Spectrum Estimation

SPECTRUM ESTIMATION

Tudor AVRAM Madalina MOISAUniversitatea Tehnică din Cluj-Napoca, Bulevardul 21 Decembrie 1989 128-130, Cluj-Napoca

Tel. 0264-401223 Fax: 0264-591689 e-mail: [email protected]

Abstract: The goal of this project is to present the DSK6713 and its uses in spectrum estimation. The spectrum is estimated using three methods, The Burg method, The modified covariance method and the periodogram method and to compare the results with a reference

spectrum.

1. IntroductionIn this chapter we will use the DSK6713 for

spectrum estimation. Three estimation methods will

be implemented:

i. Periodogram

ii. Burg

iii. M-Cov

1.1. Periodogram

The Periodogram block computes a nonparametric

estimate of the spectrum. The block averages the

squared magnitude of the FFT computed over

windowed sections of the input and normalizes the

spectral average by the square of the sum of the

window samples.

1.2.The Modified Covariance Method

The Modified Covariance Method block estimates

the power spectral density (PSD) of the input using

the modified covariance method. This method fits

an autoregressive (AR) model to the signal by

minimizing the forward and backward prediction

errors in the least squares sense. The order of the

all-pole model is the value specified by the

Estimation order parameter. To guarantee a valid

output, you must set the Estimation order parameter

to be less than or equal to two thirds the input

vector length. The spectrum is computed from the

FFT of the estimated AR model parameters.

1.3.Burg Method

The Burg Method block estimates the power

spectral density (PSD) of the input frame using the

Burg method. This method fits an autoregressive

(AR) model to the signal by minimizing (least

squares) the forward and backward prediction

errors while constraining the AR parameters to

satisfy the Levinson-Durbin recursion.

2. Simulation

2.1.The Environment Figure 1 shows the data flow for the Estimation

simulation. The input signal for the estimator is an

AR process generated by feeding an all-poles filter

with white noise. The AR coefficients generate the

reference spectrum to be compared against the

estimated one.

Figure 1- Spectrum Estimation Simulation

2.2.The Procedure1. Create a new model in Simulink® and name

it: “SpectrumEstimation.mdl”

2. Open the Simulink library browser and add a

random source object:

Figure 2- The Random Source Object

3. Double click on the random source object,

and configure its parameters to fit the white

noise characteristics we want to achieve:

Figure 3- The Random Source Object Configuration

4. Add a new digital filter to the model:

Figure 4- The Digital Filter Block

5. Double-click on the filter and fill in the

following parameters1

Figure 5- The Digital Filter Block Parameters

6. Add the 3 estimators: Periodogram, Burg and

Modified-Covariance to your model:

Figure 6- The Burg Method Block

7. Configure the FFT length of the three models to 128:

1 The Auto-Regressive process is represented by an

all-pole IIR filter. The AR coefficients are the ones in

the “Denominator coefficients” label.

Figure 7- FFT Length Configuration for Spectrum Estimation2

8. Add a new constant to your model:

Figure 8- The "DSP Constant" Block

9. This constant will have the AR coefficients

values:

Figure 9- The AR coefficients values

2 The same configuration parameters apply for the three models.

10. Add a magnitude FFT block in order to get

the spectrum from the AR coefficients:

Figure 10- The FFT Block11. Set the FFT length to 128:

Figure 11- The FFT Length12. Add a new math function object:

Figure 12- The Math Function Block

The “Math Function” block should be configured to calculate the reciprocal:

Figure 13- The Math Function Block Configuration

13. Add a new gain to your model (to represent

the white noise variance in the reference

spectrum generation) and set its value to 0.1:

Figure 14- The Gain Block

14. In order to display the Real and Estimated

spectra simultaneously, you need to add a

new concatenate object:

Figure 15- The "Matrix Concatenate" Block

and set the number of inputs of the concatenation

object to 4:

Figure 16- The "Matrix Concatenate" Block Configuration

15. The various spectra will be displayed in a

vector scope:

Figure 17- The "Vector Scope" Block

Select frequency as its input domain:

Figure 18- The "Vector Scope" Block Configuration

16. Connect the blocks as shown in Figure 19:

Figure 19 – Spectrum Estimation Simulation Model

17. When running the model3, you should see the

get the following display:

Figure 20 – Comparing the various spectrum estimators

3 You should select a different color for each channel

3. Real Time Implementation

3.1.The EnvironmentFigure 21 shows the block-diagram for the real

time implementation. The DSP will deliver two

outputs. The first is the reference spectrum; the

second is an estimated spectrum of the output of

the all-pole filter. Three real-time models will be

created, each one corresponding to an estimator.

The user will be able to select the desired estimator

through a Graphic User Interface (GUI).

Figure 21- Real Time Implementation Environment

The real-time implementation model will be

created from the simulation model, after the

following changes:

The noise generator block will be replaced

by the CODEC of the DSK6713

The virtual scope will be replaced also by

the CODEC

A target definition block (DSK6713) will

be added.

Equipment Used:

DSK6713

Dual Channel Oscilloscope

Signal Generator

Figure 22- Spectrum Estimation Equipment

3.2.Creating the Models1. Open the simulation model

“SpectrumEstimation.mdl”.

2. Remove the “Burg” and “MCov AR”

estimators.

3. Add the C6713DSK target to the model

Figure 23- The C6713DSK target Block

4. Replace the vector scope by the “Digital to

Analog” converter (DAC)

Figure 24- The DAC Block

5. Configure the DAC block to a sampling rate

to 8 KHZ and 16-bit samples.

Figure 25- The DAC Block Configuration

6. Double- click on the concatenation object

and change the number of inputs from 4 to 2.

7. Replace the white noise generator by the

“Analog to Digital” converter (ADC).

Figure 26- The ADC Block

8. Configure the ADC blocks to a sampling

rate to 8 KHZ and 16-bit samples.

Figure 27- The ADC Block Configuration

The final model should look as follows:

Figure 28 –Periodogram Real-Time Model

9. Set the AR-coefficients data type to single.

10. Configure the Model to generate and build

(without executing) the CCS code as shown:

Figure 29 –Model Configuration

11. Save the model as “Periodogram.mdl”

12. Build the model (CTRL-B)

13. Replace the Periodogram estimator block by

the Burg estimator

14. The final model should look as follows:

Figure 30 –Burg Real-Time Model

18. Save the model as “Burg.mdl”


20. Replace the Burg estimator block by the

MCov AR estimator

21. The final model should look as follows:

Figure 31 –MCov ARBurg Real-Time Model

22. Save the model as “MCcov_AR.mdl”


At this step you’ll have three .out files to be

loaded to the DSK. Each one corresponding to an

estimator.

3.3.The Graphic User Interface (GUI)

The GUI shown in Figure 32 will be used to select

the model. Upon selecting a model, its

correspondent load file will be loaded to the DSP.

Figure 32- GUI

1. Enter GUIDE in the MATLAB® command

line.

2. Choose a new GUI, and name it Spectrum

3. Add a list-box to your GUI with the string:

4. A script file “spectrum.m” will open, when

you press the “play” button. Name the

script “spectrum.m”

5. The GUI will perform two tasks:

i. Upon activating the GUI, the

default model is loaded to the

DSP.

ii. When the user selects a new

model, it is loaded to the DSP.

6. The initialization routine

“Spectrum_OpeningFcn” will be:

function Spectrum_OpeningFcn(hObject, eventdata, handles, varargin)modelName = gcs;%connect to target:CCS_Obj = connectToCCS(modelName);% Identify RTDX channel names/modesCodegenDir = fullfile(pwd, ['Periodogram' '_c6000_rtw']);OutFile = fullfile(CodegenDir, ['Periodogram' '.out']);%load the model to the DSK:CCS_Obj.load(OutFile,20);handles.CCS_Obj=CCS_Obj;handles.output = hObject;%remember the current model:handles.last_model=1;CCS_Obj.run;% Update handles structureguidata(hObject, handles);

7. Selecting a new model:

%1. halts the current model%2. loads the current model%inputs:%m - 3 levels flag that tells which model to load.%CCS_Obj - the target objectfunction ChangeModel(m,CCS_Obj)CCS_Obj.halt;switch m case 1 model='Periodogram'; case 2 model='Burg'; case 3 model= 'MCov_AR';endCodegenDir = fullfile(pwd, [model '_c6000_rtw']);OutFile = fullfile(CodegenDir, [model '.out']);CCS_Obj.load(OutFile,20);CCS_Obj.run; if last_y~=15000r.writemsg(chan_struct(2).name,1/last_y);

end

8. When the user changes the model, the list-box handler function is invoked:

function listbox1_Callback(hObject, eventdata, handles)handles.last_model=get(hObject,'Value') ;ChangeModel(handles.last_model,handles.CCS_Obj);guidata(hObject, handles);

The handler saves the new model as the current

model and invokes the change model function we

described above.

Now you can run the model, and observe the results in the oscilloscope for the various estimators.

PeriodogramBurgM-Cov

Documents

Spectrum Estimation