Discrete time fourier transform

Bài giảng "Xử lý tín hiệu số: Fourier Transform" cung cấp cho người học các kiến thức: Frequency analysis of discrete time signal, properties of Fourier transform, frequency domain characteristics of LTI systems, discrete Fourier Transform, fast Fourier Transform. Mời các bạn cùng tham khảo nội dung chi tiết.

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After studying this chapter students will be able to understand frequency analysis of signals and systems. This chapter includes content: Discrete time fourier transform DTFT, discrete fourier transform DFT, fast fourier transform FFT.

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Biến đổi Fourier thời gian rời rạcDiscrete – Time Fourier Transform (DTFT) Tín hiệu x(n) rời rạc, không tuần hoàn, chiều dài L hữu hạn Biến đổi DTFT cho phổ liên tục X(ω). xp(n) tuần hoàn chu kỳ N Tính DFS của xp(n) Xp(k Công thức biến đổi DFT N-điểm cho chuỗi chiều dài L Giải thuật biến đổi Fourier nhanhFast Fourier Transform (FFT)

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now is: The PSD-per-unit-time converges to finite values at all frequencies except those where h(t) has a discrete sine-wave (or cosine-wave) component of finite amplitude. At those frequencies, it becomes a delta-function, i.e., a sharp spike

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Examples of Discrete Transforms In this chapter we discuss the most important fixed discrete transforms. We start with the z-transform, whichis a fundamental tool for describing the input/output relationships in linear time-invariant (LTI) systems. Then we discuss several variants of Fourier series expansions, namely the discrete-time Fourier transform, thediscrete Fourier transform (DFT), and the Fourier fast transform (FFT).

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In the chapter “Fourier Series, Fourier Transforms, and the DFT” by W. Kenneth Jenkins, many important Fourier transformconcepts in continuous and discrete time are presented. The discrete Fourier transform(DFT), which forms the backbone of modern digital signal processing as its most common signal analysis tool, is also described, together with an introduction to the fast Fourier transformalgorithms.

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