November 2010
Intermediate to advanced
288 pages
8h 34m
English
book
Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation
by C. Britton Rorabaugh
Content preview from Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation
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Note 12. Discrete-Time Fourier Transform
The discrete-time Fourier transform (DTFT) is the appropriate Fourier technique to use in order to obtain a continuous-frequency spectrum for a signal that is a function of discrete time. The continuous-frequency spectrum obtained from the DTFT is periodic, with a period equal to T–1, where T is the discrete-time sampling interval. The DTFT finds widespread use within DSP, primarily because a digital filter’s unit sample response and frequency response comprise a DTFT pair.
The DTFT is defined by
12.1
and the corresponding inverse is given by
12.2
where ω is the continuous radian frequency and T is ...
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