1. Nonlinear and Time Variant Signal Processing R.C. Maher ECEN4002/5002 DSP Laboratory Spring 2002

2. ECEN4002 Spring 2002Nonlinear Signal Processing R. C. Maher2 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

3. ECEN4002 Spring 2002Nonlinear Signal Processing R. C. Maher3 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

4. ECEN4002 Spring 2002Nonlinear Signal Processing R. C. Maher4 Gain Control (cont.) Gain control framework 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 Level Detector Gain Controller x[n] c[n] y[n]=G[n] x[n] G[n]

5. ECEN4002 Spring 2002Nonlinear Signal Processing R. C. Maher5 Gain Control (cont.) Simple envelope detectors: Can also use |x[n]| 2 if( |x[n]| > c[n-1] ) c[n]=  c[n] else c[n]=  c[n] (where  >1 and  <1)

6. ECEN4002 Spring 2002Nonlinear Signal Processing R. C. Maher6 Gain Control (cont.) Gain controller function –Compressor (  <1) e.g.,  =0.25 –Expander (  >1) e.g.,  =4

7. ECEN4002 Spring 2002Nonlinear Signal Processing R. C. Maher7 Gain Curves Input, dB Output, dB  <1  =1  <<1 (limiter) threshold  =1  >1  >>1 (gate) Input, dB threshold Output, dB CompressorExpander

8. ECEN4002 Spring 2002Nonlinear Signal Processing R. C. Maher8 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

9. ECEN4002 Spring 2002Nonlinear Signal Processing R. C. Maher9 Waveshaping Apply a nonlinear “lookup” function Input Output

10. ECEN4002 Spring 2002Nonlinear Signal Processing R. C. Maher10 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

11. ECEN4002 Spring 2002Nonlinear Signal Processing R. C. Maher11 Basic Adaptive Filter Structure Adaptive Process (digital filter with varying coefficients) x[n] y[n] d[n] e[n] + - Input signal “Desired” or “reference” signal Error signal Filter response signal

12. ECEN4002 Spring 2002Nonlinear Signal Processing R. C. Maher12 Adaptive Interference Canceling Adaptive Process (digital filter with varying coefficients)  c [n] y[n]   [n] + - Correlated Noise Signal + Noise d[n]=s[n]+  [n] (s[n], e[n] uncorrelated) “Error” signal e[n]  s[n] Filter response signal Adaptive process tries to minimize E{e 2 [n]}