Wavelet Transform and why people used it to denoise 1min chart and its comparison with Fourier Transform

📈 What is a Wavelet Transform in trading research?

Wavelet Transform is a mathematical tool that breaks down a price series into different frequency components — but localized in time.

• Think of it like a microscope for charts:
  it helps you zoom into different time scales at different moments.

• Unlike a Fourier Transform (which gives you only overall cycle/frequency info but loses time info),
  Wavelet Transform keeps both:
  — what frequencies exist
  — and when they occur.

🧠 In simple words:

🛠️ In trading research, people use Wavelet Transforms to:

• Detect trend shifts (because different wavelet levels show trends vs noise separately)

• Find cyclical patterns that aren't constant (adaptive cycles)

• Denoise price data (removing useless small noise while keeping important swings)

• Study volatility clustering (volatility isn't constant over time)

• Create better technical indicators (wavelet-smoothed moving averages, wavelet-based MACD, etc.)

• Improve forecasting models (input clean data into Machine Learning models)

🔥 Example use case:

You have messy 1-minute Bitcoin prices.
You apply a Wavelet Decomposition, and split it into:

• Low-frequency component → main market trend

• High-frequency components → noise, mean-reversion, short-term spikes

Then you can:

• Trade the trend using low-frequency wavelet

• Mean-revert scalp using high-frequency spikes

• Filter out noise when building models

⚡ Types of Wavelet Transforms traders explore:

• Discrete Wavelet Transform (DWT)
  → breaks the signal into fixed layers/scales

• Continuous Wavelet Transform (CWT)
  → more detailed but computationally heavier

• Wavelet Packet Transform (WPT)
  → deeper decomposition (both approximation and detail levels are split)

Mostly, DWT is practical for trading because it's fast enough.

📚 Good references if you want to dive deeper:

• "Wavelet Applications in Financial Engineering" (academic papers)

• People like Tucker Balch (early ML trading research) used wavelets in their strategies.

• Some hedge funds have used wavelet preprocessing before feeding prices into neural networks.