即時之八度音程頻帶數位訊號分析與合成

Abstract

本論文利用數位訊號處理晶片，在同一系統中，以48kHz、24kHz、12kHz、…等2的除頻為採樣頻率，構成八度音程濾波器組的多率系統架構。從分析方向去考慮，把八度音程濾波器組設計成特定數位頻帶的帶通濾波器，探討在窄頻寬之下的帶通濾波器之量化誤差情形以及研究即時計算訊號能量的方法，實作即時八度音程音頻頻譜分析儀，並驗證其結果和精準度；而將系統架構從合成方向去考慮，把八度音程濾波器組設計成八度音程內十二個主音的單頻產生器，探討在整個系統中泛音的組合和遞減振幅的處理，以鋼琴聲音特色為目標，實作音樂合成器，將其結果與真實音樂比較。

In this thesis, there is a structure of octave filter banks generated by sampling frequencies with 48kHz, 24kHz, 12kHz, …, etc. For analysis mode, a band-pass filter with specified frequency is designed in each filter bank . The system is implemented as a digital audio spectrum analyzer. The quantized error of narrow bandwidth BPF, the algorithm of measure signal power in real time, and the accuracy of analyzer are discussed. For synthesis mode, moreover, twelve sin-wave generators with octave frequencies are designed in each filter bank. The system is implemented as a music synthesizer. The synthesized sound including its fundamental and harmonic frequencies and its damped envelope is approached to the style of piano. Their way and effect are discussed.