Nonlinear and Time Variant Signal Processing R C

Nonlinear and Time Variant Signal Processing R. C. Maher ECEN 4002/5002 DSP Laboratory Spring 2003

Introduction • Most of the signal processing algorithms considered in this course are linear and time invariant (LTI). • One nonlinear example: the “noise gate” considered in Lab #6: output depends on signal amplitude • Other important nonlinear systems: modulation (AM, PM, FM), automatic gain control, pulse shaping, and adaptive filtering ECEN 4002 Spring 2003 Nonlinear Signal Processing R. C. Maher 2

Automatic Gain Control • Gain control circuits include – Compressor: decrease dynamic range by reducing gain for high amplitude signals • Limiter: extreme form of compressor – Expander: increase dynamic range by reducing gain for low amplitude signals • Gate: extreme form of expander ECEN 4002 Spring 2003 Nonlinear Signal Processing R. C. Maher 3

Gain Control (cont. ) • Gain control framework x[n] y[n]=G[n] • x[n] Level Detector Gain c[n] Controller G[n] • c[n] can be |x[n]|, envelope of x[n], RMS value of x[n], etc. • Level detector typically has attack and release time constants ECEN 4002 Spring 2003 Nonlinear Signal Processing R. C. Maher 4

Gain Control (cont. ) • Simple envelope detectors: if( |x[n]| > c[n-1] ) c[n]= c[n] else c[n]= c[n] (where >1 and <1) • Can also use |x[n]|2 ECEN 4002 Spring 2003 Nonlinear Signal Processing R. C. Maher 5

Gain Control (cont. ) • Gain controller function – Compressor (r<1) e. g. , r=0. 25 – Expander (r>1) e. g. , r=4 ECEN 4002 Spring 2003 Nonlinear Signal Processing R. C. Maher 6

Gain Curves Compressor Expander Output, d. B r=1 r<<1 (limiter) r=1 threshold ECEN 4002 Spring 2003 Input, d. B Nonlinear Signal Processing r>1 r>>1 (gate) threshold R. C. Maher Input, d. B 7

Communications: AM and FM • Generate AM and FM communication signals using synthesis techniques discussed before • Also, perform demodulation using a product detector (quadrature) Lowpass Filter Oscillator ECEN 4002 Spring 2003 Nonlinear Signal Processing R. C. Maher 8

Waveshaping • Apply a nonlinear “lookup” function Output Input ECEN 4002 Spring 2003 Nonlinear Signal Processing R. C. Maher 9

Adaptive Filters • Basic adaptive filter is a linear system with time-varying coefficients • Coefficients (filter ‘weights’) are adjusted repeatedly at regular intervals according to an adaptive algorithm • Adaptive algorithm is generally designed to minimize the discrepancy (error) between the filter output and a reference signal ECEN 4002 Spring 2003 Nonlinear Signal Processing R. C. Maher 10

Basic Adaptive Filter Structure “Desired” or “reference” signal Input signal x[n] Adaptive Process (digital filter with varying coefficients) Filter response signal d[n] - + y[n] e[n] Error signal ECEN 4002 Spring 2003 Nonlinear Signal Processing R. C. Maher 11

Adaptive Interference Canceling Signal + Noise Adaptive process tries to minimize E{e 2[n]} Correlated Noise ec[n] Adaptive Process (digital filter with varying coefficients) d[n]=s[n]+e[n] (s[n], e[n] uncorrelated) Filter response signal - + y[n] e[n] “Error” signal e[n] s[n] ECEN 4002 Spring 2003 Nonlinear Signal Processing R. C. Maher 12