Overlapping of Signals

The programming or numeric computing platform analyses the signals and indicates the algorithms based on the overlapping signals.

Overlapping of signals is mainly caused due to three factors: 

• Formation of the propagation.
• Numerous targets.
• Compound physical effects of the propagation path.

The issue of overlapping signals takes place in each frequency domain and time. Time overlapping can be identified by the time detained in the middle of echoes. Time overlap happens when the time detained in the middle of the echoes is less than the released signal’s period.

Overlapping of signals is the length of track of the signals beyond the stop point, which is known as a signal margin. It is not easy to separate two or more than two constituent signals with similar spectrums. This kind of overlapping signal is a major issue in musical or harmonious sound severance, since the instruments have similar frequencies. 

The relationship of frequency-phase between two or more individual signals is unclear, which is the root of destructive and constructive interference and results in irregular spectrum characteristics. 

The frequency decisiveness is affected by the comparative phase of overlapping signals. It also plays an important role in monitoring the amplitude of the assorted or amalgamated signals.

How to Separate Overlapping Signals?

Time-frequency method and spectrum method help separate overlapping signals. 

In the signal clarification process, time fixation and securing a spectrum are problematic since overlapping occurs at each time and in every frequency realm. 

This is because traditional methods such as the time-frequency and spectrum methods are difficult to use to detach overlapping signals. It is difficult to disconnect signals overlapping in time through a realm opening. As the spectra of the signals are quite similar, it is difficult to detach overlapping signals via the frequency realm filtering technique.

Other Approaches to Separate Overlapping Signals

Over the last few years, numerous techniques have been proposed to solve the overlapping problem. 

Some signal overlapping examples are discrete cosine transform, chirplet transform, Fractional Fourier transform, short-time Fourier transform, discrete wavelet transform and Wigner-Ville distribution.

Fourier Transform and Inverse Fourier Transform Method

These two methods use the superresolution technique of Gerchberg to separate overlapping signals. 

To use this approach, it is mandatory to acquire the echo configuration from experiments. Hilbert transform is used to withdraw the signal received through a source and then the extracted signal is used to regulate the broadcast signal.

Signal-to-Noise Ratio (SNR)

The signals cannot be the same as the received signals and the simulated transmitted signals because of the system response, frequency shift and noise.

Fourier transform and inverse Fourier transform methods are quite diplomatic. Due to this, the Signal-to-Noise Ratio (SNR) result shows catastrophic effects.

Experiment to Perform Envelope Detection

The Hilbert transform facilitates the formation of the analytic signal. Generally, this analytical signal is used in passband signal processing and communications. 

This experiment is conducted in an empty and closed basketball hall, in which a loudspeaker and microphone are placed 2m above the base of the basketball hall. The interval in the middle of the loudspeaker or microphone to the object is more than 5 m.

After setting up the object and the loudspeaker or microphone, the mathematical sine of ten periods is produced with the help of a rectangular envelope as a transference pulse.

The produced transference pulse is emitted through a noise card using a laptop. The noise card can be a loudspeaker or a potential auditory amplifier. The transference pulse is gained first-hand using a microphone through a noise card. Hence, the signal is scrutinised as an analytic signal.

Experimental Examples

A transmission-reception system tests the outcome of this experiment with the help of a parabolic dish and by using single, double, and triple targets. The parabolic dish used in the transference-functional system has a focal length of 35 cm. It has an elliptical opening with a minor axis of 60 cm and a major axis of 65 cm.

Single Target

A wooden plank measuring 90 × 60 cm is used as an aim in a single target. This aim is kept at about 330 cm, separated from the directed auditory system.

Double Target

In this method, two wooden planks of measurements 90 × 60 cm and 60 × 40 cm are used as an aim and kept about 8 m from the auditory system.

Triple Target

In this method, three wooden planks of measurements 160 × 140 cm, 90 × 60 cm, and 60 × 40 cm are used as an aim and kept about 9.25 m away from the directed auditory system.

Conclusion

The separation of overlapping signals is a difficult task. Although, they can be separated by using experimental echo shape modelling through a hyperspectral algorithm. At a low signal-to-noise ratio, MATLAB shows an excellent presentation of the procedure. This hyperspectral algorithm technique of separating overlapping signals is tested through numerous aims and auditory transference-functional systems. This technique provides the exact location of numerous aims. This method has good accuracy in determining the time taken by the individual echoes coming from one and all aims. The technique of separating the overlapping signals can be used in various fields such as the biomedical and military sectors.