Signal Processing Toolbox. User's Guide

Filtering, Linear Systems and Transforms Overview
	Filter Implementation
		Convolution and Filtering
		Filters and Transfer Functions
		Filtering with the filter Function
	The filter Function
	Multirate Filter Bank Implementation
	Frequency Domain Filter Implementation
	Anti-Causal, Zero-Phase Filter Implementation
	Impulse Response
	Frequency Response
		Digital Domain
		Analog Domain
	Phase Response
	Group Delay and Phase Delay
	Zero-Pole Analysis
	Discrete-Time System Models
		Transfer Function
		Zero-Pole-Gain
		State Space
		Partial Fraction Expansion (Residue Form)
		Second-Order Sections (SOS)
		Lattice Structure
		Convolution Matrix
	Continuous-Time System Models
	Linear System Transformations
	Discrete Fourier Transform
Filter Design and Implementation
	Filter Requirements and Specification
	IIR Filter Design
		IIR vs. FIR Filters
		Classical IIR Filters
		Other IIR Filters
		IIR Filter Method Summary
		Classical IIR Filter Design Using Analog Prototyping
		Comparison of Classical IIR Filter Types
	FIR Filter Design
		FIR vs. IIR Filters
		FIR Filter Summary
		Linear Phase Filters
		Windowing Method
		Multiband FIR Filter Design with Transition Bands
		Constrained Least Squares FIR Filter Design
		Arbitrary-Response Filter Design
	Special Topics in IIR Filter Design
		Classic IIR Filter Design
		Analog Prototype Design
		Frequency Transformation
		Filter Discretization
	Filtering Data with Signal Processing Toolbox Software
	Selected Bibliography
Designing a Filter in fdesign — Process Overview
	Process Flow Diagram and Filter Design Methodology
		Exploring the Process Flow Diagram
		Selecting a Response
		Selecting a Specification
		Selecting an Algorithm
		Customizing the Algorithm
		Designing the Filter
		Design Analysis
		Realize or Apply the Filter to Input Data
Designing a Filter in the Filter Builder GUI
	Filter Builder Design Process
		Introduction to Filter Builder
		Design a Filter Using Filter Builder
		Select a Response
		Select a Specification
		Select an Algorithm
		Customize the Algorithm
		Analyze the Design
		Realize or Apply the Filter to Input Data
	Compensate for Delay and Distortion Introduced by Filters
	Comparison of Analog IIR Lowpass Filters
	Frequency Response of Lowpass Bessel Filter
	Speaker Crossover Filters
Filter Designer: A Filter Design and Analysis App
	Filter Design Methods
		Advanced Filter Design Methods
	Using the Filter Designer App
	Analyzing Filter Responses
	Filter Designer App Panels
	Getting Help
	Getting Started with Filter Designer
		Choosing a Response Type
		Choosing a Filter Design Method
		Setting the Filter Design Specifications
		Computing the Filter Coefficients
		Analyzing the Filter
		Editing the Filter Using the Pole-Zero Editor
		Converting the Filter Structure
		Exporting a Filter Design
		Generating a C Header File
		Generating MATLAB Code
		Managing Filters in the Current Session
		Saving and Opening Filter Design Sessions
	Importing a Filter Design
		Import Filter Panel
		Filter Structures
	FIR Bandpass Filter with Asymmetric Attenuation
	Arbitrary Magnitude Filter
Filter Visualization Tool
	Modifying the Axes
	Modifying the Plot
	Controlling FVTool from the MATLAB Command Line
Statistical Signal Processing
	Correlation and Covariance
		Background Information
		Using xcorr and xcov Functions
		Bias and Normalization
		Multiple Channels
	Spectral Analysis
		Background Information
		Spectral Estimation Method
	Nonparametric Methods
		Periodogram
		Performance of the Periodogram
		The Modified Periodogram
		Welch's Method
		Bias and Normalization in Welch's Method
		Multitaper Method
		Cross-Spectral Density Function
		Transfer Function Estimate
		Coherence Function
	Parametric Methods
		Yule-Walker AR Method
		Burg Method
		Covariance and Modified Covariance Methods
	MUSIC and Eigenvector Analysis Methods
		Eigenanalysis Overview
		Frequency Estimator Functions
	Selected Bibliography
Special Topics
	Windows
		Why Use Windows?
		Available Window Functions
		Graphical User Interface Tools
		Basic Shapes
	Get Started with Window Designer
		Window Parameters
		Window Designer Menus
	Generalized Cosine Windows
	Kaiser Window
		Kaiser Windows in FIR Design
	Chebyshev Window
	Parametric Modeling
		What is Parametric Modeling
		Available Parametric Modeling Functions
		Time-Domain Based Modeling
		Frequency-Domain Based Modeling
	Cepstrum Analysis
	Median Filtering
	Communications Applications
		Modulation
		Demodulation
		Voltage Controlled Oscillator
	Deconvolution
	Chirp Z-Transform
	Discrete Cosine Transform
	Hilbert Transform
	Walsh-Hadamard Transform
	Walsh-Hadamard Transform for Spectral Analysis and Compression of ECG Signals
	Eliminate Outliers Using Hampel Identifier
	Selected Bibliography
Convolution and Correlation
	Linear and Circular Convolution
	Confidence Intervals for Sample Autocorrelation
	Residual Analysis with Autocorrelation
	Autocorrelation of Moving Average Process
	Cross-Correlation of Two Moving Average Processes
	Cross-Correlation of Delayed Signal in Noise
	Cross-Correlation of Phase-Lagged Sine Wave
Multirate Signal Processing
	Downsampling — Signal Phases
	Downsampling — Aliasing
	Filtering Before Downsampling
	Upsampling — Imaging Artifacts
	Filtering After Upsampling — Interpolation
	Simulate a Sample-and-Hold System
	Change Signal Sample Rate
	Resampling
		resample Function
		decimate and interp Functions
		upfirdn Function
		spline Function
Spectral Analysis
	Power Spectral Density Estimates Using FFT
	Bias and Variability in the Periodogram
	Cross Spectrum and Magnitude-Squared Coherence
	Amplitude Estimation and Zero Padding
	Significance Testing for Periodic Component
	Frequency Estimation by Subspace Methods
	Frequency-Domain Linear Regression
	Measure Total Harmonic Distortion
	Measure Mean Frequency, Power, Bandwidth
	Periodogram of Data Set with Missing Samples
	Welch Spectrum Estimates
Spectrum Object to Function Replacement
	Nonparametric Spectrum Object to Function Replacement
		Periodogram PSD Object to Function Replacement Syntax
		Periodogram MSSPECTRUM Object to Function Replacement Syntax
		Welch PSD Object to Function Replacement Syntax
		Welch MSSPECTRUM Object to Function Replacement Syntax
		Multitaper PSD Object to Function Replacement Syntax
	Autoregressive PSD Object to Function Replacement Syntax
	Subspace Pseudospectrum Object to Function Replacement Syntax
Time-Frequency Analysis
	FFT-Based Time-Frequency Analysis
	Spectrogram Computation with Signal Processing Toolbox
		Functions for Spectrogram Computation
		STFT and Spectrogram Definitions
		Compare spectrogram Function and STFT Definition
		Compare spectrogram and stft Functions
		Compare spectrogram and pspectrum Functions
		Compute Centered and One-Sided Spectrograms
		Compute Segment PSDs and Power Spectra
	Cross-Spectrogram of Complex Signals
Time-Frequency Gallery
	Time-Frequency Gallery
		Short-Time Fourier Transform (Spectrogram)
		Continuous Wavelet Transform (Scalogram)
		Wigner-Ville Distribution
		Reassignment and Synchrosqueezing
		Constant-Q Gabor Transform
		Data-Adaptive Methods and Multiresolution Analysis
Signal Data Set Management
	Manage Data Sets for Machine Learning and Deep Learning Workflows
		Common AI Tasks
		Data Organization
		Data Preprocessing
		Workflow Scenarios
		Available Data Sets
Linear Prediction
	Prediction Polynomial
	Formant Estimation with LPC Coefficients
	AR Order Selection with Partial Autocorrelation Sequence
Transforms
	Complex Cepstrum — Fundamental Frequency Estimation
	Analytic Signal for Cosine
	Envelope Extraction
	Analytic Signal and Hilbert Transform
	Hilbert Transform and Instantaneous Frequency
	Detect Closely Spaced Sinusoids with the Fourier Synchrosqueezed Transform
	Instantaneous Frequency of Complex Chirp
	Single-Sideband Amplitude Modulation
	DCT for Speech Signal Compression
Signal Measurement
	RMS Value of Periodic Waveforms
	Slew Rate of Triangular Waveform
	Duty Cycle of Rectangular Pulse Waveform
	Radar Pulse Compression
	Estimate State for Digital Clock
	Distortion Measurements
	Prominence
	Determine Peak Widths
Vibration Analysis
	Modal Parameters of MIMO System
	Compute and Display Order-RPM Map
	MIMO Stabilization Diagram
	Modal Analysis of Identified Models
Signal Analyzer App
	Using Signal Analyzer App
		App Workflow
		Example: Extract Regions of Interest from Whale Song
	Select Signals to Analyze
		Select Signals from the Workspace Browser
		Filter Signals in the Signal Table
		Delete, Duplicate, and Rename Signals
		Next Step
	Preprocess Signals
		Display
		Delete, Duplicate, and Rename Signals
		Preprocessing Functions
		Preprocessing Actions
		Previous Step
		Next Step
	Explore Signals
		Plot Signals
		View Signals on Multiple Plots
		Move Signals Between Displays
		Visualize Signal Spectra
		Visualize Persistence Spectra
		Visualize Signal Spectrograms
		Visualize Signal Scalograms
		Zoom and Pan Through Signals
		Edit Time Information and Link Displays in Time
		Extract Signal Regions of Interest
		Previous Step
		Next Step
	Measure Signals
		Use Cursors to Measure Signal Data
		Calculate Signal Statistics
		Find and Annotate Signal Peaks
		Previous Step
		Next Step
	Share Analysis
		Copy Displays
		Export Signals
		Generate MATLAB Scripts and Functions
		Save and Load Signal Analyzer Sessions
		Previous Step
	Find Delay Between Correlated Signals
	Resolve Tones by Varying Window Leakage
	Resolve Tones by Varying Window Leakage
	Find Interference Using Persistence Spectrum
	Extract Regions of Interest from Whale Song
	Modulation and Demodulation Using Complex Envelope
	Find and Track Ridges Using Reassigned Spectrogram
	Extract Voices from Music Signal
	Resample and Filter a Nonuniformly Sampled Signal
	Declip Saturated Signals Using Your Own Function
	Compute Envelope Spectrum of Vibration Signal
	Denoise Noisy Doppler Signal
	Edit Sample Rate and Other Time Information
	Data Types Supported by Signal Analyzer
		Numeric Data
		MATLAB Timetables
		timeseries Objects
		Nonuniformly Sampled Signals
		Labeled Signal Sets
	Spectrum Computation in Signal Analyzer
		Spectral Windowing
		Parameter and Algorithm Selection
		Zooming
	Persistence Spectrum in Signal Analyzer
	Spectrogram Computation in Signal Analyzer
		Divide Signal into Segments
		Window the Segments and Compute Spectra
		Display Spectrum Power
	Scalogram Computation in Signal Analyzer
		Divide the Signal into Segments
		Compute the Continuous Wavelet Transform
		Display the Scalogram
	Keyboard Shortcuts for Signal Analyzer
		General Actions
		Multichannel Signals
		Zooming
		Data Cursors
	Signal Analyzer Tips and Limitations
		Select Signals to Analyze
		Preprocess Signals
		Explore Signals
		Share or Reuse Analysis
		Troubleshooting
	Customize Signal Analyzer
		Specify Line Color and Style
		Add or Remove Columns in the Signal Table
		Modify Signal Analyzer Displays
		Signal Analyzer Preferences
Simulation Data Inspector
	View Data in the Simulation Data Inspector
		View Logged Data
		Import Data from the Workspace or a File
		View Complex Data
		View String Data
		View Frame-Based Data
		View Event-Based Data
	Import Data from a CSV File into the Simulation Data Inspector
		Basic File Format
		Multiple Time Vectors
		Signal Metadata
		Import Data from a CSV File
	Microsoft Excel Import, Export, and Logging Format
		Basic File Format
		Multiple Time Vectors
		Signal Metadata
		User-Defined Data Types
		Complex, Multidimensional, and Bus Signals
		Function-Call Signals
		Simulation Parameters
		Multiple Runs
	Configure the Simulation Data Inspector
		Logged Data Size and Location
		Archive Behavior and Run Limit
		Incoming Run Names and Location
		Signal Metadata to Display
		Signal Selection on the Inspect Pane
		How Signals Are Aligned for Comparison
		Colors Used to Display Comparison Results
		Signal Grouping
		Data to Stream from Parallel Simulations
		Options for Saving and Loading Session Files
		Signal Display Units
	How the Simulation Data Inspector Compares Data
		Signal Alignment
		Synchronization
		Interpolation
		Tolerance Specification
		Limitations
	Save and Share Simulation Data Inspector Data and Views
		Save and Load Simulation Data Inspector Sessions
		Share Simulation Data Inspector Views
		Share Simulation Data Inspector Plots
		Create Simulation Data Inspector Report
		Export Data to the Workspace or a File
		Export Video Signal to an MP4 File
	Inspect and Compare Data Programmatically
		Create a Run and View the Data
		Compare Two Signals in the Same Run
		Compare Runs with Global Tolerance
		Analyze Simulation Data Using Signal Tolerances
	Limit the Size of Logged Data
		Limit the Number of Runs Retained in the Simulation Data Inspector Archive
		Specify a Minimum Disk Space Requirement or Maximum Size for Logged Data
		View Data Only During Simulation
		Reduce the Number of Data Points Logged from Simulation
Signal Labeler
	Using Signal Labeler App
		App Workflow
		Example: Label Points and Regions of Interest in Signal
	Import Data into Signal Labeler
		Supported Signal Types
		Choose a Color Scheme
		Specify Time Information
		Import Signals from the MATLAB Workspace
		Import Signals from Files
	Import and Play Audio File Data in Signal Labeler
		Supported Audio File Extensions
		Time Information
		Import Audio Signals from Files or Folder
		Import labeledSignalSet from MATLAB Workspace
		Play Audio Signals and Regions of Interest
	Create or Import Signal Label Definitions
		Import Signal Label Definitions
		Create Label Definitions
		Create Sublabel Definitions
		Edit Label or Sublabel Definitions
		Delete Label or Sublabel Definitions
	Label Signals Interactively or Automatically
		Track and Save Labeling Progress
		Label Signals Manually
		Interactive Member by Member Labeling
		Label Signals Automatically
		Label Signal Peaks Automatically Using Peak Labeler
		Label Speech Regions in Audio Signals Automatically Using Speech Detector or Speech to Text
	Custom Labeling Functions
		Create Custom Labeling Functions
		Add Custom Labeling Functions to the Gallery
		Manage Custom Labeling Functions in Gallery
	Customize Labeling View
		Visualize Signal Spectra and Spectrograms
		Use Spectrogram to Aid Labeling
	Feature Extraction Using Signal Labeler
		Extract Signal Features
		Export Features
		Save Features as Labels
	Dashboard
		View Labeling Progress
		Inspect Label Distributions
	Export Labeled Signal Sets and Signal Label Definitions
		Export Label Definitions
		Export Labeled Signal Sets
	Signal Labeler Usage Tips
		Keyboard Shortcuts
		Troubleshooting
	Label Signal Attributes, Regions of Interest, and Points
	Examine Labeled Signal Set
	Automate Signal Labeling with Custom Functions
	Label Spoken Words in Audio Signals
	Label ECG Signals and Track Progress
	Choose an App to Label Ground Truth Data
Common Applications
	Create Uniform and Nonuniform Time Vectors
	Remove Trends from Data
	Remove the 60 Hz Hum from a Signal
	Remove Spikes from a Signal
	Process a Signal with Missing Samples
	Reconstruct a Signal from Irregularly Sampled Data
	Align Signals with Different Start Times
	Align Signals Using Cross-Correlation
	Align Two Simple Signals
	Find Peaks in Data
	Find a Signal in a Measurement
	Find Periodicity Using Autocorrelation
	Extract Features of a Clock Signal
	Find Periodicity in a Categorical Time Series
	Compensate for the Delay Introduced by an FIR Filter
	Compensate for the Delay Introduced by an IIR Filter
	Take Derivatives of a Signal
	Find Periodicity Using Frequency Analysis
	Detect a Distorted Signal in Noise
	Measure the Power of a Signal
	Compare the Frequency Content of Two Signals
	Detect Periodicity in a Signal with Missing Samples
	Echo Cancelation
	Cross-Correlation with Multichannel Input
	Autocorrelation Function of Exponential Sequence
	Cross-Correlation of Two Exponential Sequences
Featured Examples
	Signal Generation and Visualization
	Signal Smoothing
	Reconstructing Missing Data
	Resampling Uniformly Sampled Signals
	Resampling Nonuniformly Sampled Signals
	Peak Analysis
	Measure Signal Similarities
	Measurement of Pulse and Transition Characteristics
	Analyzing Harmonic Distortion
	Spurious-Free Dynamic Range (SFDR) Measurement
	Extracting Classification Features from Physiological Signals
	Detecting Outbreaks and Significant Changes in Signals
	Finding a Signal in Data
	Filter Design Gallery
	Practical Introduction to Digital Filter Design
	Practical Introduction to Digital Filtering
	Introduction to Filter Designer
	Filter Analysis Using FVTool
	FIR Gaussian Pulse-Shaping Filter Design
	Generating Guitar Chords Using the Karplus-Strong Algorithm
	DFT Estimation with the Goertzel Algorithm
	Discrete Walsh-Hadamard Transform
	Single Sideband Modulation via the Hilbert Transform
	Practical Introduction to Frequency-Domain Analysis
	Practical Introduction to Time-Frequency Analysis
	Measure Power of Deterministic Periodic Signals
	Spectral Analysis of Nonuniformly Sampled Signals
	Linear Prediction and Autoregressive Modeling
	Classify ECG Signals Using Long Short-Term Memory Networks
	Classify ECG Signals Using Long Short-Term Memory Networks with GPU Acceleration
	Waveform Segmentation Using Deep Learning
	Deploy Signal Segmentation Deep Network on Raspberry Pi
	Create Labeled Signal Sets Iteratively with Reduced Human Effort
	Generate Synthetic Signals Using Conditional GAN
	Spoken Digit Recognition with Custom Log Spectrogram Layer and Deep Learning
	Signal Recovery with Differentiable Scalograms and Spectrograms
	Train Spoken Digit Recognition Network Using Out-of-Memory Features
	Classify Time Series Using Wavelet Analysis and Deep Learning
	Denoise Speech Using Deep Learning Networks
	Order Analysis of a Vibration Signal
	Vibration Analysis of Rotating Machinery
	Modal Analysis of a Simulated System and a Wind Turbine Blade
	Practical Introduction to Fatigue Analysis Using Rainflow Counting
	Accelerating Correlation with GPUs
	Learn Pre-Emphasis Filter Using Deep Learning
	Denoise EEG Signals Using Deep Learning Regression with GPU Acceleration
	Hand Gesture Classification Using Radar Signals and Deep Learning
	Human Activity Recognition Using Signal Feature Extraction and Machine Learning
	Anomaly Detection Using Autoencoder and Wavelets
	Denoise Signals with Adversarial Learning Denoiser Model
	Signal Source Separation Using W-Net Architecture
	Human Health Monitoring Using Continuous Wave Radar and Deep Learning
	Classify Arm Motions Using EMG Signals and Deep Learning
	Detect Anomalies In Signals Using deepSignalAnomalyDetector
	Detect Anomalies in Machinery Using LSTM Autoencoder
	View, Preprocess, and Write EDF File
	Generate Optimized Code on Raspberry Pi Target
Code Generation from MATLAB Support in Signal Processing Toolbox
	List of Signal Processing Toolbox Functions that Support Code Generation
	Specifying Inputs in Code Generation from MATLAB
		Defining Input Size and Type
		Inputs Must Be Constants
	Apply Lowpass Filter to Input Signal
	Zero-Phase Filtering
	Compute Modified Periodogram Using Generated C Code