 2 + windowData[2 * j + 1] ** 2);
}
spectrogram.push(magnitudes);
}
A complete code including the visualization of the spectrogram is available in the notebook: Spectral Analysis.