MATLAB Examples

Construct, visualize and analyze the antenna elements in the Antenna Toolbox.

Model an infinite ground plane and calculate fundamental antenna parameters for balanced antennas.

Construct, visualize, and analyze an antenna array from the Antenna Toolbox.

Uses infinite array analysis to model large finite arrays. The infinite array analysis on the unit cell reveals the scan impedance behavior at a particular frequency. This information is

Create and analyze a resonant coupling type wireless power transfer(WPT) system with emphasis on concepts such as resonant mode, coupling effect, and magnetic field pattern. The analysis

A switched beam array of 4 resonant dipoles. The beam switching is accomplished by using a 4 X 4 Butler matrix. The effect of the beam switching is shown by observing the outputs of 4 receiving

The spiral antenna is an inherently broadband, and bidirectional radiator. This example will analyze the behavior of an equiangular spiral antenna backed by a reflector [1]. The spiral and

This example, optimizes a 6 element Yagi-Uda antenna for higher directivity at zenith (elevation = 90 deg). The design frequency and typical dimensions of the metal structures are chosen

Demonstrates the embedded element pattern approach to model large finite arrays. Such an approach is only good for very large arrays so that the edge effects may be ignored. It is common to

Analyzes a 2-antenna diversity scheme to understand the effect that position, orientation and frequency have on received signals. The analysis is performed under the assumptions that

Discusses the PIFA designed for Wi-Fi™ applications [1]. The Planar Inverted-F Antenna(PIFA) is basically a grounded patch antenna with the patch length of \lambda /4 (open-short

In it's most basic form, a microstrip patch antenna consists of a radiating patch on one side of a dielectric substrate and a ground plane on the other side. Microstrip patch antennas radiate

Describes the modeling of a 77 GHz 2 X 4 antenna array for Frequency-Modulated Continuous-Wave (FMCW))applications. The presence of antennas and antenna arrays in and around vehicles has

How the antenna mutual coupling affects the performance of an orthogonal space-time block code (OSTBC) transmission over a multiple-input multiple-output (MIMO) channel. The

Create a crossed-dipole or turnstile antenna and array using the Conformal array. The turnstile antenna invented in 1936 by Brown [1] is a valuable tool to create a circularly-polarized

Models the inverted Amos sector antenna designed in [1]. A sector antenna is a type of directional antenna with a sector-shaped radiation pattern. The word 'sector' is used here in the

Metasurface antenna is a new concept in surface antennas, which take the advantage of periodic boundary of each radiation unit cells to group radiation unit in a more compact space. This

Compares the results published in [1] for an Archimedean spiral antenna with those obtained using the toolbox model of the spiral antenna. The two-arm Archimedean spiral antenna( r = R \phi )

Compares the impedance of a monopole analyzed in Antenna Toolbox™ with the measured results. The corresponding antenna was fabricated and measured at the Center for Metamaterials and

Compares results published in [1] for a two-arm equiangular spiral antenna on foamclad backing ( \epsilon_{r} \approx 1), with those obtained using the toolbox model of the spiral antenna

Studies a helical antenna designed in [2] with regard to the achieved directivity. Helical antennas were introduced in 1947 [1]. Since then, they have been widely used in certain

Analyzes the impedance behavior of a monopole at varying mesh resolution/sizes and at a single frequency of operation. The resistance and reactance of the monopole are plotted and compared

Design a double tuning L-section matching network between a resistive source and capacitive load in the form of a small monopole. The L-section consists of two inductors. The network

An audio plugin designed to shift the pitch of a sound in real time.

Communicate between a digital audio workstation (DAW) and MATLAB using the user datagram protocol (UDP). The information shared between the DAW and MATLAB can used to perform

Visualize the magnitude response of a tunable filter. The filters in this example are implemented as audio plugins. This example uses the visualize and audioTestBench functionality of the

An audio plugin designed to enhance the perceived sound level in the lower part of the audible spectrum.

Apply reverberation to audio by using the Freeverb reverberation algorithm. The reverberation can be tuned using a user interface (UI) in MATLAB or through a MIDI controller. This example

Use a phase vocoder to implement time dilation and pitch shifting of an audio signal.

Design and use three audio effects that are based on varying delay: echo, chorus and flanger. The example also shows how the algorithms, developed in MATLAB, can be easily ported to Simulink.

Compress the dynamic range of a signal by modifying the range of the magnitude at each frequency bin. This nonlinear spectral modification is followed by an overlap-add FFT algorithm for

Implement a Vorbis decoder, which is a freeware, open-source alternative to the MP3 standard. This audio decoding format supports the segmentation of encoded data into small packets for

Use the Levinson-Durbin and Time-Varying Lattice Filter blocks for low-bandwidth transmission of speech using linear predictive coding.

Simulate a plucked string using digital waveguide synthesis.

Simulate a digital audio multiband dynamic range compression system.

Remove a 250 Hz interfering tone from a streaming audio signal using a notch filter.

Implement a phase vocoder to time stretch and pitch scale an audio signal.

Use tools from Audio System Toolbox (TM) to measure loudness, loudness range, and true-peak value. It also shows how to normalize audio to meet the EBU R 128 standard compliance.

Demonstrates two forms of graphic equalizers constructed using building blocks from Audio System Toolbox. It also shows how to export them as VST plugins to be used in a Digital Audio

Use a multistage/multirate approach to sample rate conversion between different audio sampling rates.

Implement a real-time audio "phaser" effect which can be tuned by a user interface (UI). It also shows how to generate a VST plugin for the phaser that you can import into a Digital Audio

Apply adaptive filters to acoustic echo cancellation (AEC).

Use the Least Mean Square (LMS) algorithm to subtract noise from an input signal. The LMS adaptive filter uses the reference signal on the Input port and the desired signal on the Desired port

Apply adaptive filters to the attenuation of acoustic noise via active noise control.

Simulate the design of a cochlear implant that can be placed in the inner ear of a profoundly deaf person to restore partial hearing. Signal processing is used in cochlear implants to convert

Design octave-band and fractional octave-band filters. Octave-band and fractional-octave-band filters are commonly used in acoustics. For example, octave filters are used to perform

Multiple-Input-Multiple-Output (MIMO) systems, which use multiple antennas at the transmitter and receiver ends of a wireless communication system. MIMO systems are increasingly

Simulate a basic communication system in which the signal is first QPSK modulated and then subjected to Orthogonal Frequency Division Multiplexing. The signal is then passed through an

Use the Communications System Toolbox to visualize signal behavior through the use of eye diagrams and scatter plots. The example uses a QPSK signal which is passed through a square-root

Use the Complementary Cumulative Distribution Function (CCDF) System object to measure the probability of a signal's instantaneous power being greater than a specified level over its

The example performs Huffman encoding and decoding using a source whose alphabet has three symbols. Notice that the huffmanenco and huffmandeco functions use the dictionary created by

Provides visualization capabilities to see the effects of RF impairments and corrections in a satellite downlink. The link employs 16-QAM modulation in the presence of AWGN and uses a High

A digital communications system using QPSK modulation. In particular, this example illustrates methods to address real-world wireless communications issues like carrier frequency and

A method for digital communication with OFDM synchronization based upon the IEEE 802.11a standard. System objects from the Communication System Toolbox are utilized to provide OFDM

Compare, using eye diagrams, Gaussian minimum shift keying (GMSK) and minimum shift keying (MSK) modulation schemes.

The BER performance of several types of equalizers in a static channel with a null in the passband. The example constructs and implements a linear equalizer object and a decision feedback

Use the comm.EyeDiagram System object to perform eye diagram measurements on simulated signals.

This model shows part of the ETSI (European Telecommunications Standards Institute) EN 300 744 standard for terrestrial transmission of digital television signals. The standard

This model shows the full duplex communication between two Bluetooth® devices. Both data packets and voice packets can be transmitted between the two devices:

The application of low density parity check (LDPC) codes in the second generation Digital Video Broadcasting standard (DVB-S.2), which is deployed by DIRECTV in the United States. The

Use cyclostationary feature detection to distinguish signals with different modulation schemes, including P25 signals [ 1]. It defines four cases of signals: noise only, C4FM, CQPSK, and

Spatial multiplexing schemes wherein the data stream is subdivided into independent sub-streams, one for each transmit antenna employed. As a consequence, these schemes provide a

Use comm.EyeDiagram and comm.ConstellationDiagram in analyzing communication systems.

This model shows transmission and reception of beacon frames in an 802.11 based wireless local area network (WLAN) as described in [ 1 ]. The beacon frame is a type of management frame. It

The intersymbol interference (ISI) rejection capability of the raised cosine filter, and how to split the raised cosine filtering between transmitter and receiver, using raised cosine

Use baseband modulators and demodulators with frequency upconversion and downconversion to simulate passband communication systems. In general, it is simpler and faster to model a

Create a Huffman code dictionary using the huffmandict function.

Use the comm.EVM System object to measure the error vector magnitude (EVM) of a simulated IEEE® 802.15.4 [ 1 ] transmitter. IEEE 802.15.4 is the basis for the ZigBee specifications.

This model shows part of the frequency division duplex (FDD) downlink physical layer of the third generation wireless communication system known as wideband code division multiple access

Lowpass filter an ECG signal that contains high frequency noise.

Design lowpass filters. The example highlights some of the most commonly used command-line tools in the DSP System Toolbox. Alternatively, you can use the Filter Builder app to implement

Use System objects to do streaming signal processing in MATLAB. The signals are read in and processed frame by frame (or block by block) in each processing loop. You can control the size of each

Implement a speech compression technique known as Linear Prediction Coding (LPC) using DSP System Toolbox™ functionality available at the MATLAB® command line.

Design lowpass FIR filters. Many of the concepts presented here can be extended to other responses such as highpass, bandpass, etc.

Use an RLS filter to extract useful information from a noisy signal. The information bearing signal is a sine wave that is corrupted by additive white gaussian noise.

Visualize and measure signals in the time and frequency domain in MATLAB using a time scope and spectrum analyzer.

Model a dual-tone multifrequency (DTMF) generator and receiver. The model includes a bandpass filter bank receiver, a spectrum analyzer block showing a spectrum and spectrogram plot of

Compare three different delta-modulation (DM) waveform quantization, or coding, techniques.

Implement two common methods of envelope detection. One method uses squaring and lowpass filtering. The other uses the Hilbert transform. This example illustrates MATLAB® and Simulink®

Use a Kalman filter to estimate an aircraft's position and velocity from noisy radar measurements.

Apply adaptive filters to signal separation using a structure called an adaptive line enhancer (ALE). In adaptive line enhancement, a measured signal x(n) contains two signals, an unknown

Use the UDP Send and UDP Receive System objects to transmit audio data over a network.

Lowpass filter a noisy signal in MATLAB and visualize the original and filtered signals using a spectrum analyzer. For a Simulink version of this example, see Filter Frames of a Noisy Sine

Adaptively estimate the time delay for a noisy input signal using the LMS adaptive FIR algorithm. The peak in the filter taps vector indicates the time-delay estimate.

Model an algorithm specification for a three band parametric equalizer which will be used for code generation.

Takes the perspective of a MATLAB developer willing to author an instantaneous frequency estimator based on a Discrete Energy Separation Algorithm. It also introduces creating System

Use a recursive least-squares (RLS) filter to identify an unknown system modeled with a lowpass FIR filter. Transfer function estimation is used to compare the frequency response of the

Design arbitrary group delay filters using the fdesign.arbgrpdelay filter designer. This designer uses a least-Pth constrained optimization algorithm to design allpass IIR filters

Sample rate conversion of an audio signal from 22.050 kHz to 8 kHz using a multirate FIR rate conversion approach.

Efficiently convert sample rates between arbitrary factors.

SAR [1] is a technique for computing high-resolution radar returns that exceed the traditional resolution limits imposed by the physical size, or aperture, of an antenna. SAR exploits

Use the Convolutional Decoder block to decode data, and how to compare the hardware-friendly design with the results from LTE System Toolbox™. The workflow follows these steps:

Use the Gold Sequence Generator block to implement an LTE descrambler.

Use the Turbo Decoder block to decode data, and how to compare the hardware-friendly design with the results from LTE System Toolbox™.

Use the CRC Encoder block to encode data, and how to compare the hardware-friendly design with the results from LTE System Toolbox™. The workflow follows these steps:

Use the Convolutional Encoder block to encode data, and how to compare the hardware-friendly design with the results from LTE System Toolbox™. The workflow follows these steps:

Use the Gold Sequence Generator block to generate multiple sequences in parallel for use in channel estimation.

Use the CRC Decoder block to check encoded data, and how to compare the hardware-friendly design with the results from LTE System Toolbox™. The workflow follows these steps:

Use the OFDM Demodulator block to return the LTE resource grid from streaming samples. You can generate HDL code from this block.

Design a LTE cell search and MIB recovery system optimized for HDL code generation and hardware implementation.

Verify a hardware-targeted Turbo Decoder design using frames of data from MATLAB®.

Implement a variable-size FFT using a single FFT core.

Filtered OFDM (F-OFDM) applies a filter to the symbols after the IFFT in the transmitter to improve bandwidth while maintaining the orthogonality of the complex symbols. This example

Gives an overview of a hardware design for an LTE cell search and MIB recovery system.

The LTE Cell Search and MIB Recovery example uses frequency division duplexing (FDD) mode. This example extends the LTE Cell Search and MIB Recovery example to add time division duplexing

Verify a hardware-targeted Turbo Decoder design using streaming data from MATLAB®.

How multiple Channel State Information (CSI) processes provide the network with feedback for Coordinated Multipoint (CoMP) operation. In this example User Equipment (UE) data is

Demonstrates how to measure the Channel Quality Indicator (CQI) reporting performance using the LTE System Toolbox™ under conformance test conditions as defined in TS36.101 Section

How an over-the-air LTE waveform can be generated and analyzed using the LTE System Toolbox™, the Instrument Control Toolbox™ and a Keysight Technologies® RF signal generator and

Generate an Enhanced Physical Downlink Control Channel (EPDCCH) transmission using the LTE System Toolbox™.

Demonstrates how to measure the Rank Indicator (RI) reporting performance using the LTE System Toolbox™ under conformance test conditions as defined in TS36.101 Section 9.5.1.1 [ 1 ].

Use the LTE System Toolbox™ to create a frame worth of data, pass it through a fading channel and perform channel estimation and equalization. Two figures are created illustrating the

Generate a test model using LTE System Toolbox™.

How the LTE System Toolbox™ can be used to fully synchronize, demodulate and decode a live eNodeB signal. Before the User Equipment (UE) can communicate with the network it must perform cell

How an over-the-air LTE waveform can be captured and analyzed using the LTE System Toolbox™, the Instrument Control Toolbox™ and an RF signal analyzer.

In the LTE system, a UE must detect and monitor the presence of multiple cells and perform cell reselection to ensure that it is "camped" on the most suitable cell. A UE "camped" on a particular

How the LTE System Toolbox™ can be used to create Physical Downlink Shared Channel (PDSCH) Bit Error Rate (BER) curves under Additive White Gaussian Noise (AWGN) in a simple Graphical User

Generate an HSDPA FRC H-Set using LTE System Toolbox™.

Measures the EVM within a downlink Reference Measurement Channel (RMC) signal and a downlink Test Model (E-TM) signal, according to the EVM measurement requirements specified in TS

Demonstrates how to measure the Physical Downlink Shared Channel (PDSCH) throughput of a transmit/receive chain using the LTE System Toolbox™.

Generate a time domain waveform containing a Physical Downlink Shared Channel (PDSCH), corresponding Physical Downlink Control Channel (PDCCH) transmission and the Physical Control

Demonstrates Hybrid Automatic Repeat reQuest (Hybrid-ARQ) Incremental Redundancy (IR) in the Downlink Shared Channel (DL-SCH) transmission using the LTE System Toolbox™.

How the Adjacent Channel Leakage Power Ratio (ACLR) can be measured within a downlink Reference Measurement Channel (RMC) signal using the LTE System Toolbox™.

Use the Time Difference Of Arrival (TDOA) positioning approach in conjunction with the Release 9 Positioning Reference Signal (PRS) to calculate the position of a User Equipment (UE)

Demonstrates the effect of inter-cell interference on PDSCH throughput. A serving cell and two interfering eNodeBs are considered. The conditions specified in TS 36.101, Section

The example aids understanding of the control region used in an LTE downlink subframe and its channel structure by showing how a Downlink Control Information (DCI) message is generated and

Build an LTE compliant OFDM Modulator and Detector for implementation with HDL Coder™, and use LTE System Toolbox™ to verify the HDL implementation model.

How the LTE System Toolbox™ can be used to model a TS36.104 "PRACH Detection Requirements" conformance test. The probability of correct detection of the Physical Random Access Channel

How the LTE System Toolbox™ can be used to model a TS36.104 Physical Random Access Channel (PRACH) false alarm probability conformance test. In this case the probability of erroneous

Generate a receiver operating characteristic (ROC) curve of a radar system using a Monte-Carlo simulation. The receiver operating characteristic determines how well the system can

The example presents a scenario consisting of a rotating monostatic radar and a target with a radar cross-section described by a Swerling 1 model. In this example, the radar and target are

The example presents a scenario of a rotating monostatic radar and a target having a radar cross-section described by a Swerling 3 model. In this example, the radar and target are stationary.

The example presents a scenario of a rotating monostatic radar and a target having a radar cross-section described by a Swerling 4 model. In this example, the radar and target are stationary.

The example illustrates the use of Swerling target models to describe the fluctuations in radar cross-section. The scenario consists of a rotating monostatic radar and a target having a

Create a custom cardioid microphone, and plot the power response pattern at 500 and 800 Hz.

Implements an adaptive DPCA pulse canceller for clutter and interference rejection. The scenario is identical to the one in docid:phased_ug.bsx47qr except that a stationary broadband

Implements a DPCA pulse canceller for clutter rejection. Assume you have an airborne radar platform modeled by a six-element ULA operating at 4 GHz. The array elements are spaced at one-half

Create and beamform a 10-element ULA. Assume the carrier frequency is 1 GHz. Set the array element spacing to be one-half the carrier wavelength.

Display the angle-Doppler response of a stationary array to a stationary target. The array is a six-element uniform linear array (ULA) located at the global origin (0,0,0) . The target is

This scenario is identical to the one presented in docid:phased_ug.bsyvlco . You can run the code for both examples to compare the ADPCA pulse canceller with the SMI beamformer. The example

Estimate angles of arrival from two separate signal sources when both angles fall within the main lobe of the array response a uniform linear array (ULA). In this case, a beamscan DOA

Illustrates the nonzero Doppler shift exhibited by a stationary target in the presence of array motion. In general, this nonzero shift complicates the detection of slow-moving targets

Use an LCMV beamformer to point a null of the array response in the direction of an interfering source. The array is a 10-element uniform linear array (ULA). By default, the ULA elements are

Perform wideband conventional time-delay beamforming with a microphone array of omnidirectional elements. Create an acoustic (pressure wave) chirp signal. The chirp signal has a

Plot the response of an acoustic microphone element and an array of microphone elements to validate the performance of a beamformer. The array must maintain an acceptable array pattern

Use the phased.SumDifferenceMonopulseTracker System object™ to track a moving target. The phased.SumDifferenceMonopulseTracker tracker solves for the direction of a target from

Illustrates how to apply digital beamforming to a narrowband signal received by an antenna array. Three beamforming algorithms are illustrated: the phase shift beamformer (PhaseShift),

Determine the position of the source of a wideband signal using generalized cross-correlation (GCC) and triangulation. For simplicity, this example is confined to a two-dimensional

Convert an azimuth angle of and an elevation angle of to a broadside angle.

Illustrates microphone array beamforming to extract desired speech signals in an interference-dominant, noisy environment. Such operations are useful to enhance speech signal quality

Beamform a plane wave arriving at a 10 element ULA of isotropic antenna elements. The operating frequency of the array is 100 MHz.

Illustrates using beamscan, MVDR, and MUSIC for direction of arrival (DOA) estimation. Beamscan is a technique that forms a conventional beam and scans it over directions of interest to

Compute the time-domain response of a simple bandpass filter:

Calculate the cascaded gain, noise figure, and 3rd order intercept (IP3) of a chain of RF stages. Each stage is represented by a frequency independent "black box", specified with its own

Design a broadband matching network between a resistive source and inductive load using optimization with direct search methods.

Extract the S-parameters of a Device Under Test (DUT) using the deembedsparams function.

Use the RF Toolbox to determine the input and output matching networks that maximize power delivered to a 50-Ohm load and system. Designing input and output matching networks is an important

Use RF Toolbox™ to model a differential high-speed backplane channel using rational functions. This type of model is useful to signal integrity engineers, whose goal is to reliably connect

Verify the design of input and output matching networks for a Low Noise Amplifier (LNA) by plotting its gain and noise.

Use RF Toolbox™ functions to calculate the TDR (Time-Domain Reflectometry) and TDT (Time-Domain Transmission) of a differential high-speed backplane channel.

Design broadband matching networks for a low noise amplifier (LNA). In an RF receiver front end, the LNA is commonly found immediately after the antenna or after the first bandpass filter

Use Simulink® to simulate a differential high-speed backplane channel. The example first reads a Touchstone® data file that contains single-ended 4-port S-parameters for a differential

Create and use RF Toolbox™ circuit objects. In this example, you create three circuit (rfckt) objects: two transmission lines and an amplifier. You visualize the amplifier data using RF

Perform statistical analysis on a set of S-parameter data files. First, read twelve S-parameter files representing twelve similar RF filters into the MATLAB workspace and plot them. Next,

Use RF Toolbox™ functions to generate a Verilog-A module that models the high-level behavior of a high-speed backplane. First, it reads the single-ended 4-port S-parameters for a

Use RF Toolbox™ to import N-port S-parameters representing high-speed backplane channels, and converts 16-port S-parameters to 4-port S-parameters to model the channels and the

Write out the data in rfckt objects you create in the MATLAB® workspace into an industry-standard data file: Touchstone®. You can use these files in third-party tools.

Build and simulate an RC tree circuit using the RF Toolbox.

Create an rfckt.mixer object and plot the mixer spurs of that object.

Manipulate RF data directly using rfdata objects. First, you create an rfdata.data object by reading in the S-parameters of a two-port passive network stored in the Touchstone® format data

Use the 'NPoles' parameter to improve the quality of the output of rationalfit. By default, the rationalfit function uses 48 or fewer poles to find the rational function that best matches the

Use the 'Weight' parameter to improve the quality of the output of rationalfit. By default, the rationalfit function minimizes the absolute error between the data and the rational

Use the 'DelayFactor' parameter to improve the quality of the output of rationalfit.

Avoid aliasing when downsampling a signal. If a discrete-time signal's baseband spectral support is not limited to an interval of width radians, downsampling by results in aliasing.

Use downsample to obtain the phases of a signal. Downsampling a signal by M can produce M unique phases. For example, if you have a discrete-time signal, x, with x(0) x(1) x(2) x(3), ..., the M

Many measurements involve data collected asynchronously by multiple sensors. If you want to integrate the signals, you have to synchronize them. The Signal Processing Toolbox™ has

People predisposed to blood clotting are treated with warfarin, a blood thinner. The international normalized ratio (INR) measures the effect of the drug. Larger doses increase the INR and

Assess the order of an autoregressive model using the partial autocorrelation sequence. For these processes, you can use the partial autocorrelation sequence to help with model order

Perform and interpret basic frequency-domain signal analysis. The example discusses the advantages of using frequency-domain versus time-domain representations of a signal and

Create a signal consisting of three noisy sinusoids and a chirp, sampled at 200 kHz for 0.1 second. The frequencies of the sinusoids are 1 kHz, 10 kHz, and 20 kHz. The sinusoids have different

Resolve closely spaced sine waves using subspace methods. Subspace methods assume a harmonic model consisting of a sum of sine waves, possibly complex, in additive noise. In a

In general terms, one way of estimating the PSD of a process is to simply find the discrete-time Fourier transform of the samples of the process (usually done on a grid with an FFT) and

Use the discrete Fourier transform to construct a linear regression model for a time series. The time series used in this example is the monthly number of accidental deaths in the United

Obtain nonparametric power spectral density (PSD) estimates equivalent to the periodogram using fft . The examples show you how to properly scale the output of fft for even-length inputs,

Reduce bias and variability in the periodogram. Using a window can reduce the bias in the periodogram, and using windows with averaging can reduce variability.

The modified periodogram windows the time-domain signal prior to computing the DFT in order to smooth the edges of the signal. This has the effect of reducing the height of the sidelobes or

An improved estimator of the PSD is the one proposed by Welch. The method consists of dividing the time series data into (possibly overlapping) segments, computing a modified periodogram of

The following sections discuss the performance of the periodogram with regard to the issues of leakage, resolution, bias, and variance.

One application of Welch's method is nonparametric system identification. Assume that H is a linear, time invariant system, and x ( n ) and y ( n ) are the input to and output of H , respectively.

Use the cross spectrum to obtain the phase lag between sinusoidal components in a bivariate time series. The example also uses the magnitude-squared coherence to identify significant

Measure the power of deterministic periodic signals. Although continuous in time, periodic deterministic signals produce discrete power spectra.

Use zero padding to obtain an accurate estimate of the amplitude of a sinusoidal signal. Frequencies in the discrete Fourier transform (DFT) are spaced at intervals of F_s/N , where F_s is the

Generate 1024 samples of a chirp sampled at 1024 kHz. The chirp has an initial frequency of 50 kHz and reaches 100 kHz at the end of the sampling. Add white Gaussian noise such that the

Perform and interpret basic time-frequency signal analysis. In practical applications, many signals are nonstationary. This means that their frequency-domain representation (their

The periodogram can be interpreted as filtering a length L signal, x_L(n) , through a filter bank (a set of filters in parallel) of L FIR bandpass filters. The 3 dB bandwidth of each of these

The magnitude-squared coherence between two signals x ( n ) and y ( n ) is

Use wavelets to analyze electrocardiogram (ECG) signals. ECG signals are frequently nonstationary meaning that their frequency content changes over time. These changes are the events of

Fourier-domain coherence is a well-established technique for measuring the linear correlation between two stationary processes as a function of frequency on a scale from 0 to 1. Because

Use the continuous wavelet transform (CWT) to analyze signals jointly in time and frequency.

Add an orthogonal quadrature mirror filter (QMF) pair to the Wavelet Toolbox™. While Wavelet Toolbox™ already contains many of the most widely used orthogonal QMF families, including the

Use wavelets to detect changes in the variance of a process. Changes in variance are important because they often indicate that something fundamental has changed about the data-generating

To construct and use orthogonal and biorthogonal filter banks with the Wavelet Toolbox software. The classic critically sampled two-channel filter bank is shown in the following figure.

Use lifting to progressively change the properties of a perfect reconstruction filter bank. The following figure shows the three canonical steps in lifting: split, predict, and update.

There are a number of different variations of the wavelet transform. This example focuses on the maximal overlap discrete wavelet transform (MODWT). The MODWT is an undecimated wavelet

Use the continuous wavelet transform (CWT) to analyze signals jointly in time and frequency. The example discusses the localization of transients where the CWT outperforms the short-time

Use wavelet coherence and the wavelet cross-spectrum to identify time-localized common oscillatory behavior in two time series. The example also compares the wavelet coherence and

Use wavelet synchrosqueezing to obtain a higher resolution time-frequency analysis. The example also shows how to extract and reconstruct oscillatory modes in a signal.

The difference between the discrete wavelet transform ( DWT ) and the continuous wavelet transform ( CWT ).

Reconstruct a frequency-localized approximation of Kobe earthquake data. Extract information from the CWT for frequencies in the range of [0.030, 0.070] Hz.

Uses wavefun to demonstrate how the number of vanishing moments in a biorthogonal filter pair affects the smoothness of the corresponding dual scaling function and wavelet. While this

The example shows how to denoise a signal using interval-dependent thresholds.

Denoise a 1-D signal using cycle spinning and the shift-variant orthogonal nonredundant wavelet transform. The example compares the results of the two denoising methods.

Discusses the problem of signal recovery from noisy data. The general denoising procedure involves three steps. The basic version of the procedure follows the steps described below:

Denoise an image using cycle spinning with 8^{2} = 64 shifts.

The purpose of this example is to show the features of multivariate denoising provided in Wavelet Toolbox™.

Use wavelets to denoise signals and images. Because wavelets localize features in your data to different scales, you can preserve important signal or image features while removing noise.

The purpose of this example is to show the features of multiscale principal components analysis (PCA) provided in the Wavelet Toolbox™.

Starting from a given image, the goal of true compression is to minimize the number of bits needed to represent it, while storing information of acceptable quality. Wavelets contribute to

The purpose of this example is to show how to compress an image using two-dimensional wavelet analysis. Compression is one of the most important applications of wavelets. Like de-noising,

Demonstrates the impact of changing the TGac delay profile, and it shows how fluorescent lighting affects the time response of the channel.

Perform basic VHT data recovery. It also shows how to recover VHT data when the received signal has a carrier frequency offset. Similar procedures can be used to recover data with the HT and

Build non-HT PPDUs by using the waveform generator function or by building each field individually.

How the performance of an IEEE® 802.11ac™ link can be improved by beamforming the transmission when channel state information is available at the transmitter.

Build HT PPDUs by using the waveform generator function or by building each field individually.

Create a basic WLAN link model using WLAN System Toolbox™. An IEEE® 802.11ac™ [ 1 ] VHT packet is created, passed through a TGac channel. The received signal is equalized and decoded in order to

Generate a multi-user VHT waveform from individual components. It also shows how to generate the same waveform by using the wlanWaveformGenerator function. The data fields from the two

Build VHT PPDUs by using the waveform generator function or by building each field individually.

Build S1G PPDUs by using the waveform generator function.

The transmit and receive processing for a 802.11ac™ multi-user downlink transmission over a fading channel. The example uses linear precoding techniques based on a

Build DMG PPDUs by using the waveform generator function.

Simulate an IEEE® 802.11n™ HT link in Simulink® with WLAN System Toolbox™.

Measure the packet error rate of an IEEE® 802.11ac™ VHT link using an end-to-end simulation with a fading TGac channel model and additive white Gaussian noise.

Simulate a test to measure the receiver minimum input sensitivity as specified in Section 22.3.19.1 of the IEEE® 802.11ac™ standard [ 1 ].

Measure the packet error rate of an IEEE® 802.11n™ HT link using an end-to-end simulation with a fading TGn channel model and additive white Gaussian noise.

Measure packet error rates of IEEE® 802.11p™ and 802.11a™ links using an end-to-end simulation with a fading channel model and additive white Gaussian noise. For similar link parameters,

Measure the packet error rate of an IEEE® 802.11ah™ S1G short preamble link using an end-to-end simulation with a fading TGah indoor channel model and additive white Gaussian noise.

Measure the packet error rate of an IEEE® 802.11ad™ DMG OFDM PHY link using an end-to-end simulation with an AWGN channel.

Dynamic rate control by varying the Modulation and Coding scheme (MCS) of successive packets transmitted over a frequency selective multipath fading channel.

Measure the packet error rate of an IEEE® 802.11ad™ DMG single carrier (SC) PHY AWGN link using an end-to-end simulation.

Measure the packet error rate of an IEEE® 802.11ad™ DMG control PHY AWGN link using an end-to-end simulation.

Transmit a VHT waveform through a noisy MIMO channel. Extract the L-SIG, VHT-SIG-A, and VHT-SIG-B fields and verify that they were correctly recovered.

Generate, transmit, recover and view a VHT MIMO waveform.

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