APPLICATION OF A WAVELET-BASED RECEIVER FOR THE COHERENT DETECTION OF FSK SIGNALS Dr. Robert Barsanti, Charles Lehman SSST March 2008, University of New Orleans. Overview. Introduction FSK Signals Wavelet Domain Filtering Wavelet Domain Correlation Receiver Simulations and Results Summary.
APPLICATION OF A WAVELET-BASED RECEIVER FOR THE COHERENT DETECTION OF FSK SIGNALS Dr. Robert Barsanti, Charles LehmanSSST March 2008, University of New Orleans
In binary frequency shift keying modulation, the binary information is transmitted using signals at two different frequencies. These signals can be represented as
The symbol A represents the signal amplitude, and T is the bit duration. It is easy to show that the bit energy is given by
This figure shows an example of a binary FSK signal. Notice that the transmitted signal case a constant envelope and abrupt phase changes at the beginning of each signal interval.
Sample at t = T
THREE STEP DENOISING
1. PERFORM DWT
2. THRESHOLD COEFFICIENTS
3. PERFORM INVERSE DWT
DWT of a noise free FSK signal.
DWT of noisy FSK signal.
Some S8 Symmlets at Various Scales and Locations
time index k
1. Can be defined by a wavelet function (Morlet & Mexican hat)
2. Can be defined by an FIR Filter Function (Haar, D4, S8)
Pair of Half Band Quadrature Mirror Filters (QMF)
Two Channel Perfect Reconstruction QMF Bank
Analysis + Synthesis = LTI system
J = 4
J = 3
J = 2
J = 1
Let the DWT coefficient be a series of noisy observations y(n)
then the following parameter estimation problem exists:
y(n) = f(n) +s z(n), n = 1,2,….
z ~N(0,1) and s = noise std.
s is estimated from the data by analysis of the coefficients
at the lowest scale.
s = E/0.6475 where E is the absolute median deviation
* Hard Thresholding (keep or kill)
* Soft Thresholding (reduce all by Threshold)
The Threshold Value is determined as a multiple
of the noise standard deviation,
eg., T = ms where typically 2< m <5