What's Next?

What's Next

You have built the core algorithms of digital signal processing from scratch. Here are natural next steps:

  • Fast Fourier Transform (FFT) — The DFT you implemented runs in O(N2)O(N^2). The Cooley-Tukey FFT reduces this to O(Nlog⁡N)O(N \log N), making real-time processing possible
  • Filter Design — Kaiser windows, Parks-McClellan equiripple FIR, and Butterworth/Chebyshev IIR filters designed in the frequency domain
  • Audio DSP — Pitch shifting, time stretching, reverb, vocoder, and audio compression (MP3/AAC)
  • Communications — OFDM, QAM modulation, channel equalization, and spread-spectrum techniques
  • Machine Learning — Mel spectrograms, MFCCs, and convolutional networks applied to audio and time series

Further Reading

  • Discrete-Time Signal Processing by Oppenheim & Schafer — The definitive graduate text on DSP
  • The Scientist and Engineer's Guide to Digital Signal Processing by Steven Smith — Free online, very approachable
  • Understanding Digital Signal Processing by Lyons — Practical intuition-first approach, highly recommended
  • DSPRelated.com — Articles, tutorials, and a community for DSP practitioners
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