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Introduction to Nonlinear and Time-Variant Signal Processing Techniques

This course material explores nonlinear and time-variant signal processing within the DSP Laboratory framework. Unlike linear and time-invariant systems, nonlinear systems like noise gates, modulation techniques (AM, PM, FM), and adaptive filtering process signals based on their characteristics. Gain control mechanisms—such as compressors, limiters, and expanders—are examined in-depth, detailing how they manage dynamic range. Additionally, it covers adaptive filters, which adjust to minimize discrepancies between output and reference signals, enhancing noise cancellation.

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Introduction to Nonlinear and Time-Variant Signal Processing Techniques

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  1. Nonlinear and Time VariantSignal Processing R.C. Maher ECEN4002/5002 DSP Laboratory Spring 2003

  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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