Wavelet transform has been used in signal processing fields such as noise reduction or data compression. The decomposed wavelet coefficients smaller than the given amplitude are suppressed using thresholding and finally the data is transformed to the original domain using inverse wavelet transform.
Motivation
Literature Survey
- Outcome of Literature Survey
- Major Challenges / Problems in FMCW Received signals
- More about FMCW Radar
- Characteristic features of FMCW Radar
Position accuracy is directly related to the accuracy of the timing device used and is therefore important. The distance measurement is performed by comparing the actual frequency of the received signal with a given reference (directly transmitted signal).
Contribution of Thesis
- Why DWT Based Denoising
- The main Aim of the project
- Project Stages and activities performed
- The Major Programming Tasks
The duration of the transmitted signal is much longer than the time required to measure the maximum installed range of the radar. The main work of the project is divided into two phases consisting of important activities listed below.
Thesis Organization
What are wavelets
What is wavelet Analysis
These features are often the most important part of the signal and Fourier analysis is not suitable for detecting them. Wavelet analysis is a new and promising set of tools and techniques for analyzing these signals.
Why wavelet Transform
A pathological condition can sometimes be diagnosed more easily if the frequency content of the signal is analyzed. The answer depends on the individual application and the nature of the signal. The upper graph in Figure 2.5 is the (half symmetrical) frequency spectrum of the signal in Figure 2.4.
Remember that in stationary signals, all frequency components that exist in the signal exist over the entire duration of the signal. Some of the most famous are EKG (electrical activity of the heart, electrocardiograph), EEG (electrical activity of the brain, electroencephalograph) and EMG (electrical activity of the muscles). When the time localization of the spectral components is needed, a transformation is needed that gives the TIME-FREQUENCY REPRESENTATION of the signal.
Wavelet transform is able to provide the time and frequency information simultaneously, providing a time-frequency representation of the signal. The width of this window must be equal to the segment of the signal. This window function is first placed at the very beginning of the signal. The result of this transformation is the FT of the first T/2 seconds of the signal.
Continuous Wavelet Transform
The problem with the STFT has something to do with the width of the window function used. To be technically correct, this width of the window function is known as the support of the window. The results of the CWT are many wavelet coefficients C, which are a function of scale and position.
Multiplying each coefficient by the appropriate scaled and shifted wavelet gives the constituent wavelets of the original signal. If we are talking about sinusoids, for example, the effect of the scale factor is very easy to see. The width of the window changes as the transform is calculated for each individual spectral component, which is probably the most significant property of the wavelet transform.
Where db2 is the name of the waveform we want to use for the analysis. You may notice that the actual lengths of the detail and approximation coefficient vectors are slightly more than half the length of the original signal. The other half of the story is how these components can be assembled back into the original signal without loss of information.
The downsampling of the signal components performed during the decomposition phase introduces a distortion called aliasing. We have seen that it is possible to reconstruct our original signal from the coefficients of approximations and details. Carrier frequency sweeping is done between the two frequencies and with the length of the frequency shift time, the maximum range can be varied.
From the above results, it is confirmed that even at low input SNR, the DWT method using db3 wavelet gives very good results by improving the SNR of the signal.
Discrete Wavelet Transform
Types of wavelets
Basics of FMCW Radar Altimeter
FMCW Radar Altimeter
Considered a much more accurate and therefore safer technology for applications other than satellites and radars, FMCW is generally cheaper and uses continuous transmission power. It uses the time it takes for a radio signal to reflect from the surface back to the aircraft to measure the distance above the ground.
Applications of FMCW Radar Altimeter
Range Formula
The decomposition and reconstruction filter coefficients for various waves under study such as dmey, coif1, sym2, & debouches db1, db2, db3, db4, db6 can be generated in MATLAB and used along with signal as input, i.e. in view of hardware complexity, the wave having less filter coefficients is finalized i.e. Mixed signal => 160KHz (ie X) pure sine wave (which is the desired signal after the mixed signal is denoised) + noise (5 KHz slope and its 2nd harmonic component).
From the above results it is confirmed that for low complexity architecture with less filter coefficients db3 wavelet is the best. FMCW radar signal modeling and denoising method using DWT with finalized best wavelet db3 in MATLAB. I/P SNR: Amplitudes of difference signal and Ramp and its harmonics are selected so that the SNR of mixed signal is for two cases.
Photo: Comparison of denoised outputs of MATLAB models for 3-phase HPF with fc=20K, and using DWT architecture with db3 wavelet. So VHDL architecture can be implemented with 80 samples and can be used for denoising FMCW Radar altimeter signal. The DWT with db3 wavelet-based denoising under low signal-to-noise ratio (SNR) conditions is very suitable for FMCW Radar Altimeter used in anti-radiation missiles, smart bombs, fighter jets, helicopters and other RF carrier-based defense applications and cellular communication, etc. . .
Considering signals with low SNR and low hardware complexity, among the various waveguides studied, i.e. dmey, coif, sym and debouches like db1, db2, db3, db4, db6, best found db3 wavelet (fewer number of filter coefficients for better results) which provides excellent performance due to different results. With a smaller number of sample data, the results are also satisfactory, which is very important for applications based on low-complexity hardware, in addition to the denoising of non-stationary signals for applications such as FMCW radar altimeter, where the denoising method is proven to give very good results.
Denoising using various wavelets
MATLAB Model for denoising
For the turn to be well defined, the signal must be extended (underlined) at both ends, e.g. Since the carriers of communication systems have a basic sine cosine wave and noise, if it is of a similar nature and larger amplitude, it will be difficult to separate the signal and any real signal can be represented as a combination of sine/cosine waves. Most of the noise signals we observe in practice are limited to a known frequency range, so the basic input mixed signals are two sine waves of 160 Hz (carrier or message) and 10 Hz (noise) and are chosen to maintain a view of microwave communication , in which the noise will be on the lower side of the operating frequency range.
Note that due to successive subsampling by 2, the signal length must be a power of 2, or at least a multiple of the power of 2, for the DWT scheme to be efficient. Noisy I/p signal to DWT based noise reduction architecture consists of the following for MATLAB db3 wavelet based noise reduction model. The sampling rate for MATLAB is generally 6 to 20 times, so it is selected as 1280 kHz and the number of selected samples for case1 is 1280, case2 is 80 and SNR, correlation, regression and R-squared parameters are compared with filtered o/p of 3-stage Butterworth HPF with fc=20KHz.
Input mixed / Noisy signal frequency spectrum with 5KHz, 10KHz, WGN(randn), difference signal of 160KHz, 1280 samples, with fs=1280KHz. Image: Shows amplitudes of noise alone in w0, w1, w2 detailed coefficients in MATLAB to determine hard threshold level. VHDL coding: Xilinx ISE Design suite 14.3 tool is used for FPGA as target device, VHDL structural modules are developed to implement the hardware architecture of db3 Wavelet consisting of 3-stage analysis and synthesis banks by designing high-pass and low-pass filters (decomposition .. amp; Reconstruction) and component instantiation is done in 3 steps.
With a smaller number of sample data, the results are also found satisfactory, which is very important for low-complexity hardware-based application, apart from denoising non-. Out of dmey, coif1, sym2, & debouches db1, db2, db3, db4, db6 wavelets, db3 delivers very good results for damping target frequencies while excluding unwanted harmonic of the ramp frequency and in view of low complexity vs.
MATLAB Code of important functionality
Signal Model & its frequency spectrum
Y=> signal data denoised and reconstructed using DWT or HP filtering The parameter results obtained using MATLAB are shown in Table-I. Noise: 5 KHz + 10 KHz (2nd Harmonic) ramp signal both 10 times the amplitude of the difference signal and White Gaussian Noise. The results of FMCW DWT-db3 based model of MATLAB & VHDL o/p have been verified and found satisfactory.
DWT Denoising results of various wavelets
DWT Denoising performance parameters comparison
Setup & Signal for denoising
Specifications for Denoising
Denoising is performed by hard thresholding the detail coefficients to specifically remove WGN and setting the level 3 approximation coefficients to zero to remove the 5KHz and 10KHz components along with the white noise. The module is designed for reading files and passing data as i/p to decomposition and also for writing to a txt file. Four points are used in the code to reduce the hardware complexity, a) the "for" loops are implemented using the counter method, b) the multiplier is implemented using a shifter and add/subtract in a combinational logic subroutine, c) taking only 80 input samples, d ) db3 has less no.
Image: Synthesized design: Denoising architecture of db3, VHDL Code synthesized in Xilinx ISE Design compiler (above), resources used from vertex-7 target FPGA (below fig). It outperforms the HPF approach even under low SNR RF inputs, resulting in improved SNR and other parameters.
Signal Modelling using Best wavelet
Denoising procedure of FMCW Signal
Consolidated Results
H/W Architecture Design using VHDL for FPGA Target
Applications
Conclusion
