Nonlinear and Time Variant Signal Processing

1 / 12

# Nonlinear and Time Variant Signal Processing - PowerPoint PPT Presentation

Nonlinear and Time Variant Signal Processing. R.C. Maher ECEN4002/5002 DSP Laboratory Spring 2003. Introduction. Most of the signal processing algorithms considered in this course are linear and time invariant (LTI).

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Nonlinear and Time Variant Signal Processing' - breena

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Nonlinear and Time VariantSignal Processing

R.C. Maher

ECEN4002/5002 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

Nonlinear Signal Processing R. C. Maher

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

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

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

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

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

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

Waveshaping
• Apply a nonlinear “lookup” function

Output

Input

Nonlinear Signal Processing R. C. Maher

• 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

“Desired” or “reference” signal

d[n]

Filter response signal

Input signal

+

(digital filter with varying coefficients)

-

x[n]

y[n]

e[n]

Error signal

Nonlinear Signal Processing R. C. Maher

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

+

(digital filter with varying coefficients)

-

ec[n]

y[n] e[n]

“Error” signal

e[n]  s[n]

Nonlinear Signal Processing R. C. Maher