The cone-shape distribution function, also known as the Zhao–Atlas–Marks time-frequency distribution,
[Leon Cohen, Time Frequency Analysis: Theory and Applications, Prentice Hall, (1994)] (acronymized as the ZAM distribution or ZAMD
), is one of the members of
Cohen's class distribution function.
It was first proposed by Yunxin Zhao, Les E. Atlas, and
Robert J. Marks II in 1990. The distribution's name stems from the twin cone shape of the distribution's kernel function on the
plane. The advantage of the cone kernel function is that it can completely remove the cross-term between two components having the same center frequency. Cross-term results from components with the same time center, however, cannot be completely removed by the cone-shaped kernel.
Mathematical definition
The definition of the cone-shape distribution function is:
:
where
:
and the kernel function is
:
The kernel function in
domain is defined as:
:
Following are the magnitude distribution of the kernel function in
domain.
Following are the magnitude distribution of the kernel function in
domain with different
values.
As is seen in the figure above, a properly chosen kernel of cone-shape distribution function can filter out the interference on the
axis in the
domain, or the ambiguity domain. Therefore, unlike the
Choi-Williams distribution function, the cone-shape distribution function can effectively reduce the cross-term results form two component with same center frequency. However, the cross-terms on the
axis are still preserved.
The cone-shape distribution function is in the
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation ...
Time-Frequency Toolbox and
National Instruments
National Instruments Corporation, doing business as NI, is an American multinational company with international operation. Headquartered in Austin, Texas, it is a producer of automated test equipment and virtual instrumentation software. Comm ...
' LabVIEW Tools for Time-Frequency, Time-Series, and Wavelet Analysis
National Instruments. LabVIEW Tools for Time-Frequency, Time-Series, and Wavelet Analysis
TFA Cone-Shaped Distribution VI
See also
* Cohen's class distribution function
* Choi-Williams distribution function
*Wigner distribution function
The Wigner distribution function (WDF) is used in signal processing as a transform in time-frequency analysis.
The WDF was first proposed in physics to account for quantum corrections to classical statistical mechanics in 1932 by Eugene Wigner, ...
* Ambiguity function
*Short-time Fourier transform
The short-time Fourier transform (STFT), is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practice, the procedure for computing STFTs is to divid ...
References
{{Reflist
Time–frequency analysis
Transforms