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In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.
The Discrete Fourier Transform (DFT) is the equivalent of the continuous Fourier Transform for signals known only at instants separated by sample times (i.e. a finite sequence of data). Let be the continuous signal which is the source of the data. Let samples be denoted . The Fourier Transform of the original signal,, would be ...
This Jupyter notebook is meant to introduce the concepts of Discrete Fourier Transform (DFT) as a fundamental tool of signal processing. The theoretical foundations of the Fourier transform are
The Fourier series represents a pe-riodic time-domain sequence by a periodic sequence of Fourier series coeffi-cients. On the other hand, the discrete-time Fourier transform is a representa-tion of a discrete-time aperiodic sequence by a continuous periodic function, its Fourier transform.
Understanding the Fourier transform and the spectrum is the foundation for turning analog information into digital information. The question is: How accurately can a discrete set of sampled values of a continuous function represent the function at other values?
Discrete Fourier Transform [11,12] is a method to transform a periodic, discrete signal from time domain to frequency domain with finite range of data samples. Fast Fourier transform is the widely used efficient and fast algorithm for its evaluation.
Lecture 9: The Discrete Fourier Transform. Topics covered: Sampling and aliasing with a sinusoidal signal, sinusoidal response of a digital filter, dependence of frequency response on sampling period, periodic nature of the frequency response of a digital filter. Instructor: Prof. Alan V. Oppenheim.
