`pwelch` — Estimate power spectral density using Welch's method.

pwelch(x) estimates the power spectral density of a signal by averaging modified periodograms of overlapped, windowed segments. Optional arguments select the window, overlap, FFT length, sampling frequency, frequency range, and spectrum scale.

Syntax

pxx = pwelch(x, window, noverlap, nfft, fs, freqrange)
[pxx, f] = pwelch(x, window, noverlap, nfft, fs, freqrange)

Inputs

Name	Type	Required	Default	Description
`x`	`NumericArray`	Yes	—	Input signal vector or matrix with one signal per column.
`window`	`Any`	No	`[]`	Window vector or scalar segment length.
`noverlap`	`NumericScalar`	No	`[]`	Number of overlapped samples.
`nfft`	`NumericArray`	No	`[]`	FFT length or explicit frequency vector.
`fs`	`NumericScalar`	No	—	Sampling frequency in Hz.
`freqrange`	`StringScalar`	No	—	Frequency range selector (`onesided`, `twosided`, or `centered`) and spectrum type (`psd` or `power`).

Returns

Name	Type	Description
`pxx`	`NumericArray`	Power spectral density estimate.
`f`	`NumericArray`	Frequency vector in radians/sample or Hz when fs is supplied.

Returned values from pwelch depend on how many outputs the caller requests.

Errors

Identifier	When	Message
`RunMat:pwelch:ArgCount`	The argument count is outside supported forms.	`pwelch: expected pwelch(x, [window, [noverlap, [nfft_or_f, [fs, [freqrange_or_scale]]]]])`
`RunMat:pwelch:InvalidSignal`	Input signal is not a numeric vector or matrix.	`pwelch: x must be a nonempty numeric vector or 2-D matrix`
`RunMat:pwelch:InvalidWindow`	Window input is invalid.	`pwelch: window must be a nonempty vector or positive integer length`
`RunMat:pwelch:InvalidOverlap`	Overlap is invalid.	`pwelch: noverlap must be a nonnegative integer less than window length`
`RunMat:pwelch:InvalidNfft`	FFT length is invalid.	`pwelch: nfft must be a positive integer at least as large as the window length`
`RunMat:pwelch:InvalidFs`	Sampling frequency is invalid.	`pwelch: fs must be a positive finite scalar`
`RunMat:pwelch:InvalidRange`	Frequency range selector is invalid.	`pwelch: freqrange must be 'onesided', 'twosided', or 'centered'; spectrum type must be 'psd' or 'power'`
`RunMat:pwelch:Internal`	Output tensor construction fails internally.	`pwelch: internal error`

How `pwelch` works

pxx = pwelch(x) returns a one-sided PSD estimate for real inputs and a two-sided estimate for complex inputs.
Matrix inputs are processed column-wise; pxx has one output column per input column. Single input produces single pxx and f outputs, while double and admitted typed-integer input produce double outputs.
[pxx, f] = pwelch(...) also returns the frequency grid. Without fs, frequencies are in radians/sample; with fs, frequencies are in Hz.
The window argument may be a vector or a scalar segment length. A scalar creates a Hamming window of that length; [] uses a default Hamming window sized for roughly eight 50%-overlapped sections, capped at 256 samples.
noverlap defaults to half the window length and must be less than the window length.
nfft defaults to max(256, length(window)), must be at least the window length, and controls the FFT grid. A real frequency vector may be supplied in the same position to evaluate the PSD at explicit frequencies.
The optional range selector accepts 'onesided', 'twosided', or 'centered'.
The optional spectrum type accepts 'psd' (default) or 'power'; 'power' omits the density bandwidth normalization.
The compatibility target documents single and double signal, window, and frequency data. RunMat mode additionally accepts all eight typed-integer classes for the signal and numeric controls after proving every value is exactly representable at the binary64 Welch boundary, and retains logical signal/control admission as a separately declared extension; strict compatibility mode rejects those extensions before provider dispatch.

Examples

PSD of a sine wave

fs = 1000;
t = (0:999) / fs;
x = sin(2*pi*100*t);
[pxx, f] = pwelch(x, hamming(256), 128, 512, fs);

Use a scalar window length

[pxx, w] = pwelch(randn(1,1024), 128, 64, 256);

Two-sided spectrum

x = exp(1i*2*pi*(0:127)/16);
[pxx, w] = pwelch(x, 64, 32, 128, 'twosided');

Centered spectrum in Hz

[pxx, f] = pwelch(randn(1,512), [], [], 512, 2000, 'centered');

Column-wise spectra for a matrix

x = [sin(2*pi*(0:255)'/16), cos(2*pi*(0:255)'/32)];
[pxx, f] = pwelch(x, 64, 32, 128, 'power');

Evaluate at explicit normalized frequencies

w = linspace(0, pi, 64);
[pxx, wout] = pwelch(randn(1,512), hamming(128), 64, w);

Using `pwelch` with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how pwelch changes the result.

Run a small pwelch example, explain the result, then change one input and compare the output.

FAQ

Can I pass a Hamming window from the hamming builtin?⌄

Yes. pwelch(x, hamming(n), noverlap, nfft, fs) uses the provided window directly. Passing the scalar n instead creates the same kind of Hamming segment window internally.

Does pwelch include the Nyquist bin?⌄

For one-sided output and even nfft, yes. The output length is nfft/2 + 1, with DC first and the Nyquist bin last.

Does pwelch plot when no outputs are requested?⌄

RunMat currently returns values using normal output-count semantics instead of opening a plot. Use the returned pxx and frequency vector with plotting functions explicitly.

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how pwelch is executed, line by line, in Rust.

View the source for pwelch in Rust on GitHub
Learn how the RunMat runtime works
Found a bug? Open an issue with a minimal reproduction.

About RunMat

RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.

RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.

Getting started · Benchmarks · Pricing

`pwelch` — Estimate power spectral density using Welch's method.

Syntax

pxx = pwelch(x, window, noverlap, nfft, fs, freqrange)
[pxx, f] = pwelch(x, window, noverlap, nfft, fs, freqrange)

Inputs

Name	Type	Required	Default	Description
`x`	`NumericArray`	Yes	—	Input signal vector or matrix with one signal per column.
`window`	`Any`	No	`[]`	Window vector or scalar segment length.
`noverlap`	`NumericScalar`	No	`[]`	Number of overlapped samples.
`nfft`	`NumericArray`	No	`[]`	FFT length or explicit frequency vector.
`fs`	`NumericScalar`	No	—	Sampling frequency in Hz.
`freqrange`	`StringScalar`	No	—	Frequency range selector (`onesided`, `twosided`, or `centered`) and spectrum type (`psd` or `power`).

Returns

Name	Type	Description
`pxx`	`NumericArray`	Power spectral density estimate.
`f`	`NumericArray`	Frequency vector in radians/sample or Hz when fs is supplied.

Returned values from pwelch depend on how many outputs the caller requests.

Errors

Identifier	When	Message
`RunMat:pwelch:ArgCount`	The argument count is outside supported forms.	`pwelch: expected pwelch(x, [window, [noverlap, [nfft_or_f, [fs, [freqrange_or_scale]]]]])`
`RunMat:pwelch:InvalidSignal`	Input signal is not a numeric vector or matrix.	`pwelch: x must be a nonempty numeric vector or 2-D matrix`
`RunMat:pwelch:InvalidWindow`	Window input is invalid.	`pwelch: window must be a nonempty vector or positive integer length`
`RunMat:pwelch:InvalidOverlap`	Overlap is invalid.	`pwelch: noverlap must be a nonnegative integer less than window length`
`RunMat:pwelch:InvalidNfft`	FFT length is invalid.	`pwelch: nfft must be a positive integer at least as large as the window length`
`RunMat:pwelch:InvalidFs`	Sampling frequency is invalid.	`pwelch: fs must be a positive finite scalar`
`RunMat:pwelch:InvalidRange`	Frequency range selector is invalid.	`pwelch: freqrange must be 'onesided', 'twosided', or 'centered'; spectrum type must be 'psd' or 'power'`
`RunMat:pwelch:Internal`	Output tensor construction fails internally.	`pwelch: internal error`

How `pwelch` works

pxx = pwelch(x) returns a one-sided PSD estimate for real inputs and a two-sided estimate for complex inputs.
Matrix inputs are processed column-wise; pxx has one output column per input column. Single input produces single pxx and f outputs, while double and admitted typed-integer input produce double outputs.
[pxx, f] = pwelch(...) also returns the frequency grid. Without fs, frequencies are in radians/sample; with fs, frequencies are in Hz.
The window argument may be a vector or a scalar segment length. A scalar creates a Hamming window of that length; [] uses a default Hamming window sized for roughly eight 50%-overlapped sections, capped at 256 samples.
noverlap defaults to half the window length and must be less than the window length.
nfft defaults to max(256, length(window)), must be at least the window length, and controls the FFT grid. A real frequency vector may be supplied in the same position to evaluate the PSD at explicit frequencies.
The optional range selector accepts 'onesided', 'twosided', or 'centered'.
The optional spectrum type accepts 'psd' (default) or 'power'; 'power' omits the density bandwidth normalization.
The compatibility target documents single and double signal, window, and frequency data. RunMat mode additionally accepts all eight typed-integer classes for the signal and numeric controls after proving every value is exactly representable at the binary64 Welch boundary, and retains logical signal/control admission as a separately declared extension; strict compatibility mode rejects those extensions before provider dispatch.

Examples

PSD of a sine wave

fs = 1000;
t = (0:999) / fs;
x = sin(2*pi*100*t);
[pxx, f] = pwelch(x, hamming(256), 128, 512, fs);

Use a scalar window length

[pxx, w] = pwelch(randn(1,1024), 128, 64, 256);

Two-sided spectrum

x = exp(1i*2*pi*(0:127)/16);
[pxx, w] = pwelch(x, 64, 32, 128, 'twosided');

Centered spectrum in Hz

[pxx, f] = pwelch(randn(1,512), [], [], 512, 2000, 'centered');

Column-wise spectra for a matrix

x = [sin(2*pi*(0:255)'/16), cos(2*pi*(0:255)'/32)];
[pxx, f] = pwelch(x, 64, 32, 128, 'power');

Evaluate at explicit normalized frequencies

w = linspace(0, pi, 64);
[pxx, wout] = pwelch(randn(1,512), hamming(128), 64, w);

Using `pwelch` with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how pwelch changes the result.

Run a small pwelch example, explain the result, then change one input and compare the output.

FAQ

Can I pass a Hamming window from the hamming builtin?⌄

Yes. pwelch(x, hamming(n), noverlap, nfft, fs) uses the provided window directly. Passing the scalar n instead creates the same kind of Hamming segment window internally.

Does pwelch include the Nyquist bin?⌄

For one-sided output and even nfft, yes. The output length is nfft/2 + 1, with DC first and the Nyquist bin last.

Does pwelch plot when no outputs are requested?⌄

RunMat currently returns values using normal output-count semantics instead of opening a plot. Use the returned pxx and frequency vector with plotting functions explicitly.

Signal

Elementwise

Trigonometry

acos · acosh · asin · asinh · atan · atan2 · atanh · cos · cosd · cosh · cospi · deg2rad · pol2cart · rad2deg · sin · sind · sinh · sinpi · tan · tand · tanh

Reduction

Structure

bandwidth · isdiag · ishermitian · issymmetric · istril · istriu · symrcm

Rounding

ceil · fix · floor · mod · rem · round

Factor

chol · decomposition · eig · eigs · lu · qr · svd

Solve

cond · det · inv · linsolve · norm · null · pinv · rank · rcond · rref · vecnorm

Optim

coneprog · fminbnd · fminunc · fsolve · fzero · integral · linprog · lsqcurvefit · lsqnonlin · optimoptions · optimset · quad · secondordercone

Ops

cross · ctranspose · dot · mldivide · mpower · mrdivide · mtimes · pagemtimes · pagetranspose · trace · transpose

Symbolic

digits · int · limit · piecewise · sym · syms · vpa

Fft

fft · fft2 · fftn · fftshift · ifft · ifft2 · ifftn · ifftshift

Interpolation

griddedInterpolant · interp1 · interp1q · interp2 · pchip · ppval · spline

Discrete

lcm · primes

Ode

ode15s · ode23 · ode45

Poly

polyder · polyfit · polyint · polyval · roots

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how pwelch is executed, line by line, in Rust.

View the source for pwelch in Rust on GitHub
Learn how the RunMat runtime works
Found a bug? Open an issue with a minimal reproduction.

About RunMat

RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.

RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.

Getting started · Benchmarks · Pricing

pwelch — Estimate power spectral density using Welch's method.

Syntax

Inputs

Returns

Errors

How pwelch works

Examples

PSD of a sine wave

Use a scalar window length

Two-sided spectrum

Centered spectrum in Hz

Column-wise spectra for a matrix

Evaluate at explicit normalized frequencies

Using pwelch with coding agents

FAQ

Related Math functions

Signal

Elementwise

Trigonometry

Reduction

Structure

Rounding

Factor

Solve

Optim

Ops

Symbolic

Fft

Interpolation

Discrete

Ode

Poly

Open-source implementation

About RunMat

Download RunMat

pwelch — Estimate power spectral density using Welch's method.

Syntax

Inputs

Returns

Errors

How pwelch works

Examples

PSD of a sine wave

Use a scalar window length

Two-sided spectrum

Centered spectrum in Hz

Column-wise spectra for a matrix

Evaluate at explicit normalized frequencies

Using pwelch with coding agents

FAQ

Related Math functions

Signal

Elementwise

Trigonometry

Reduction

Structure

Rounding

Factor

Solve

Optim

Ops

Symbolic

Fft

Interpolation

Discrete

Ode

Poly

Open-source implementation

About RunMat

Download RunMat

`pwelch` — Estimate power spectral density using Welch's method.

How `pwelch` works

Using `pwelch` with coding agents

`pwelch` — Estimate power spectral density using Welch's method.

How `pwelch` works

Using `pwelch` with coding agents