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.

Control each individual element in a linear or rectangular array. You can use this technique to change the size and tilt of the antenna, or to model dead elements etc. with individual elements

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 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 reciving

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

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

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 /4 (open-short microstrip

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

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

Calculate an antenna's field strength on flat earth and display it on the web map. The example also shows how to export the contour lines to KML, which can then be visualized on Earth browsers

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

Analyzes the effect of mutual coupling on Multiple Input Multiple Output (MIMO) communications. The transmitter and receiver have two dipole antenna elements each. The channel is

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

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

Analyzes the impedance behavior of a center-fed dipole antenna at varying mesh resolution/size and at a single frequency of operation. The resistance and reactance of the dipole are

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 ) can

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

Measure total harmonic distortion and noise level of audio input and output devices.

Presents a utility that can be used to analyze the timing performance of signal processing algorithms designed for real-time streaming applications.

Measure the latency introduced when using the audio device reader and audio device writer in MATLAB or Simulink. The procedure presented here allows you to tune parameters that affect

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

Use UDP to send information from a digital audio workstation (DAW) to MATLAB using a generated audio plugin. The information can used to perform visualization in real time in MATLAB on

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.

Implement a real time audio "phaser" effect which can be tuned by a user interface (UI).

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.

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

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

Plot a Gray-coded 8-QAM constellation.

Plot a PSK constellation having 16 points.

Filter a 16-QAM signal using a pair of square root raised cosine matched filters. Plot the eye diagram and scatter plot of the signal. After passing the signal through an AWGN channel,

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

Plot a QAM constellation having 32 points.

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

Use the convolutional encoder and Viterbi decoder System objects to simulate a punctured coding system. The complexity of a Viterbi decoder increases rapidly with the code rate.

A digital communications system using QPSK modulation. The example uses Communications System objects to simulate the QPSK transceiver. In particular, this example illustrates methods

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

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

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

Use the COMMSCOPE.EYEDIAGRAM object to perform eye diagram measurements on simulated signals.

Simulate multiple-input multiple-output (MIMO) multipath fading channels based on the IEEE® 802.16 channel models for fixed wireless applications. The example uses a MIMO multipath

Simulate multipath fading channels based on the COST 207 and GSM/EDGE channel models, using the Rayleigh and Rician multipath fading channel objects and the Doppler objects from

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 constellation diagrams to view QPSK transmitted and received signals which are pulse shaped with a raised cosine filter.

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

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

This examples shows you how to filter an ECG signal that has high-freqquency noise, and remove the noise by low-pass filtering.

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.

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

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.

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

Model a dual-tone multifrequency (DTMF) generator and receiver. The model includes a bandpass filter bank receiver, a spectrogram plot of the generated tones, and a shift register to store

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®

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

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 Fixed-Point Converter App to convert an IIR filter from a floating-point to a fixed-point implementation. Second-order sections (also referred as biquadratic) structures work

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.

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

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

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

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.

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

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.

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

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, according to the EVM measurement requirements specified in TS 36.104, Annex E [ 1 ].

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

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 TS36.101, Section

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

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

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

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

Demonstrates the multicodeword transmission and reception in the uplink.

This examples shows how to model a point-to-point MIMO-OFDM system with beamforming. The combination of multiple-input-multiple-output (MIMO) and orthogonal frequency division

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

Form an antenna array with a custom antenna radiation pattern and then analyze the array's response pattern. Such a pattern can be either from measurement or from simulation.

Use Phased Array System Toolbox™ to solve some array synthesis problems.

Assess the performance of both coherent and noncoherent systems using receiver operating characteristic (ROC) curves. It assumes the detector operates in an additive complex white

Discusses the detection of a deterministic signal in complex, white, Gaussian noise. This situation is frequently encountered in radar, sonar and communication applications.

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

The design of a moving target indication (MTI) radar to mitigate the clutter and identify moving targets. For a radar system, clutter refers to the received echoes from environmental

When you create antenna arrays such as a uniform linear array (ULA), you can use antennas that are built into Phased Array System Toolbox™. Alternatively, you can use Antenna Toolbox™

Gives a brief introduction to space-time adaptive processing (STAP) techniques and illustrates how to use Phased Array System Toolbox™ to apply STAP algorithms to the received pulses.

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),

Design a monostatic pulse radar to estimate the target range. A monostatic radar has the transmitter colocated with the receiver. The transmitter generates a pulse which hits the target and

Illustrates how to use the ambiguity function to analyze waveforms. It compares the range and Doppler capability of several basic waveforms, e.g., the rectangular waveform and the linear

Model an automotive adaptive cruise control system using the frequency modulated continuous wave (FMCW) technique. This example performs range and Doppler estimation of a moving

Illustrates several high-resolution direction of arrival (DOA) estimation techniques. It introduces variants of the MUSIC, root-MUSIC, ESPRIT and root-WSF algorithms and discusses

Introduces constant false alarm rate (CFAR) detection and shows how to use CFARDetector and CFARDetector2D in the Phased Array System Toolbox™ to perform cell averaging CFAR detection.

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

Model a 77 GHz 2x4 antenna array for Frequency-Modulated Continuous-Wave (FMCW) radar applications. The presence of antennas and antenna arrays in and around vehicles has become a

Detect a signal in complex, white Gaussian noise using multiple received signal samples. A matched filter is used to take advantage of the processing gain.

Model and visualize a variety of antenna array geometries with Phased Array System Toolbox™. These geometries can also be used to model other kind of arrays, such hydrophone arrays and

Compares triangle sweep FMCW and MFSK waveforms used for simultaneous range and speed estimation for multiple targets. The MFSK waveform is specifically designed for automotive radar

Specify a phased.ReceiverPreamp System object™ with a gain of 20 dB, a noise figure of 5 dB, and a reference temperature of 290 degrees kelvin.

Model subarrays, commonly used in modern phased array systems, using Phased Array System Toolbox™ and perform analyses.

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 it's 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 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

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

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

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,

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

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

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

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

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.

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

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

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.

Many measurements involve data collected asynchronously by multiple sensors. If you want to integrate the signals and study them in tandem, you have to synchronize them. Use xcorr for that

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,

Design and implement an FIR filter using two command line functions, fir1 and designfilt, and the interactive Filter Designer app.

You want to differentiate a signal without increasing the noise power. MATLAB®'s function diff amplifies the noise, and the resulting inaccuracy worsens for higher derivatives. To fix

Spectral coherence helps identify similarity between signals in the frequency domain. Large values indicate frequency components common to the signals.

Use findpeaks to find values and locations of local maxima in a set of data.

The Hilbert transform estimates the instantaneous frequency of a signal for monocomponent signals only. A monocomponent signal is described in the time-frequency plane by a single

The zplane function plots poles and zeros of a linear system. For example, a simple filter with a zero at -1/2 and a complex pole pair at and is

Use the cross-correlation sequence to estimate the phase lag between two sine waves. The theoretical cross-correlation sequence of two sine waves at the same frequency also oscillates at

The presence of noise often makes it difficult to determine the spectral content of a signal. Frequency analysis can help in such cases.

Introduce autocorrelation into a white noise process by filtering. When we introduce autocorrelation into a random signal, we manipulate its frequency content. A moving average filter

Measured signals can show overall patterns that are not intrinsic to the data. These trends can sometimes hinder the data analysis and must be removed.

Several ways to simulate the output of a sample-and-hold system by upsampling and filtering a signal.

Use the cross-correlation sequence to detect the time delay in a noise-corrupted sequence. The output sequence is a delayed version of the input sequence with additive white Gaussian

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.

Alternating current in the United States and several other countries oscillates at a frequency of 60 Hz. Those oscillations often corrupt measurements and have to be subtracted.

Measurement uncertainty and noise sometimes make it difficult to spot oscillatory behavior in a signal, even if such behavior is expected.

Find and plot the cross-correlation sequence between two moving average processes. The example compares the sample cross-correlation with the theoretical cross-correlation. Filter an

Create confidence intervals for the autocorrelation sequence of a white noise process. Create a realization of a white noise process with length samples. Compute the sample

The impulse response of a digital filter is the output arising from the unit impulse sequence defined as

Sometimes data exhibit unwanted transients, or spikes. Median filtering is a natural way to eliminate them.

The power of a signal is the sum of the absolute squares of its time-domain samples divided by the signal length, or, equivalently, the square of its RMS level. The function bandpower allows

It is often difficult to characterize oscillatory behavior in data by looking at time measurements. Spectral analysis can help determine if a signal is periodic and measure the different

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.

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.

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

Create a signal consisting of exponentially weighted sine waves. The signal has two 25-Hz components -- one centered at 0.2 seconds and one centered at 0.5 seconds. It also has two 70-Hz

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

The 'peppers' image is corrupted with Gaussian additive noise with and cleaned using the GFM and GLG models.

Use wavelet cross-correlation to measure similarity between two signals at different scales.

The 'peppers' image is corrupted with Gaussian additive noise with and cleaned using INLA.

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

The GLG model and the GFM model are both fitted to the wavelet coefficients of the 'lena' image. The fitted densities are compared to the observed distribution of coefficients

Create and visualize a dictionary consisting of a Haar wavelet down to level 2.

how to perform orthogonal matching pursuit on a 1-D input signal that contains a cusp.

Compare matching pursuit with a nonlinear approximation in the discrete Fourier transform basis. The data is electricity consumption data collected over a 24-hour period. The example

Obtain the nondecimated (stationary) wavelet transform of a noisy frequency-modulated signal.

Obtain the 2-D DWT of an input image.

Obtain the wavelet packet transform of a 1-D signal. The example also demonstrates that frequency ordering is different from Paley ordering.

Denoise a signal using discrete wavelet analysis.

Use wfilters, wavefun, and wpfun to obtain the filters, wavelet, or wavelet packets corresponding to a particular wavelet family. You can visualize 2-D separable wavelets with wavefun2.

Perform time-frequency analysis using the continuous wavelet transform (CWT). Continuous wavelet analysis provides a time-scale/time-frequency analysis of signals and images. The

Recover content from a HT format waveform.

Generate S1G, VHT, HT-mixed, and non-HT format waveforms. Vary configuration parameters and plot the waveforms to highlight differences in waveforms and sample rates.

Demonstrates passing WLAN VHT, HT, and non-HT format waveforms through appropriate fading channel models. When simulating a WLAN communications link, viable options for channel

Create HT configuration objects. It also shows how to change the default property settings by using dot notation or by overriding the default settings by using Name,Value pairs when

Recover contents from a VHT format waveform.

Steps through recovery of non-HT format waveform content.

Create non-HT configuration objects. It also shows how to change the default property settings by using dot notation or by overriding the default settings by using Name,Value pairs when

Recovery configuration objects are used to specify receiver algorithms and settings to use for recovery. This example shows how to create recovery configuration objects. It also shows how

Create VHT configuration objects. It also shows how to change the default property settings by using dot notation or by overriding the default settings by using Name,Value pairs when

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 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

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,

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