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ATOMS : Time Frequency Toolbox details
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Time Frequency Toolbox

162 functions to analyze non-stationary signals using time-frequency distributions
(1201 downloads for this version - 118447 downloads for all versions)
Holger Nahrstaedt
François Auger
Owner Organization
TU Berlin / FG Regelungssysteme
Clement DAVID
Holger Nahrstaedt
Administrator ATOMS
Creation Date
March 21, 2023
Source created on
Scilab 2023.0.x
Binaries available on
Scilab 2023.0.x:
Windows 64-bit
Scilab 2024.0.x:
Windows 64-bit
Install command
--> atomsInstall("stftb")
            This Toolbox was ported from

It implements various kinds of time-frequency analysis with a special emphasis
on quadratic energy distributions of the Cohen and affine classes, along with
their version enhanced by the reassignment method. Signals generation,
processing / post-processing routines (with display utilities) and demos are
also included.

PDF manual:
Report bugs @

Ambiguity plane functions
Caf2tfr — From ambiguity plane to time frequency plane
Cambifunb — Ambiguity function
Ctfrker — Time frequency representation kernel

Miscellaneous functions
Chtl    — Hough transform for detection of lines in images
Ctfrdist — Time frequency distance
Ctfrreas — Time Frequency Representation reassignment
Cwindow — Creates a window of length N with a given shape

Time-Frequency representations
Ctfrbj  — Born-Jordan time-frequency distribution
Ctfrbud — Butterworth time-frequency distribution
Ctfrcw  — Choi-Williams time-frequency distribution
Ctfrgrd — Generalized rectangular time-frequency distribution
Ctfrmh  — Margenau-Hill time-frequency distribution
Ctfrmhs — Margenau-Hill-Spectrogram time-frequency distribution
Ctfrmmce — Minimum mean cross-entropy combination of spectrograms
Ctfrpage — Page time-frequency distribution
Ctfrpmh  — Pseudo Margenau-Hill time-frequency distribution
Ctfrppage — Pseudo Page time-frequency distribution
Ctfrpwv — Pseudo Wigner-Ville time-frequency distribution
Ctfrri  — Rihaczek time-frequency distribution
Ctfrridb — Reduced Interference Distribution with Bessel kernel
Ctfrridbn — Reduced Interference Distribution with binomial kernel
Ctfrridh — Reduced Interference Distribution with Hanning kernel
Ctfrridt — Reduced Interference Distribution with Triangular kernel
Ctfrrsp — Reassigned Spectrogram
Ctfrsp  — Spectrogram Time Frequency distribution of a signal X
Ctfrspwv — Smoothed Pseudo Wigner-Ville time-frequency distribution
Ctfrstft — Short time Fourier transform
Ctfrwv  — Wigner-Ville time-frequency distribution
Ctfrzam — Zao-Atlas-Marks time-frequency distribution

Ambiguity Functions
ambifunb — Narrow-band ambiguity function
ambifuwb — Wide-band ambiguity function

Choice of the Instantaneous Amplitude
amexpo1s — Generate one-sided exponential amplitude modulation
amexpo2s — Generate bilateral exponential amplitude modulation
amgauss — Generate gaussian amplitude modulation
amrect  — Generate rectangular amplitude modulation
amtriang — Generate triangular amplitude modulation

Bilinear Time-Frequency Processing in the Affine Class
istfraff — is it an affine time frequency representation
lambdak — Evaluate lambda function for Affine Wigner distribution
tfrbert — Unitary Bertrand time-frequency distribution
tfrdfla — D-Flandrin time-frequency distribution
tfrscalo — Scalogram, for Morlet or Mexican hat wavelet
tfrspaw  — Smoothed Pseudo Affine Wigner time-frequency distributions
tfrunter — Unterberger time-frequency distribution

Bilinear Time-Frequency Processing in the Cohen's Class
tfrbj  — Born-Jordan time-frequency (T-F) distribution
tfrbud — Butterworth T-F distribution
tfrcw  — Choi-Williams T-F distribution
tfrgrd — Generalized rectangular T-F distribution
tfrmh  — Margenau-Hill T-F distribution
tfrmhs — Margenau-Hill-Spectrogram T-F distribution
tfrmmce — Minimum mean cross-entropy combination of spectrograms
tfrpage — Page T-F distribution
tfrpmh  — Pseudo Margenau-Hill T-F distribution
tfrppage — Pseudo Page T-F distribution
tfrpwv — Pseudo Wigner-Ville T-F distribution
tfrri  — Rihaczek T-F distribution
tfrridb — Reduced Interference Distribution with Bessel kernel
tfrridbn — Reduced Interference Distribution with a binomial kernel
tfrridh — Reduced Interference Distribution with Hanning kernel
tfrridt — Reduced Interference Distribution with triangular kernel
tfrsp   — Spectrogram T-F distribution
tfrspbk — Smoothed Pseudo K-Bertrand T-F distribution
tfrspwv — Smoothed Pseudo Wigner-Ville T-F distribution
tfrwv  — Wigner-Ville  T-F distribution
tfrzam — Zao-Atlas-Marks T-F distribution

Frequency-Domain Processing
ffmt     — Fast Fourier Mellin Transform
frpowerspec — Compute the energy spectrum of the signal
frspec   — Compute the spectrum of the signal
iffmt    — Inverse fast Mellin transform
locfreq  — Frequency localization caracteristics
parafrep — parametric frequency representation of a signal
sgrpdlay — Group delay estimation of a signal
tftb_fft — matlab compatible fft
tftb_ifft — matlab compatible ifft

Choice of the Instantaneous Frequency
fmconst — Signal with constant frequency modulation
fmhyp  — Signal with hyperbolic frequency modulation
fmlin  — Signal with linear frequency modulation
fmodany — Signal with arbitrary frequency modulation
fmpar   — Parabolic frequency modulated signal
fmpower — Signal with power-law frequency modulation
fmsin  — Signal with sinusoidal frequency modulation
gdpower — Signal with power-law group delay
if2phase — Generate the phase from the instantaneous frequency

Linear Time-Frequency Processing
tffilter — Time frequency filtering of a signal
tfrgabor — Gabor representation of a signal
tfristft — Inverse Short time Fourier transform
tfrstft — Short time Fourier transform
tfrsurf — extract the biggest energy dots

scale   — Scale a signal using the Mellin transform
sigmerge — Add two signals with given energy ratio in dB

Noise Realizations
noisecg — Analytic complex gaussian noise
noisecu — Analytic complex uniform white noise

contwtgn — compute a continuous wavelet transform
contwtgnmir — Continuous wavelet transform of mirrored 1-D signals
correlmx — correlation matrix of a signal
d2statio — Distance to stationarity
disprog  — Display progression of a loop
divider  — Find dividers of an integer
dwindow  — Derive a window
fzero    — solves the scalar nonlinear equation such that F(X) == 0
gaussn   — generate the order n derivative of the gaussian window
imextrac — imextrac(Image) extract and isolate dots in a binary image
integ    — Approximate 1D integral of a discrete signal
integ2d  — Approximate 2-D integral
istfr1   — is a time frequency representation of type 1 (freq>0 or <0)
istfr2   — is a time frequency representation of type 2 (only freq>0)
izak     — Inverse Zak transform
kaytth   — Kay-Tretter filter computation
odd      — Round towards nearest odd value
rem      — Return the remainder of the division x/y
rot90    — rotate the given 2-D array by 90 degrees
umaxbert — Get the maximum value of u for Bertrand distribution
umaxdfla — Get the maximum value of u for D-Flandrin distribution
umaxunte — Get the maximum value of u for Unterberger distribution
vecmodulo — Congruence of a vector
zak      — Zak transform

Post-Processing or Help to the Interpretation
friedman — FRIEDMAN Instantaneous frequency density
holder  — Estimate the Holder exponent through an affine TFR
htl     — Hough transform for detection of lines in images
margtfr — Marginals and energy of a time-frequency representation
midpoint — Mid-point construction used in the interference diagram
momftfr — Frequency moments of a time-frequency representation
momttfr — Time moments of a time-frequency representation
plotsid — Schematic interference diagram of FM signals
renyi   — Measure Renyi information
ridges  — Extraction of ridges
tfrideal — Ideal TFR for given instantaneous frequency laws

Reassigned Time-Frequency Processing
tfrrgab — Reassigned Gabor spectrogram time-frequency distribution
tfrrmsc — Reassigned Morlet Scalogram time-frequency distribution
tfrrpmh — Reassigned pseudo Margenau-Hill time-frequency distribution
tfrrppag — Reassigned pseudo Page time-frequency distribution
tfrrpwv — Reassigned pseudo Wigner-Ville distribution
tfrrsp  — Reassigned Spectrogram
tfrrspwv — Reassigned smoothed pseudo Wigner-Ville distribution
tfrrstan — Reassigned Stankovic distribution

Choice of Particular Signals
altes   — Altes signal in time domain
anaask  — Amplitude Shift Keying (ASK) signal
anabpsk — Binary Phase Shift Keying (BPSK) signal
anafsk  — Frequency Shift Keying (FSK) signal
anapulse — Analytic projection of unit amplitude impulse signal
anaqpsk — Quaternary Phase Shift Keying (QPSK) signal
anasing — Lipschitz singularity
anastep — Analytic projection of unit step signal
atoms   — Linear combination of elementary Gaussian atoms
chirp   — Evaluate a chirp signal at time t
dopnoise — Complex noisy doppler signal
doppler  — Complex Doppler signal
griffitc — Test signal example C of Griffiths' paper
klauder — Klauder wavelet in time domain
mexhat  — Mexican hat wavelet in time domain
pulstran — Pulse
sawtooth — Sawtooth wave
tftb_window — Window generation

Time-Domain Processing
ifestar2 — Instantaneous frequency estimation using AR2 model.
instfreq — Instantaneous frequency estimation
loctime — Time localization caracteristics

Visualization and backup
plotifl — Plot normalized instantaneous frequency laws
tfrparam — parametric time-frequency representation
tfrqview — Quick visualization of time-frequency representations
tfrsave — Save the parameters of a time-frequency representation
tfrview — Visualization of time-frequency representations
Files (3)
[12.35 MB]
Windows 64-bit binary for Scilab 2023.0.x

[4.05 MB]
Source code archive

[16.79 MB]
Windows 64-bit binary for Scilab 2024.0.x

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