Learn how to generate a 1000 Hz plus 3000 Hz sinusoidal wave with additive noise,
apply a Chebyshev Type II filter, compute a FFT and power spectral density, display
simulation results in a vector scope, and downsample the output of a buffer.
Files for This Tutorial
filterPSD.scm
A finished version of the models you build in the tutorials along with any files
required to complete the tutorials are available at this location:
<installation_directory>/tutorial_models/.
Generating a Sinusoidal Wave with Additive Noise
Create a model and define a diagram context for a sinusoidal wave with additive
noise.
On the ribbon, select New
Model, then Save Model.
In the dialog that appears, enter the path to your working directory with the
file name: filterPSD_practice.scm.
From the Palette Browser, add the following blocks into the
modeling window:
From Activate > SignalGenerators, drag and drop one SampleClock
block, one Random block, and two
SineWaveGenerator blocks.
From Activate > MathOperations, drag and drop 1 Sum block.
For each block, enter the parameter values as indicated, and click
OK.
On the SampleClock block, double-click, and for
Sample period, enter: 1/Fs.
On the Random block, double-click, and for
Distribution, from the drop down list, select
Normal.
On the first SineWaveGenerator block,
double-click, and for Frequency, enter:
2*pi*1000.
On the second SineWaveGenerator block,
double-click, and for Frequency, enter:
2*pi*3000.
On the Sum block, double-click, and for Number of
inputs, enter: 3; for all Input Ports, enter:
"+" .
Connect the blocks and adjust the links like this:
On the ribbon, select the Diagram tool .
On the Context tab, enter: Fs = 10000, and click
Apply.
Applying a Chebyshev Type II Low Pass Filter
Apply the OML function, Cheby2, in a diagram context.
The Cheby2 function generates the coefficient of the transfer function of the low pass
filter.
On the ribbon, select the Diagram tool .
On the Context tab, enter the command:
[num,den]=cheby2(3,20,2000/5000);
This command generates the coefficient of the transfer function of the low
pass filter, which has an order of 3, a cut-off frequency of 2000 Hz, and a stop
band attenuation of 20 dB. The returned variables num and
den are used as coefficients of the numerator and
denominator of a discrete transfer function representing the
filter.
From the Palette Browser > Activate > Dynamical, drag and drop one DiscrTransFunc block
into the diagram.
On the DiscrTransFunc block, double-click, and enter
these parameter values:
Connect the blocks so that the sine wave with additive noise passes through the
digital low pass filter implemented with a discrete transfer function:
Computing the FFT and Power Spectral Density
Define blocks in your model to compute the Fast Fourier Transform and Power Spectral
Density.
From the Palette Browser > Activate > Buffers, drag one Buffer block into the
diagram.
On the Buffer block, double-click. In the block dialog,
for length, enter: N.
From the Palette Browser > Activate > MatrixOperations, drag one FFT block into the diagram.
Connect the blocks like this:
On the ribbon, select the Diagram tool .
On the Context tab, enter the variable: N=1024.
This variable specifies for 1,024 points of data to be sampled and sent to
the FFT block.
Note: The one-sided power spectral density is computed with the
equation P= 2 ∗ |ff |
^
2/(F∗N)
From the Palette Browser > Activate > MathOperations, drag one Abs and one
Power block into the diagram.
On the Power block, double-click. In the block dialog,
for power, enter: 2.
From the Palette Browser > Activate > MathOperations, drag one Gain block into the
diagram.
On the Gain block, double-click. In the block dialog,
for Gain, enter: 2/ (Fs*N).
Connect the blocks like this:
From the Palette Browser > Activate > MatrixOperations, drag one MatrixExtractor block into the
diagram.
On the MatrixExtractor block, double-click, enter the
following parameter values, and click OK:
For Index vector I, select : (all), which is the
default.
For Index vector J, select Defined as parameter,
and enter [1:N/2+1].
Select One-based indexing.
Connect the blocks like this:
Click and drag your mouse to area-select the blocks FFT,
Abs, Power, and
Gain.
With the blocks selected, from the ribbon, click, Create Super
Block.
In the tree of the Property Editor, under General, click the field for
Name, and enter PSD.
The super block reflects the new name:
Displaying Results with a VectorScope Block
View simulation results in a power spectrum density graph.
From the Palette Browser, add the following blocks into
your diagram:
From Activate > MatrixOperations, drag and drop one Transpose
block.
From Activate > SignalViewers, drag and drop one VectorScope
block.
From Activate > SignalGenerators, drag and drop one Constant
block.
On the Constant block, double-click. In the block
dialog, for the parameter Constant, enter
[0:Fs/N:Fs/2]', and click OK.
On the VectorScope block, double-click. From the block
dialog, select the box for External X Value and
Plot after simulation ends, and click
OK.
Assemble and connect the blocks like this:
On the ribbon, select Run.
Double-click the VectorScope block.
The VectorScope window appears displaying a plot of the simulation
results. To fit the view of the plot into the window, middle-mouse click.
On the Y-axis block, right-click. In the floating panel
that appears, from the Scale drop down list, select
db10.
The power spectrum density graph appears as you see in the following figure.
Two peaks at frequencies are present: 1000Hz and 3000Hz. The 3000Hz peak is
lower because the original signal is attenuated by the Chebychev low-pass
filter.
Downsample the Output of the Buffer
Reduce the sampling frequency of the buffer.
From the Palette Browser > Activate > ActivationOperations, drag and drop one ReSampleClock block
into the diagram.
Both activation input ports of the Buffer block are triggered by the
SampleClock block at 10,000Hz. This trigger forces the blocks downstream,
including the FFT and VectorScope blocks, to run at 10,000Hz which can result in
unnecessary computation and scope generation. The addition of the ReSampleClock
block ensures that the Buffer block updates the output only when
required.
Assemble and connect the blocks as you see in the following figure:
On the ReSampleClock block, double-click. From the block
dialog that appears, for Down Sampling Factor, enter
N.
Changing this parameter ensures the outgoing activation is triggered
whenever N points are sampled by the Buffer block when
full.
On the ribbon, select Run.
Running the simulation takes less time to finish than in the previous
iteration, though the results are similar:
, then Save Model
.
.
Note: The one-sided power spectral density is computed with the equation P= 2 ∗ |ff | ^ 2/(F∗N)
.
.
.
Running the simulation takes less time to finish than in the previous iteration, though the results are similar: