《信号与系统》课件 ch5.ppt

作业：5.21(a)(b)(c)(f)5.22(a)(b)(c)(g)5.235.255.26(a)(b)5.34 * Example 5.13 Determine the discrete-time Fourier transform of the sequence Since the Fourier transform of x[n] is periodic with period 2π, and with the form of square wave, so we consider signal g(t), which is a periodic square wave with period 2π, and with the Fourier series coefficients of g(t) are Let T1 = π/2, then we have ak = x[k], taking ak and g(t) into the analysis equation: * Renaming k as n and t as ω, we have Replacing n by –n , we obtain Thus, * 7. Systems characterized by linear constant-coefficient difference equations is a ratio of polynomials in the variable . coefficients of the numerator polynomial = coefficients appearing on the right side of the difference equation. coefficients of the denominator polynomial = coefficients appearing on the left side of the difference equation. * Example 5.14 Consider a causal LTI system that is characterized by the difference equations and let the input to this system be Determine the output y[n]. The form of the partial-fraction expansion in this case is * So that, Consequently, * 8. Discrete-Time Frequency-Selective Filter 1 –2π –π –ωc 0 ωc π 2π ω ideal low-pass filter –2π –π π 2π ω ideal high-pass filter –2π –π π 2π ω ideal band-pass filter 1 –π π ω ideal band-stop filter * 9. Sampling of Discrete-Time Signals xp[n] x[n] Χ x[n] n p[n] n xp[n] n Impulse-train sampling 1) Impulse-Train Sampling * 2π/N ωs 2π ω spectrum of sampling sequence –2π –ωM ωM 2π ω 1 spectrum of original signal 1/N –ωM ωM ωs 2π ω (ωs – ωM) spectrum of sampled signal