Đang tải... (xem toàn văn)
Bài giảng Xử lý tín hiệu số - Chapter 7: Frequency analysis of signals and systems has contents: Discrete time fourier transform DTFT, discrete fourier transform DFT, fast fourier transform FFT,... and other contents.
Chapter p Frequency Analysis of Signals and Systems Ha Hoang Kha, Ph.D.Click to edit Master subtitle style Ho Chi Minh City University of Technology @ Email: hhkha@hcmut.edu.vn CuuDuongThanCong.com https://fb.com/tailieudientucntt Frequency analysis of signal involves the resolution of the signal into its freq frequency enc (sinusoidal) (sin soidal) components components The process of obtaining the spectrum of a given signal using the basic mathematical tools is known w as frequency q y or spectral p analysis y The term spectrum is used when referring the frequency content of a signal g The process of determining the spectrum of a signal in practice base on actual measurements of signal is called spectrum estimation The instruments of software programs used to obtain spectral estimate of such signals are kwon as spectrum analyzers Ha H Kha CuuDuongThanCong.com Frequency analysis of signals and systems https://fb.com/tailieudientucntt The frequency analysis of signals and systems have three major uses in DSP DSP: 1) The numerical computation of frequency spectrum of a signal 2) The efficient implementation of convolution by the fast Fourier transform ((FFT)) 3) The coding of waves, such as speech or pictures, for efficient transmission and storage g Ha H Kha CuuDuongThanCong.com Frequency analysis of signals and systems https://fb.com/tailieudientucntt Content Discrete time Fourier transform DTFT Discrete Fourier transform DFT Fast Fourier transform FFT Ha H Kha CuuDuongThanCong.com Transfer functions and Digital Filter Realizations https://fb.com/tailieudientucntt Discrete-time Fourier transform (DTFT) The Fourier transform of the finite-energy discrete-time signal x(n) is defined as: ∞ X (ω ) = ∑ x(n)e − jω n n =−∞ where h ω=2πf/fs f/f The spectrum X(w) is in general a complex-valued function of f frequency: X (ω ) =| X (ω ) | e jθ (ω ) where h θ (ω ) = arg(( X (ω )) with i h -π ≤ θ (ω ) ≤ π | X (ω ) | θ (ω ) : is the magnitude spectrum : is the phase spectrum Ha H Kha CuuDuongThanCong.com Frequency analysis of signals and systems https://fb.com/tailieudientucntt Determine and sketch the spectra of the following signal: a)) x(n) = δ (n) b) x(n) = a nu (n) with |a|