From Continuous- to Discrete-Time Fourier Transform by Sampling Method
From Continuous- to Discrete-Time Fourier Transform by Sampling Method
The purpose of this Demonstration is to show the relation between the continuous-time Fourier transform (CTFT) of a signal (t) and the corresponding discrete-time Fourier transform (DTFT) of the signal generated from (t) by sampling.
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This Demonstration also illustrates the use of different algorithms to reconstruct (t) from .
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The time domain signal (t) consists of two harmonics. You can vary the amplitude and the frequency of each harmonic as well as the sampling frequency, the duration of (t), and the delay time. The magnitude and the phase spectra of (t) and of are also displayed. A number of plotting options are available to help analyze the results generated.
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It is observed that if the CTFT is an aperiodic and continuous function, the DTFT is a continuous function, periodic in . The maximum frequency present in the DTFT is in radians (or in cycles). In addition, there is a scaling effect: the magnitude spectrum of is smaller than the magnitude spectrum of (t), where is the sampling period. The units of the DTFT are radians, while the units of the CTFT are in radians per second.
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