Objectives
The objective of this experiment is to perform time-frequency analysis of stationary and non-stationary signals. Some of these signals are actual signals acquired from operating machine and equipment.
Introduction
The objective of time-frequency analysis is to decompose energy of a signal in both time and frequency. This decomposition helps to operate the signal in a controlled way and to construct signal with the specific properties. The basic tool to implement this decomposition is the Classical Fourier transform. Classical Fourier Transform are generally most suitable for the time-stationary signals. For the signals that evolve in time, we can use
1. Linear time-frequency representations (such as short-time Fourier transforms, wavelet transforms etc.)
2. Quadratic time-frequency representations (for instance Cohen's class, including the Wigner distribution originating from quantum mechanics)
Need for Time-Frequency analysis
The two classical representation of a signal are the time-domain s(t) and frequency domain s(f) representation. In both the representations, the variables t and f are treated as mutually exclusive. Hence in order to obtain a representation in terms of one variable, the other one should be integrated out. The frequency representation is essentially averaged over the values of the time representation at all times, and the time representation is essentially averaged over the values of the frequency representation at all frequencies. In the time frequency distribution the variable t and f are not mutually exclusive, but are present together. The time frequency distribution is localized in t and f.
Characteristics of time frequency representation:
The use of time-frequency distribution is based on particular?s assumption concerning the properties of the Time-Frequency distribution. The following characteristics illustrate uses of time-frequency distribution.
1. The raw signal can be analyzed in the time-frequency (t,f) domain to identify its characteristics such as frequency variation, time variation, number of components, relative amplitudes, etc.
2. The component can be separated from each other as well as from background noise by filtering in time frequency (t,f) domain .
3. Synthesize the filtered time-frequency representation in time domain./p>
4. Specific components can be analyzed separately such as tracking of instantaneous amplitude, instantaneous frequency, instantaneous bandwidth, etc.
5. A mathematical model of a signal can be chosen which clearly shows the significant characteristics, such as IF.
