to practical problems. Consequently, when the signal we tend to sample is composed of single component, we use the WDF; however, if the signal consists of more than one component, using the Gabor transform, Gabor-Wigner distribution function, or other reduced interference TFDs may achieve better results. The Balian–Low theorem formalizes this, and provides a bound on the minimum number of time–frequency samples needed. Modulation and multiplexing Conventionally, the operation of modulation and multiplexing concentrates in time or in frequency, separately. By taking advantage of the time–frequency distribution, we can make it more efficient to modulate and multiplex. All we have to do is to fill up the time–frequency plane. We present an example as below. As illustrated in the upper example, using the WDF is not smart since the serious cross-term problem make it difficult to multiplex and modulate. Electromagnetic wave propagation We can represent an electromagnetic wave in the form of a 2 by 1 matrix which is similar to the time–frequency plane. When electromagnetic wave propagates through free-space, the Fresnel diffraction occurs. We can operate with the 2 by 1 matrix by LCT with parameter matrix where z is the propagation distance and is the wavelength. When electromagnetic wave pass through a spherical lens or be reflected by a disk, the parameter matrix should be and respectively, where ƒ is the focal length of the lens and R is the radius of the disk. These corresponding results can be obtained from Optics, acoustics, and biomedicine Light is an electromagnetic wave, so time–frequency analysis applies to optics in the same way as for general electromagnetic wave propagation. Similarly, it is a characteristic of acoustic signals, that their frequency components undergo abrupt variations in time and would hence be not well represented by a single frequency component analysis covering their entire durations. As acoustic signals are used as speech in communication between the human-sender and -receiver, their undelayedly transmission in technical communication systems is crucial, which makes the use of simpler TFDs, such as the Gabor transform, suitable to analyze these signals in real-time by reducing computational complexity. If frequency analysis speed is not a limitation, a detailed feature comparison with well defined criteria should be made before selecting a particular TFD. Another approach is to define a signal dependent TFD that is adapted to the data. In biomedicine, one can use time–frequency distribution to analyze the electromyography (EMG), electroencephalography