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Motivation. In signal processing, time–frequency analysis [3] is a body of techniques and methods used for characterizing and manipulating signals whose statistics vary in time, such as transient signals. It is a generalization and refinement of Fourier analysis, for the case when the signal frequency characteristics are varying with time.
Time–frequency representation. A time–frequency representation (TFR) is a view of a signal (taken to be a function of time) represented over both time and frequency. [1] Time–frequency analysis means analysis into the time–frequency domain provided by a TFR. This is achieved by using a formulation often called "Time–Frequency ...
These two methods actually form two different time–frequency representations, but are equivalent under some conditions. The bandpass filters method usually uses analog processing to divide the input signal into frequency bands; the magnitude of each filter's output controls a transducer that records the spectrogram as an image on paper. [3]
Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. [1] The instantaneous phase (also known as local phase or simply phase) of a complex-valued function s (t), is the real-valued function: where arg is the complex argument function.
Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light. For example, if a heart beats at a frequency of 120 times per minute (2 hertz), the period—the interval between beats—is half a second ...
Frequency analysis [2] is the analysis of how often, or how frequently, an observed phenomenon occurs in a certain range. Frequency analysis applies to a record of length N of observed data X 1, X 2, X 3. . . X N on a variable phenomenon X. The record may be time-dependent (e.g. rainfall measured in one spot) or space-dependent (e.g. crop ...
In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than time, as in time series. [1] Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency ...
A simple way to derive the spectrum of a chirp using a computers, is to sample the time-domain waveform at a frequency well above the Nyquist limit and use an FFT algorithm to obtain the desired result. As this approach was not an option for the early designers, they resorted to analytic analysis, or and to graphical or approximation methods.