Spectral Estimation

Periodogram, Welch, and Lomb-Scargle PSD, coherence, transfer function, frequency reassignment

Analyze the spectral content of uniformly or nonuniformly sampled signals using periodogram, pwelch, or plomb. Sharpen periodogram estimates using reassignment. Determine frequency-domain coherence between signals. Estimate transfer functions based on input and output measurements. Study MIMO systems in the frequency domain.

Apps

Signal Analyzer

Visualize and compare multiple signals and spectra

Functions

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Estimators

`cpsd`	Cross power spectral density
`findpeaks`	Find local maxima
`mscohere`	Magnitude-squared coherence
`periodogram`	Periodogram power spectral density estimate
`plomb`	Lomb-Scargle periodogram
`pmtm`	Multitaper power spectral density estimate
`poctave`	Generate octave spectrum
`pspectrum`	Analyze signals in the frequency and time-frequency domains
`pwelch`	Welch’s power spectral density estimate
`refinepeaks`	Refine peak value and location estimates (Since R2024b)
`spectralEntropy`	Spectral entropy for signals and spectrograms
`tfestimate`	Transfer function estimate

dB Conversion

`db`	Convert energy or power measurements to decibels
`db2mag`	Convert decibels to magnitude
`db2pow`	Convert decibels to power
`mag2db`	Convert magnitude to decibels
`pow2db`	Convert power to decibels

Data Management

`resize`	Resize data by adding or removing elements (Since R2023b)
`paddata`	Pad data by adding elements (Since R2023b)
`trimdata`	Trim data by removing elements (Since R2023b)

Topics

Nonparametric Methods
Learn about the periodogram, modified periodogram, Welch, and multitaper methods of nonparametric spectral estimation.
Detect a Distorted Signal in Noise
Use frequency analysis to characterize a signal embedded in noise.
Measure the Power of a Signal
Estimate the width of the frequency band that contains most of the power of a signal. For distorted signals, determine the power stored in the fundamental and the harmonics.
Amplitude Estimation and Zero Padding
Obtain an accurate estimate of the amplitude of a sinusoidal signal using zero padding.
Bias and Variability in the Periodogram
Reduce bias and variability in the periodogram using windows and averaging.
Compare the Frequency Content of Two Signals
Identify similarity between signals in the frequency domain.
Find Periodicity Using Frequency Analysis
Spectral analysis helps characterize oscillatory behavior in data and measure the different cycles.
Significance Testing for Periodic Component
Assess the significance of a sinusoidal component in white noise using Fisher's g-statistic.
Cross Spectrum and Magnitude-Squared Coherence
Obtain the phase lag between sinusoidal components and identify frequency-domain correlation in a time series.
Price Weather Derivatives (Financial Instruments Toolbox)
This example demonstrates a workflow for pricing weather derivatives based on historically observed temperature data.

Featured Examples

Practical Introduction to Frequency-Domain Analysis

Perform and interpret basic frequency-domain signal analysis using simulated and real data.

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Power Spectral Density Estimates Using FFT

Obtain nonparametric PSD estimates equivalent to the periodogram using the FFT directly.

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Frequency-Domain Linear Regression

Construct a linear regression model for a time series using the discrete Fourier transform.

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Detect Periodicity in a Signal with Missing Samples

Use the Lomb-Scargle periodogram to study the periodicity of an irregularly sampled signal.

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Find Periodicity in a Categorical Time Series

Perform spectral analysis of data whose values are not inherently numerical.

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