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Nonlinear and Time Variant Signal Processing

Nonlinear and Time Variant Signal Processing. R.C. Maher ECEN4002/5002 DSP Laboratory Spring 2002. Introduction. Most of the signal processing algorithms considered in this course are linear and time invariant (LTI).

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Nonlinear and Time Variant Signal Processing

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

  2. 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 Nonlinear Signal Processing R. C. Maher

  3. 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 Nonlinear Signal Processing R. C. Maher

  4. 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 x[n] y[n]=G[n] • x[n] Level Detector Gain Controller c[n] G[n] Nonlinear Signal Processing R. C. Maher

  5. 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 a>1 and b<1) Nonlinear Signal Processing R. C. Maher

  6. Gain Control (cont.) • Gain controller function • Compressor (r<1) e.g., r=0.25 • Expander (r>1) e.g., r=4 Nonlinear Signal Processing R. C. Maher

  7. Gain Curves Compressor Expander Output, dB Output, dB r=1 r<1 r<<1 (limiter) r>1 r=1 r>>1 (gate) threshold Input, dB threshold Input, dB Nonlinear Signal Processing R. C. Maher

  8. 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 Nonlinear Signal Processing R. C. Maher

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

  10. 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 Nonlinear Signal Processing R. C. Maher

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

  12. Adaptive Interference Canceling Signal + Noise d[n]=s[n]+e[n] (s[n], e[n] uncorrelated) Adaptive process tries to minimize E{e2[n]} Filter response signal Correlated Noise + Adaptive Process (digital filter with varying coefficients) - ec[n] y[n] e[n] “Error” signal e[n]  s[n] Nonlinear Signal Processing R. C. Maher

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