In this module, we will use concepts of signals and systems to model the [[human speech production mechanism]]. The [[source-filter model]] represents this process by combining a sound source with a linear acoustic filter. ## System Modelling - [[source-filter model]] - [[microphone]] - [[system]] - [[causal system]] ## Linear Time-Invariant (LTI) Systems - [[discrete-time LTI system]] - [[discrete-time unit impulse]] - [[impulse response]] - [[difference equation]] ## Transfer Function - [[transfer function]] - [[frequency response]] - [[z-transform]] - [[time shifting property of the z-transform]] - [[convolution property of the z-transform]] - [[rational transfer function]] ## Filtering - [[infinite impulse response (IIR) system]] - [[finite impulse response (FIR) system]] - [[ideal low-pass filter]] - [[window function]] - [[spectral features of window functions]] ## Acoustical Model - [[formant]] - [[continuous-time resonator]] - [[second-order all-pole IIR system]] - [[cascade combination]] ## Linear Prediction - [[linear prediction]] - [[residue]] - [[linear prediction coefficients]] - [[minimizing the energy of the residue]] - [[solving LPC equations]] - [[autocorrelation method]] ## Problems - [[ztran-o01 two real poles]] - [[syst-o01 first order FIR]] - [[syst-o02 first order IIR]] ## Optional Readings ### [[Huang 2001]], Chapter 5: Digital Signal Processing, [pdf](https://fenix.tecnico.ulisboa.pt/downloadFile/1970943312400268/SLP-chap5.pdf) - 5.1 Digital Signals and Systems - 5.2 Continuous-Frequency Transforms