# MATLAB/SIMULINK FOR DIGITAL COMMUNICATION EBOOK

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ecogenenergy.info with modern digital communications in the MATLAB and Simulink simulation environment. An extensive. Are you interested in simulation of communication systems in Matlab and do not Simulation of Digital Communication Systems Using Matlab ebook by . Problem-Based Learning in Communication Systems Using MATLAB and Simulink. MATLAB/Simulink for Digital Communication, Written for students and engineers, this book provides a reference for studying communication systems. The aim of.

Commonly used math blocks are also incorporated into the Simulink model. Use of the bertool is shown to be a convenient technique to obtain BER performance over a range of bit energy to noise spectral density values.

Sample-based and frame-based computations are presented where it is seen that frame-based computations are vector based and provide faster computation. The chapter concludes with Simulink computations employing ixed-point arithmetic. Simulink modeling of QAM BER is performed for both average and peak power conditions, again with various alphabet sizes. Using an example of QAM signaling in conjunction with a nonlinear power ampliier highlights the power of Simulink to model a communication system and determine its performance in a case where theoretical results are not available.

Comparison of simulated and theoretical per- formance conirms the facility to reliably estimate performance. The ability of the spectrum analyzer to exhibit a wide selection of spectral estimation techniques and parameters is demonstrated. Comparisons of theoret- ical with simulated results are performed. This chapter concludes with a Simulink model that investigates the BER performance of coherently detected FSK in a multipath channel with Rician fading. A Simulink example is provided to demonstrate the degradation due to multi- path with and without coding.

In each of these cases, an interleaver is introduced. A concluding section presents Simulink models for selected block codes and modulations with STBC and interleaving in Rayleigh fading. This chapter presents topics in Simulink incorporating convolutional error control coding in an AWGN and a fading channel. CHAPTER 12 Adaptive equalization has been used extensively to compensate for the degra- dations from time- dispersive multipath channels.

Simulation is required in each of these cases and Simulink is the tool that achieves the desired results. In particular Simulink models are developed for the fol- lowing situations: The choice of topics is meant to illustrate the multiplicity of applications that can be investigated using Simulink modeling. The website also provides Simulink models for the problem sets, and for instructors, answers to the problems can be obtained through the website.

The MathWorks technical staff provided valuable help in identifying and correcting Simulink model issues and for this we are extremely grateful. MATLAB Central is also a signiicant source of user-developed Simulink models that often enable the developer to obtain a satisfactory resolution of a complex problem.

We want to thank Dr. The model presented in this chapter is a simple one: The Communications System Toolbox provides a collection of MATLAB functions and simulation blocks that can be utilized for a wide range of digital communications systems simulation models.

While MATLAB and Simulink are available for a variety of operating systems, all of the descriptions and examples presented in this book are implemented on Windows-based computers.

Product descriptions from this documentation are provided as follows: In some instances, a notice is generated indicating that the model was developed in an earlier release. Companion Website: It supports system-level design, simulation, auto- matic code generation, and continuous test and veriication of embed- ded systems.

Simulink provides a graphical editor, customizable block libraries, and solvers for modeling and simulating dynamic systems. Upon gaining familiarity with Simulink, the user will discover that multiple paths can be followed in developing a Simulink model.

The choice of the path is left to the user but each path will lead to the same solution. The topics covered in this chapter are: Other desk- top views may be selected under the Home menu; see the Layout tabs on the toolbar.

The left-hand panel displays the Current Folder, which can con- tain MATLAB or Simulink models in addition to user-developed igures and user iles resident in the folder.

The upper right-hand panel is the Workspace, where variables deined in the Com- mand Window are displayed, and the lower right-hand panel is the Command History, where the user can view or rerun commands entered at the command line. In Figure 1. Items under new include: This opens the window shown in Figure 1. The Simulink Library Browser shows a listing of available Simulink blocks.

The focus in this book is on modeling digital communication systems, and the blocks you will ind most useful are contained in the basic Simulink block library as well as in the Communications System Toolbox and the DSP System Toolbox. Simulink library blocks used throughout this book are listed here. This will open a blank Simulink model window, shown in Figure 1.

Note that on the title bar at the top of the window, this model is labeled untitled. In the model window, the user may select the duration of the model execution, shown here to be set at This will ix the duration of each of the simulations to be demonstrated in this chapter.

To rename the model, on the toolbar, select File or File: The renamed model is shown in Figure 1. First, in the library window Figure 1. Next, add a scope to the model by returning to the Simulink Library Browser and clicking on -Sinks, selecting scope, and dragging a copy into the model window, now shown in Figure 1.

In the igure, the Sine Wave block has been connected to the Scope by clicking on the arrowhead at the Sine Wave output and dragging a line to the corresponding arrowhead at the input to the Scope. Another block, entitled Model Info, is shown in Figure 1. This utility is very useful for conveniently displaying the parameters of each simulation model and identifying pertinent information about the model.

The Sine type and Time t selections shown in the igure will be suitable for most simulations. The Sine Wave block parameters window can also be opened by selecting the block in the model window and right-clicking the mouse, which displays a list of options, and selecting Block Parameters Sin. The user will normally ind options that can be selected for each block in addition to entering parameter values.

As an example, in this block the user has a choice under Sine type to select either Time-based or Sample- based computation; under Time t the user can select Use simulation time or Use external signal. To provide a stream-lined introduction to model building, the presentation in this text will omit detailed discussions of many options. The Simulink documentation, accessible by clicking on the Help button, provides more extensive information on the optional selections.

The gear-like icon on the toolbar opens the Scope Parameters window, which has three pages. On the General page, shown in Figure 1. Since the scope can be set to display multiple axes for multiple inputs , the time ticks might be applied to all axes select all , or to none, or to the bottom axis only.

The History page of the Scope Parameters window is shown in Figure 1. Here the user can specify the number of simulation data points to be displayed on the scope and can elect to have the data stored to workspace. On the Style page of the Scope Parameters window, shown in Figure 1. Figure 1. General Page. Double-clicking on the Scope block opens the Scope display window, shown in Figure 1. Examining the signal trace on the Scope display conirms the signal source settings made in Figure 1.

History Page. Style Page. In this model, under the Display tab, selecting Sample Time and then all adds a data label Cont indicating that continuous time has been chosen, a direct result of choosing Sine type as Time based in Figure 1.

The model colors are now changed, as seen in Figure 1. A Sample Time Legend is also displayed, as shown in Figure 1. In this case, the Sine Wave block is black, labeled Cont for continuous with a zero value; the Model info block is magenta with data value and type Inf, indicating that there is no time associated with this block, that is, it exists as long as the simulation is active.

One cycle completed in 6. Simulink blocks are designed to accept signals and parameter values as vector inputs. As an example, the time-based Sine Wave model in Figure 1. Note in the model window that the Sine Wave output is labeled 2D1 and the input to the Scope is labeled 2, both resulting from setting the frequency to the vector value [1 10]. After running the simulation, the Scope will display the two sampled sinusoids, as seen in Figure 1.

A third way of reconiguring the Sine Wave block is discussed in Section 1. Sine Wave window; the Sample time is set to 0. Figures 1. The color red in the blocks and data line indicates that the output from the Sine Wave block is a discrete vector with 0. Upon running the simulation, the scope output, shown in Figure 1. The To Workspace block causes the output data from the Sine Wave block to be saved and examined for subsequent use such as plotting. The output block is labeled here as simout, a label that can be changed after irst double clicking on the block.

Refer to the MathWorks documentation for further information on the use of Model Explorer. The menu in the center panel lists all the blocks in the selected model. By clicking on any model block in the list, the user can display information about that block. For example, Figure 1. This provides another avenue for reconiguring the Sine Wave block to generate multiple frequencies, discussed earlier. To add labels to Figure 1. Selecting Figure Properties from the Edit tab pro- duces the window shown in Figure 1.

Changes can now be made to colors, style, axis properties, and labels. After adding labels, inserting a title, and changing colors, the revised igure is displayed in Figure 1. Two sinusoids 2 1. By click- ing on the Help button in the Model Configuration Parameters win- dow, the MathWorks documentation describes several aspects of this window including: Using a ixed-step solver, the step size remains constant throughout the simulation whereas use of a variable-step solver allows the step size to vary from step to step in accordance with the speciied error tolerance.

The error diagnostic explains the problem as seen in Figure 1. The MathWorks documentation provides a comprehensive treatment of each block and available tools.

The remaining chapters focus on the use of Simulink for modeling digital communications systems, without delving deeply into aspects of the full Simulink capability. Other references that the user is likely to ind helpful are listed in Appendix B. Care must be taken by the user in that the error message identiies a problem but the solution may reside in a block other than the highlighted block.

The Simulink toolbar has a check button that can invoke the Model Advisor to help the user correct the problem. Show the Simulink Model and include an information block.

Display each wave on a separate trace in the scope and label all axes. Find the demux block in the Simulink library. Develop a Simulink model for x t with an included information block. Assume a 10 s simulation time. Note that x t represents the irst three terms of the Fourier series of the square wave. Use a 10 s simulation time and Goto and From routing blocks from Signal Routing to simplify the model.

Display x t and cos t on a scope with labeled axes. From the Simulink library, add an AM modulation block to the simu- lation and form the difference between x t and the output of the AM library block. Display x t , cos t , the AM block output and the difference on a scope with four traces. Insert x axis title on bottom trace only; do not label y-axis but add a title to each plot.

Assume a 2 s simulation and sine wave block parameters as follows: Show the model with an included information block. Provide titles for each trace and label only the x-axis. Speciic topics include: The Simulink model parameters for this example are speciied as follows: Sine Wave are provided in Figure 2.

Figure 2. As a result, the plot from the scope is produced as shown in Figure 2. Selecting Edit Figure Properties from the Edit menu in the plot allows the user to change the igure scales, color, line width, etc.

To Workspace. The variable tout is the sample values of time displayed every 0. Table 2. Next a change is made to include a phase shift in the sine wave block as displayed in Figure 2. A Simulink model for determining the spectrum and power spectrum of a sinusoidal signal is shown in Figure 2.

In this igure, it can be observed that the 1 Schonhoff, T. Data windowing controls the width of the main spectral lobe and sidelobe leakage. The rectangular window used to produce Figure 2. This window provided a closer estimate of the spectrum peak in comparison with the theoretical value.

The spectrum calculations using an FFT have demonstrated the need to utilize a window function to control the main lobe width and sidelobe leakage. The length of the FFT, the buffer over- lap, the number of averages and the window selection directly determine the accuracy of the spectrum. Show the Simulink Model using the running Variance block and include an information block. Assume a s simulation time. Display the output in the scope and label all axes.

Show the results in a Display block and compare with the theoretical value. Use a 0.

Display the results in the scope. Show the Simulink model with the simulated average powers and compare the result with the theoretical powers. Develop a model that allows each sinusoid to be displayed separately and label all axes in the scope output. Selecting the sine block from the Simulink section of the Simulink library 2. Selecting the sine block from the DSP sources in the Simulink library Assume the phase is zero, the sample time is 0.

Compute the power for both signals b. Plot the scope output and compare the results 2. Assume the follow- ing parameters: Show the Simulink Model with an information block. For a 10 s sim- ulation time compute the power of the squared sine wave using the running Variance and running RMS blocks and show the results in Display blocks b.

Display the output in the scope and label all axes c. Repeat Part a. Compare the results in Parts a. Mod- ify the scope to display the sine output and the output of the AWGN block a. Display the revised Simulink model. Change the run time to s and report the results of the signal power from the output of the AWGN block and explain the difference from Part a.

Explain the result- ing change in the power from the output of the AWGN block 2. Insert a buffer overlap while retaining the FFT length. Com- pute the spectrum magnitude. With no buffer overlap reduce the FFT length to Compute the spectrum magnitude and the power spectrum magnitude using the spectrum analyzer. Use the DSP sine wave block as a source and compute the spectrum using 10 spectral averages. Speciically these topics include: The menu selection for the Random Integer source block is shown in Figure 3.

The outputs of this block are random double precision numbers that are either 0 or 1. A corresponding phase offset occurs in the BPSK demodulator. If the phase offsets angles between the modulator and demodulator do not agree, then errors will be made.

Implementation considerations may force such a disagreement and the degradation experienced can then be determined. Pressing the data tab reveals that the output is also double precision as shown in Figure 3. Figure 3. The data type button shown in Figure 3. Table 3. The routing symbols labeled S are connectors for the data, used to avoid cluttering the model, with an extra line.

The simulation time is extended to s allowing the input and output sequences to be observed in the scope display as seen in Figure 3. In Figure 3. Figures 3. Using scope 3, Figure 3. The next step in this simulation, shown in Figure 3. The parameter selections in the error rate calculation block are shown in Figure 3.

The receive delay and computation delay are both set to zero for this example. The computation delay allows transient behavior in the received data to be excluded from the BER estimate. The inal step in the construction of this model is to display the signal and port data types as shown in Figure 3. This selection is available in the Simulink model window menu under Display.

## Simulation of Digital Communication Systems Using Matlab

In general, the sample time may be changed to explore the vagaries of the channel, which may change at much smaller time intervals. Often an increase in the number of samples per symbol is desired as the case occurs when synchronization techniques are being investigated.

Appendix 3. The time instants at which the signal is deined are the signal sample times, and the associated signal values are the signal samples. For a periodically sampled signal, the equal interval between any pair of consecutive sample times is the signal sample period, Ts. The sample rate, Fs , is the reciprocal of the sample period. It represents the number of samples in the signal per second.

Note that the accuracy of the simu- lated result improves with an increasing number of demodulated symbols. In the simulated case, a better estimate of the BER at low BER is obtained by using a larger number of transmitted symbols. TABLE 3. There are situations where it is not possible to simply introduce the AWGN block in the simulation and the noise must be added directly. However, it is important to understand that under the proper simula- tion conditions both the AWGN block and the Gaussian noise block used with an adder produce the same results.

Note that the seed num- bers are different for the real and imaginary parts of the complex Gaussian noise generator to ensure statistical independence between the quadrature noise components. Running variance blocks are used to compute the signal power for several signals, which are then displayed in the model.

From the displays, it can be observed that the noise power from display 2 is 0. The simulated BER is 0. The model shown in Figure 3. It is not apparent from the model and the signal powers displayed that these models should produce the same result.

The imaginary part is discarded in the demodulator so that including the imaginary Gaussian noise block is unnecessary. It should be noted that complex Gaussian noise is not needed since the BPSK demodulator takes the real part of the input signal to form its decision. A frame consists of a sequential sequence of samples from a single channel or multiple channels; the user must specify the frame size as an integer number of samples.

Frame-based simulations execute faster and are often needed for matrix computations, where it is inconvenient to use sample-based computation. Running 0. In this model, addi- tional blocks, identiied as scatter blocks, display the constellation of the QPSK demodulator and the received input to the QPSK demodulator. On the right side of Figure 3. In this model, each variance of the real and imaginary parts of the complex Gaussian noise is 0.

In these cases, the power of Simulink is not apparent. Fixed point numbers are represented in binary by means of their word length denoted by ws, a binary point and a fraction of length, n. The ixed point structure, shown in the Figure 3. The MSB is assumed to be a sign bit, s, that is assigned 1 for signed representation and 0 for unsigned. The discussion provided here follows the MATLAB desig- nation where the ixed point number is expressed as ixdt s,ws,n.

The selection of the word size and fraction length is based on the eventual implementation in an ASIC or FPGA device where the word size controls the range of the values to be represented and the fraction length controls the precision. More detail on ixed point representations is available in the MathWorks documentation under the category ixed point numbers. In the model shown in Figure 3. The input parameters for the convert block are shown in Figure 3.

Since the BPSK modulator would normally be part of the ixed point implementation, the same ixed point representation ixdt 1,8,4 is used. The results shown in Figure 3. The choice- of word length and fraction length is usually a compromise involving the numerical range of the numbers to be represented, the precision of these numbers and the quantization errors introduced to deliver the best representation of the digitized signals for the planned hardware implementa- tion.

Saturation may occur if the upper and lower limits of the numbers are exceeded with the consequence that inaccurate estimation or unpredictable errors occur.

An example of ixed point issues identiied thus far is obtained by comput- ing BER results for selected ixed point combinations using the model shown in Figure 3.

Use of a fraction length greater than 4 causes saturation in this model. Simulation results using AWGN blocks and Gaussian noise generator blocks yield identical performance with properly chosen parameters. Use of a large sample size produces excellent agreement between theoretical and simulated BER performance. The AWGN block or a Gaussian noise block may be selected for either sample-based or frame-based simulation.

A ixed point example is included where theoretical performance is dificult or impossible to obtain. Does the BER remain the same as the case with 1 s symbol duration? Why does it take longer to execute with 0. Is the BER the same as the case with sample-based simulation? Does the simulation take the same time to complete? The results show the degradation from a ixed channel phase offset compared to the case where no offset exists.

Does this produce the same results? Filter specs: FIR, minimum, single rate; freq specs: Execute the simulation using s and observe the spectrum ana- lyzer output. What are the frequency limits for the lowpass ilter? Add a running variance block at the output of the Gaussian noise block, the output of the sine wave block, the output ofthe low pass ilter, and the output of the adder. What power levels are obtained? Make the following changes in the low pass ilter: Explain what the differences are due to compared with part a.

Topics presented here are listed as follows: As a speciic example, Figure 4.

Gray coding is stipulated as well. As an example, the constellation for 8-PSK is shown in Figure 4. Figure 4. The BER results shown in Figure 4. An important choice in simulating the QAM BER perfor- mance is whether the performance is obtained for peak or average power. Peak power is often an important consideration when the power must be constrained to stay within the power ampliier PA limits to avoid satura- tion.

In the next example, BER is computed using average power; subsequent examples will demonstrate the need for peak power computations. The normalization can be set to average power, peak power, or minimum dis- tance between symbols.

It is now seen that the simulated and theoretical results are in good agreement. Good agreement is observed between the theoretical and simulation results. The degradation is most easily observed by examining Figure 4. As a result, a penalty in BER is incurred relative to average power operation when the results are compared with those in the previous section.

In general, power ampliiers exhibit memoryless, nonlinear behavior. One of the power ampliier models, attributable to Saleh1 , will be studied here to estimate the impact on BER performance. This example highlights the utility of Simulink for a practical case where no theoretical results are available. COM, pp. Saleh notes that an rms error of 0.

These equations and values of the parameters have been found to it measured TWT data. The BER without the nonlinear device is 0. The signal constellation at the output shows scattering and warp- ing of the rectangular QAM constellation resulting in a poor BER.

When a QAM modulator output is the input to a nonlinear device, the input voltage is backed off to force the modulated waveform to remain within the linear portion of the device. Since the Saleh model is an ideal monotonic function up to the saturation point, an ideal predistortion device can be implemented that exactly compensates for the distortion by computing an inverse function of the nonlinear characteristic.

Speciically, the S function presented here accomplishes the exact compensation and is a perfect linearizer. The S function, labeled nlinvd. The m-ile listing is given as follows: The BER without the nonlinear device and with the included predistortion block is 0.

It is now evident that the predistortion device compensates exactly for the Saleh nonlinearity. The scatter plots, shown in Figure 4. Note that the actual implementation of the predistortion device will degrade BER performance.

Goto [Tx] scatter scatter scatter [Tx] 0. The use of the bertool was applied extensively in the BER com- putations. QAM signaling required a study of both peak and average power to address issues with saturation in nonlinear PAs. The power of Simulink was revealed in the example where a nonlinear device was introduced in the simulation to address the case where no theoretical results are available.

The incorporation of a user-deined S function, developed in MATLAB, was also illustrated to allow the user to modify the simulation when no library block is available. What is the theoretical peak power degradation? What is the approximate degradation obtained in the simulation? What is the simulated BER in this case? Show the scatter plot at the nonlinearity output. Change the third order intercept point to 35 dBm and determine the simulated BER and the scatter plot at the nonlinearity output.

In the simulation, the spectrum scope computes the FFT with a rectangular window, spectral averages with no overlap, a FFT size and a These settings are obtained by selecting spectrum settings under the View tab in the spectrum scope. Figure 5. Using a utility block not shown in Figure 5.

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As shown in Figure 5. Good agreement can be observed between the theoretical and simulated results. Speciic input parameters are as follows: Wireless Communications Prentice Hall, p.

Using the Simulink model in Figure 5. The spectrum analyzer uses averages with a Hann window and no overlap.

## Communication Systems Modeling and Simulation using MATLAB and Simulink

The constants in the simulation are selected to force the gain at zero frequency to be approximately 0 dB.

The spectrum analyzer was used extensively and shown to offer a wide selection of spectral estimation techniques and parameters. A sine wave has a power of 0. Explain why the modulator output power is 1 W. How does this result com- pare with the MSK power spectrum? Speciically these topics include the following: Here it is useful to review the theoretical BER performance for Rayleigh fading channels in order to establish a framework for Simulink model construction.

Appendix 6. The time-varying nature of the channel is also characterized by its power spectral density S f. A summary of the model parameters is speciied as follows: The estimated BER is 0.

Figure 6. Salehi, Digital Communications, 5th ed, pp. Running 1 [tx] [tx] VAR 0. This function is required to track the channel time-variability where the receiver implementation ordinarily incorporates an automatic gain control AGC. In this model, the box for selection of Rician fading channel parameters is checked to open the channel visualization at the start of the simulation.

In this simu- lation, speciic parameters include the Rician K factor that speciies the ratio of the specular component to the diffuse multipath components, the Doppler shift associated with the specular line-of-sight component, and the max- imum Doppler shift associated with the diffuse multipath components.

Figures 6. The Simulink model for this case is provided in Figure 6. Multipath parameters are not speciied in this simulation since lat fading is assumed. Note that increasing the value of the Rice factor suggests a stronger dominant received signal component, thus resulting in an improved Figure 6. Good agreement is observed between theoretical and simulated BER for all cases. Introducing added parameters allows the insertion of multi- path as a vector of path delays and a vector of average path gains.

Here two paths are introduced with a main path and a second delayed path that has an average path gain deined as X. The average overall path gain is normalized to 0 dB. Using the Simulink model in Figure 6. It is observed that a null in the frequency response, resulting from the presence of multipath, occurs at 0. Comparing Figure 6. To conirm this result, Figure 6.

## Modeling of Digital Communication Systems Using SIMULINK

The error probability is then seen to be 0. The model shown in Figure 6. The interference introduced by the multipath is seen to cause a severe increase in BER even when the second multipath component is 3 dB lower than the main path. Using the bertool, Figure 6.

The model parameters are speciied as follows: As the multipath gain X gets larger, signiicant loss in BER occurs. When the channel exhibits fading, BER performance for speciic modulations depends on the selected fading model and is severely degraded from performance in AWGN.

Examples provided here included Rayleigh and Rican fading models. Simulink models allow the BER performance in the presence of multipath to be readily estimated. This capability provided by Simulink is important since estimation of BER in the presence of multipath is not easily obtained analytically. E In Appendix 3. Salehi, Digital Communications, 5th ed pp. What is the resulting BER? Using a modiied simulation based on the same Rician and AWGN parameter selections, show that over the 10, s simulation time, the main component magnitude is on average greater than the sec- ond component magnitude.

What is the magnitude of these components after 10, s in your simulation? What is the resulting BER and how do you explain the change?

## Recommended For You

Find the frequency null and explain its location. Determine and explain the magnitude of the normalized spectrum from Prob 6.

Increase the delay to 4 s and determine the location of the null. The time-varying nature of the channel is again characterized by its power spectral density S f according to the Jakes fading model presented in Chapter 6. This plot was obtained from the spectrum analyzer with scope settings: Figure 7.

Good agreement is observed between the theo- retical and simulated BER performance. The the- oretical result for the probability of error Pb is summarized in Appendix 7. A summary of the model parameters is provided as follows: In Figure 7.

The model shown in Figure 7. Daniel Wong. M H Alsuwaiyel. Analog, Digital and Multimedia Telecommunications. Omar Fakih Hamad. Combinatorial Algorithms. Kwonhue Choi. Graph Theory with Algorithms and its Applications. Santanu Saha Ray. Fuzzy Control and Identification.

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Goff Hill.Note in the model window that the Sine Wave output is labeled 2D1 and the input to the Scope is labeled 2, both resulting from setting the frequency to the vector value [1 10]. The Simulink models presented for hard decisions in Figure TABLE Figures 1. Items under new include: However, when the channel exhibits fading, BER performance for speciic modulations depends on the selected fading model and is severely degraded from perfor- mance in AWGN. The Rayleigh channel model is again the one used in Figure Goodreads helps you keep track of books you want to read.

For a 10 s sim- ulation time compute the power of the squared sine wave using the running Variance and running RMS blocks and show the results in Display blocks b. Practical Digital Signal Processing.

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