STATUS: unstable Time-Frequency representation of time-series. More...

#include "definitions.h"
#include "complex.h"
#include "array.h"
#include "optarg.h"
#include <math.h>

This graph shows which files directly or indirectly include this file:

Data Structures
struct	Spectrogram
	Complex spectrogram (Time-Frequency-Representation) of a signal. More...
Typedefs
typedef Array (	WindowFunction )(int, double)
	A Window Function.
Functions
Spectrogram *	spectrogram (const Array sig, Spectrogram spectgram, OptArgList *optargs)
	Easy interface for spectrogram calculation.
void	spectrogram_free (Spectrogram *s)
	Free memory associated with Spectrogram.
Spectrogram *	spectrogram_init (int N_freq, int N_time)
	Initialize Spectrogram.
Array *	spectrogram_powerspectrum (const Spectrogram *spect)
	Calculate the powerspectrum for a Spectrogram.
Spectrogram *	spectrogram_stft (const Array sig, double sampling_rate, const Array Window, int N_freq, int N_time, double corner_freqs[2], int timepoints, Spectrogram spectgram)
	Calculate spectrogram of a signal (using STFT).
Array *	window_dirichlet (int n, double noparam)
	Dirichlet (Rectangular) window.
Array *	window_gaussian (int n, double sigma)
	Gaussian window.
Array *	window_hamming (int n, double noparam)
	Hamming window.
Array *	window_hanning (int n, double noparam)
	Hanning (Hann) window.
Array *	window_kaiser (int n, double alpha)
	Kaiser Window.

Detailed Description

STATUS: unstable Time-Frequency representation of time-series.

A time-frequency represenation (TFR) of a signal displays the varying frequency content of a signal over time.

Todo:: add some docu here

Note:: the test-functions for this functionality are not excessive.

Definition in file time_frequency.h.

Typedef Documentation

typedef Array*(* WindowFunction)(int, double)

A Window Function.

Parameters:

	n	is the number of points in the window
	param	is a parameter depending on the choice of the window (e.g. sigma for gaussian)

Definition at line 51 of file time_frequency.h.

Function Documentation

Spectrogram* spectrogram	(	const Array *	sig,
		Spectrogram *	spectgram,
		OptArgList *	optargs
	)

Easy interface for spectrogram calculation.

Parameters:

sig - data to be spectrogrammified (1D DOUBLE array)

spectgram - if NULL, own memory is alloated, else use this pointer.

optargs

may contain:

sample_frequency=double of the signal, default is 500 (should really be provided!)
winfct=void* windowing function, default is window_hanning
timepoints=int* compute the spectrogram at selected time-points; this array is N_time long
winlength=int size of the window, default is MAX( SQR( sqrt(next_pow2( n ))-3 ), 5 )
winparam=double parameter for the window-function (e.g. sigma for gaussian); default=0.0
N_freq=int number of frequency bins, default is winlength*4
N_time=int number of time bins, default is n
corner_freqs=double* (array with two double entries), default is (0.0,250.0)

Definition at line 38 of file time_frequency.c.

void spectrogram_free ( Spectrogram * s )

Free memory associated with Spectrogram.

Definition at line 302 of file time_frequency.c.

Spectrogram* spectrogram_init	(	int	N_freq,
		int	N_time
	)

Initialize Spectrogram.

Parameters:

	N_freq	resolution (number of points) in frequency
	N_time	resolution in time

Returns:: a freshly allocated Spectrogram struct

Definition at line 282 of file time_frequency.c.

Array* spectrogram_powerspectrum ( const Spectrogram * s )

Calculate the powerspectrum for a Spectrogram.

Returns a s->N_time x s->N_freq matrix the absolute value squared of the complex numbers in spectrogram.

Parameters:

s

- the spectrogram

Returns:: the powerspectrum for all time-points

Definition at line 264 of file time_frequency.c.

Spectrogram* spectrogram_stft	(	const Array *	sig,
		double	sampling_rate,
		const Array *	Window,
		int	N_freq,
		int	N_time,
		double	corner_freqs[2],
		int *	timepoints,
		Spectrogram *	spectgram
	)

Calculate spectrogram of a signal (using STFT).

This function is inspired by (read: 'was shamelessly ripped of from') the TIME-FREQUENCY TOOLBOX by Emmanuel Roy - Manuel DAVY (http://www-lagis.univ-lille1.fr/~davy/toolbox/Ctftbeng.html) It's a bit more efficient and uses different storage formats. It doesn't work on complex signals.

THE ALGORITHM

Given a signal to analyze in time and frequency, computes the Short Time Fourier Transform (STFT) :

${STFT}(t,f) = \int x(s)h(t-s)e^{-2i\pi f s} ds$

This function is complex valued. Its computation requires a window, which can be computed with one of the window_*() functions.

Parameters:

	sig	- data to be spectrogrammified (1D DOUBLE array)
	sampling_rate	- sampling frequency of signal
	window	- window for calculating the STFT (1D DOUBLE Array); get from window_*() functions
	N_freq	- number of frequency bins = number of rows in the TFR matrix (the next power of 2 is chosen for N_freq)
	N_time	- number of cols in the TFR matrix
	corner_freqs	- corner frequencies (lower, upper) for the returned spectrum at each time-sample in Hz; maximal would be {0, srate/2}
	timepoints	compute the spectrogram at selected time-points; this array is N_time long
	spectgram	- if NULL, own memory is alloated, else use this pointer.

Returns:: the spectrogram

Definition at line 144 of file time_frequency.c.

Array* window_dirichlet	(	int	n,
		double	noparam
	)

Dirichlet (Rectangular) window.

$w(x) = 1;$

Parameters:

	n	- ODD number for window (else it is incremented by one)
	noparam	ignored (just for comparability to WindowFunction)

Returns:: 1D DOUBLE array of size n

Definition at line 323 of file time_frequency.c.

Array* window_gaussian	(	int	n,
		double	sigma
	)

Gaussian window.

$w(n) = e^{-\frac{1}{2}\left( \frac{n-(N-1)/2}{\sigma(N-1)/2}\right)^2 }$

with $\sigma\le 0.5$

Parameters:

	n	- ODD number for window (else it is incremented by one)
	sigma	- gaussian std

Returns:: 1D DOUBLE array of size n

Definition at line 349 of file time_frequency.c.

Array* window_hamming	(	int	n,
		double	noparam
	)

Hamming window.

$w(n) = 0.53836 - 0.46164 \cos\left( \frac{2\pi n}{N-1}\right)$

Parameters:

	n	- ODD number for window (else it is incremented by one)
	noparam	ignored (just for comparability to WindowFunction)

Returns:: 1D DOUBLE array of size n

Definition at line 374 of file time_frequency.c.

Array* window_hanning	(	int	n,
		double	noparam
	)

Hanning (Hann) window.

$w(n) = 0.5\left(1- \cos\left( \frac{2\pi n}{N-1}\right)\right)$

Parameters:

	n	- ODD number for window (else it is incremented by one)
	noparam	ignored (just for comparability to WindowFunction)

Returns:: 1D DOUBLE array of size n

Definition at line 399 of file time_frequency.c.

Array* window_kaiser	(	int	n,
		double	alpha
	)

Kaiser Window.

http://en.wikipedia.org/wiki/Kaiser_window

Parameters:

	n	- ODD number for window (else it is incremented by one)
	alpha	- parameter for window's steepness

Returns:: 1D DOUBLE array of size n

Definition at line 423 of file time_frequency.c.

src/time_frequency.h File Reference

Data Structures

Typedefs

Functions

Detailed Description

Typedef Documentation

Function Documentation