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- W1578967897 abstract "The calculation of quadratic time-frequency representations of discrete-time signals has always been accompanied by poorly mastered approximations. The change of variable by which the continuous-time variables are replaced by their discrete-time equivalent is merely an abusive notation and is certainly not satisfactory mathematically. This chapter presents the expression of quadratic time-frequency representations of a discrete-time signal along with its formal proof. The starting point of this proof is twofold: the signal's sampling equation and the classical integral expression of the time-frequency representation of a continuous-time signal. Surprising properties of the representations obtained are then demonstrated. Thus, the discrete-time characteristic of the signal is generally not found in its time-frequency representations, which, in fact, prove to be continuous-time! The relationships between the proposed expression and other works on this subject are also studied. They enable an appreciation of its interest with respect to the so-called aliased and non-aliased representations. Finally, some characteristic properties of the spectral analysis of chirps are described. Their interest lies in a less restrictive conditioning of the kernel than the one found for the representations of continuous-time signal." @default.
- W1578967897 created "2016-06-24" @default.
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- W1578967897 date "2008-01-01" @default.
- W1578967897 modified "2023-09-26" @default.
- W1578967897 title "Quadratic Time-Frequency Analysis II: Discretization of Cohen's Class" @default.
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- W1578967897 doi "https://doi.org/10.1002/9780470611203.ch6" @default.
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