Question 1

What are wavelets?

Accepted Answer

Wavelets are mathematical functions that decompose signals into different frequency components while preserving time information. Unlike Fourier transforms which only tell you what frequencies exist, wavelets tell you both what frequencies exist and when they occur. This makes them ideal for analyzing non-stationary signals like financial time series, audio, and sensor data.

Question 2

What is the difference between VectorWave and IronWave?

Accepted Answer

VectorWave is our Java wavelet library (Java 25+) with SIMD acceleration via the Vector API; ideal for JVM-based applications and enterprise systems. IronWave is our Rust wavelet library optimized for ultra-low-latency applications with sub-microsecond performance; perfect for high-frequency trading and embedded systems. Both provide the same core wavelet transforms (DWT, MODWT, SWT, CWT) with production-grade reliability.

Question 3

When should I use MODWT instead of DWT?

Accepted Answer

Use MODWT (Maximal Overlap Discrete Wavelet Transform) when you need shift-invariance, which is critical for financial time series analysis, volatility estimation, and any application where the alignment of features matters. MODWT works with any signal length and provides better statistical properties. Use DWT when you need compression or the most compact representation, as it is critically sampled with no redundancy.

Question 4

Which wavelet should I use for financial analysis?

Accepted Answer

For financial time series, Daubechies Db4 with MODWT is the most common choice, offering a good balance of time and frequency localization. Use Haar for jump detection and microstructure analysis. For smoother trend analysis, consider Symlets (Sym4) which have better phase properties. For volatility clustering detection, Morlet wavelets with CWT provide rich time-frequency information.

Question 5

How do I get started with wavelet analysis?

Accepted Answer

Start with our Quick Start guides: for Java applications, see the VectorWave Quick Start at https://docs.morphiqlabs.com/docs/vectorwave/getting-started/quick-start. For Rust applications, see the IronWave Quick Start at https://docs.morphiqlabs.com/docs/ironwave/getting-started/quick-start. Both guides walk you through installation, basic transforms, and common use cases like denoising and multi-scale analysis.

Question 6

What is wavelet denoising and how does it work?

Accepted Answer

Wavelet denoising removes noise from signals while preserving important features like edges and trends. It works by transforming the signal into wavelet coefficients, applying a threshold to remove small coefficients (which typically represent noise), and reconstructing the signal. Common thresholding methods include Universal, SURE, Minimax, and BayesShrink. VectorWave and IronWave both provide built-in denoising functions with multiple threshold options.