《数字信号处理》期末考试卷参考答案(TA级)

(10). The DTFT of a sequence x[n] is denoted as )(ωj e X , then the DTFT of the time shifted version x[n-1] of x[n] is ( ).
(11). We can use three basic operations to construct an arbitary complicated discrete-time LTI system. These three basic operations are addition, ( ) and unit delay.
(12). A causal LTI discrete-time system is described by the difference equation ][]2[15.0]1[8.0][n x n y n y n y =-+--, then the transfer function is ( ).
(13). The continuous-time signal xa(t) = 3cos(200πt) + 5cos(1200πt) is sampled at a 2000Hz rate generating a discrete-time sequence x[n], then the expression of the discrete-time sequence is x[n] = ( ).
(14). The DTFT of a sequence x[n] is denoted as )(ωj e X , then the DTFT of ][0n x e n j ω is ( ).
(15). Suppose that )(ωj e X is the DTFT of a real sequence x[n], the magnitude spectrum )(ωj e X is an ( ) function of ω.
(16). For a real and nonperiodic sequence x[n], its DTFT is ( ) and periodic of ω, and the period is 2π.
(17). Given two N-point real sequences g[n] and h[n], we construct a complex sequence x[n] = g[n] + jh[n]. Assume that the N-point DFT of x[n] is known and denoted by X[k], then we can determine the N-point DFTs G[k] and H[k] from X[k], and G[k] = ( ).
(18). A sequence x[n] = {1, -1, 1, -1, -1, 1}, let X(e j ω) be the DTFT of x[n], then X(e j π) = ( ).
(19). The fundamental period of the discrete-time sequence x[n] = cos(0.1πn) is ( ).
(20). Under the sampling frequency F T = 1000Hz, the corresponding analog frequency of the sequence x[n] = cos(0.2πn) is ( ) Hz.
2、Determine the linear convolution of x[n] and h[n], where
]
[3.0][][2.0][n n h n n x n
n μμ== (12’)
3、Solving the following difference equation(12’)
][]2[02.0]1[3.0][n x n y n y n y =-+-+
Determine the unit step response.
4、Determine the transfer function of the system described by the following block diagram: (12’)
5、The windowed Fourier series method is often used in FIR digital filter design. The parameters of several commonly used window functions are listed in the following table. Now given the frequency specifications of an FIR digital lowpass filter below:
dB p 1=α, dB s 40=α, πω2.0=p , πω4.0=s
⊕
]
[n y
(a). Choose an appropriate window function. (6’) (b). Determine the order of the FIR digital filter. (6’)
6、A sequence x[n] is generated by sampling a real continuous-time signal x a (t) with sampling frequency F T = 1000Hz. Its 16-point DFT X[k] is:
X[k] =[0 -j4 -j4 -j4 -j4 0 0 0 0 0 0 0 j4 j4 j4 j4]
Or expressed as ⎪⎩
⎪
⎨⎧==-=otherwise k j k j k X ,015,14,13,12,
44,3,2,1,
4][ Assume that the time-domain and the frequency-domain sampling processes have no aliasing.
(1). Determine the IDFT x[n] of X[k]. (6’)
(2). Determine the expression of the continuous-time signal x a (t). (6’)。