西北工业大学2021年数字信号处理口试复习
This is the teacher's concept review question near the end of the term, which can be combined with these concept questions to assist in the review. The oral exam and this question bank are not completely duplicated
. In order to facilitate future review and consolidation, record this blog's
final exam basic concepts review questions
Autor: torque
chapter 2
模拟信号、离散时间信号和数字信号三者的特点是什么？
Analog signal: both time t and amplitude are continuous, and there is a definite value instantaneously
Discrete-time signal: time is discrete, and amplitude is continuous
Digital signal: The signal amplitude is quantized, and the time and amplitude are not continuous
数字信号和离散时间信号相同吗？
Not the same, the digital signal is the signal after quantization. discontinuous in magnitude.
离散时间信号x(n)的n下标如何表示时间？
X(n)=X(nT), in many cases it can be completely determined by n, T can be omitted, or take T as 1
DSP系统中最常见的三种基本运算是哪几种？
1. Addition and subtraction 2. Number multiplication 3. Sequence shift
DSP的延时操作是怎么实现的？
shift the sequence to the right
非时变系统的特点是什么？
The performance of the system does not change over time. The response of the system is independent of the moment when the input signal is applied to the system
系统一般因果性的概念是什么？
The output of the system at the current moment is only related to the current moment and the input before the current moment, and has nothing to do with the future input
系统一般稳定性的概念是什么？？
A system in which bounded inputs produce bounded outputs
线性非时变系统（LTI或LSI）输入和输出的时域关系是什么？？
The output is equal to the linear convolution of the input sequence and the unit sampled response of the system
LTI系统的单位冲激响应h(n)如何表述它的因果性和稳定性？
Causality: when n<0, h(n)=0 Stability: h(n) is absolutely summable (when n tends to infinity, the value of h(n) accumulated from negative infinity to positive infinity is less than positive infinity
非因果系统能实现吗？为什么？
It cannot be realized, it violates the law of causality in physics, it is impossible to have an effect and then a cause
LTI系统卷积的物理意义是什么？？
The processing method or processing rule of the input sequence by the LTI system
When sampling an analog low-pass band-limited signal, what is the theoretical minimum sampling frequency without distortion?
Twice the highest frequency of the analog signal
模拟信号被采样以后，频域怎样变化？？
The spectrum becomes a continuous period, which is the result of the infinite period extension of the continuous signal spectrum before sampling with the sampling frequency as the period, and the spectrum amplitude becomes 1/T of the original amplitude.
实际中采样模拟信号用什么器件实现？它的输出是离散时间信号还是数字信号？
A/DC converter, digital signal is obtained after quantization
一个模拟信号和它采样后序列的频率关系是什么？
Ω / fs = ω
DAC能实现数字信号到模拟信号的理想重构吗？为什么？?
No, the DAC is a non-ideal low-pass filter, the recovered analog signal is approximate
理论上离散时间信号重构模拟信号的最佳内插函数是哪一种函数？
Sa(π/T(t-nT))
Chapter 3
LTI系统对正弦序列的响应有什么特点？
The response is simply the result of the input signal changing the amplitude and phase, not the frequency
LTI系统幅频响应的物理意义是什么？ ？
The selectivity of the system to signals of different frequencies
LTI系统相频响应的物理意义是什么？？
The processing time of the system for signals of different frequencies
序列傅里叶变换DTFT的定义式是什么？
序列傅里叶变换DTFT是信号的频谱，频谱的物理概念是什么？？
Amplitude and phase distribution of sinusoidal components of different frequencies contained in a sequence
序列频谱（DTFT）是周期函数吗？周期等于多少？
is a periodic function with a period of 2
DTFT频谱在一个周期 内的负频率范围是什么？
[Π ， 2Π]
为什么要对信号进行傅里叶变换？它比时域分析好在哪里？
1. Because some characteristics of the signal are not easy to reflect in the time domain, but can highlight its characteristics in the
frequency domain. 2. Frequency domain analysis converts differential or difference equations into algebraic equations.
LTI系统的频域描述关系式是什么？
Y(ejω)=X(ejω)H(ejω) The product of the system frequency response and the input in the frequency domain
LTI系统的频率响应函数和单位冲激响应的关系是什么？
The DTFT of unit impulse response is the frequency response function
系统幅频响应的物理意义是什么？
The selectivity of the system to signals of different frequencies
系统相频响应的物理意义是什么？
The processing time of the system for signals of different frequencies
一个序列的Z变换与DTFT的关系是什么？
The Z-transform generalizes frequencies from the real range to complex numbers, since DTFT is a special case of the Z-transform, on the unit circle
与傅里叶变换相比，Z变换的优点是什么？
Convergence conditions are not as strict as Fourier transforms
Z变换收敛域的概念是什么？
The set of Z values that allow X(Z) = ΣX(n)Z^(-n) to converge
一个稳定因果系统的系统函数的收敛域有什么特点？
The region of convergence includes the unit circle and infinity if and only if all the poles of the system function H(Z) lie within the unit circle
一个因果有限长序列的z变换收敛域存在吗？有什么特点？
Exist, the convergence region starts from (0,∞] does not contain 0 and contains ∞
系统函数H(z)和单位冲激响应是什么关系？
The Z transform of the unit impulse response of a system is its system function
系统函数H(z)和系统的频率响应函数的关系是什么？
The value of H(Z) on the unit circle is the frequency response function
系统函数的零点和极点对幅频响应的影响是什么？？
1. When the pole is close to the unit circle, the amplitude-frequency response will have a peak at the frequency where the pole is located. The closer the pole is to the unit circle, the sharper the peak; Close to the unit circle, the deeper the valley bottom, when the zero point is on the unit circle, the amplitude-frequency response is zero
2. The zero and pole at the origin do not affect the amplitude-frequency response characteristics of the system, but only affect the phase-frequency characteristics.
系统函数的极点是否可以在Z平面的单位圆上？为什么？
If the system is stable, the system poles cannot be on the unit circle. If the system is unstable, that's fine. And if the zeros and poles of the system are on the unit circle, then it is also possible, because it can cancel
什么是FIR系统？它的系统函数有什么特点？？
Finite Impulse Response System. The unit impulse response has a finite time domain. Features: All-zero system. no poles other than the origin
什么是IIR系统？它的系统函数有什么特点？？
Infinite Impulse Response System. The time domain of the unit impulse response is infinite. Features: All-pole and zero-pole system, no zeros other than the origin
常系数差分方程表示系统的优点是什么？？
External characterization method, that is, the relationship between input and output, regardless of the internal state variables of the system
系统的网络结构表示系统的意义是什么？？
Indicates the operating structure and specific implementation of the system
Chapter 4
DFS适用于哪一类序列的频谱计算？
discrete periodic sequence
DFT适用于哪一类序列的频谱计算？
Discrete Sequences of Finite Length
DFT和DTFT的表示的频域信息相同吗？它们有什么区别？？
The same, but the information represented in the frequency domain of the DFT is obtained by sampling the [0,2π] information in the frequency domain of the DTFT
对一个序列进行DFT计算，序列的频谱DTFT如何变化？
Sampling at N points in the range of [0, 2π] to obtain discrete signals
工程实际中对序列进行频谱分析采用的是DTFT还是DFT？为什么？
DFT, because the computer deals with discrete finite-length signals, and the spectrogram of DTFT is a continuous periodic signal
一个N点有限长序列的DTFT、DFT和Z变换都存在吗？它们的关系是什么？
all exist. DFT is the result of uniform sampling of Z transform on the unit circle, it is the sampling of N points at equal intervals within a period of DTFT, and DTFT is the Z transform on the unit circle
为什么DFT可以用在工程实际中？
The frequency domain of DFT is discretized, and the operations can be arranged in the computer system, and there are a variety of fast algorithms that can speed it up
DFT比DTFT好在哪里？
DFT makes the signal finite and discretized in the frequency domain, so that the computer can process the signal in the frequency domain. In particular, DFT has a variety of fast algorithms, which can greatly improve the speed of signal processing.
Chapter 5
FFT名称的含义是什么？它是一种新的傅里叶变换吗？
Fast Fourier Transform is not, just a fast algorithm for DFT
发明FFT算法的目的是什么？它有什么好处？
Faster Fourier transform calculations for better adaptation to engineering problems. Saves a lot of computation, reducing N2 complex multiplications and N(N-1) complex additions to 〖N/2 log〗_2N complex multiplications Nlog_2N complex additions
对一个N点序列，直接计算DFT的复数乘法计算量是多大？FFT的计算量是多大？
N ^ 2 〖N / 2 log〗 _2N + Nlog_2N
一个N点序列的N点FFT和DFT的结果相等吗？
Same
FFT算法可以减少计算量的最主要思路是什么？
The DFT of N points is decomposed into 2 N/2 points using symmetry and periodicity. Using the formula, the X(k) of N points can be calculated
按时间抽取基2-FFT算法的抽取规律是什么？
The code bit is inverted. Before the sequence enters the FFT, the sequence is input according to the inversion of the binary code system in natural order.
FFT算法中码位倒置规律和同址运算概念是什么？
Co-location operation: The result of each butterfly operation is stored in the storage unit occupied by the original input data
Code point inversion: The x(n) entered is sorted according to the inversion of the binary code system in natural order
Chapter 6
数字滤波器分为哪两种类型？
FIR and IIR digital filters
Classic and modern filters
数字滤波器的通带指标含义是什么？阻带指标含义是什么？?
Passband index: The cutoff frequency of the passband is the maximum frequency of the passband and the maximum attenuation of the
passband Stopband index: The cutoff frequency of the stopband is the minimum frequency of the stopband and the minimum attenuation of the stopband
3分贝截止频率的概念是什么？
The corresponding cutoff frequency when the amplitude response is attenuated by 3 dB
理想滤波器能实现吗？为什么？?
cannot be achieved because its unit impulse response is acausal and infinitely long
巴特沃斯滤波器的特点是什么？?
1. When Ω=0, there is no attenuation
. 2. The larger the N, the slower the passband attenuation. It is the flattest amplitude-frequency response filter
. 3.3db The frequency does not change with the order.
通带最平坦滤波器是哪一种滤波器？
Butterworth filter
冲激响应不变设计法的缺点是什么？?
1. There is no direct mapping relationship from S to Z.
2. There is frequency aliasing distortion.
3. Only suitable for low-pass and band-pass filter design, not high-pass and band-stop filter design
双线性变换设计法可以设计高通滤波器吗？为什么？?
Yes, map the entire imaginary axis of the S plane to the unit circle of the Z plane. The simple algebraic conversion relationship between the two can eliminate aliasing
. Chapter 7
FIR滤波器实现第一类线性相位特性的条件是什么？它能实现吗？
h(n) = h(Nn-1) energy
系统具有线性相位特性处理信号的优点是什么？?
When implementing the filter, when N is an even number, only N/2 multipliers are required, and when N is an odd number, (N+1)/2 multipliers are required, and N multipliers are required if the linear phase condition is not satisfied. . and the delay is the same for all frequency signals
具有线性相位的FIR滤波器零点分布的特点是什么？
4 zeros, mirror image, conjugate distribution. Z,1/Z,Z*,1/Z*
FIR滤波器窗函数设计法的阻带指标由什么因素决定？?
main lobe to side lobe ratio
吉布斯效应是什么？?
Due to the fluctuations in the passband and stopband caused by the windowing cut-off, the attenuation of the stopband is deteriorated, and the transition band is introduced.
窗函数设计法中，增加FIR滤波器长度N可以改进阻带和通带技术指标吗？为什么？？
No, increasing N can only reduce the main lobe width and make the transition band narrower. but cannot change the side lobe amplitude
N点长度的线性相位FIR滤波器的处理延时等于多少？
(N-1)/2 sample intervals
FIR滤波器的频率取样设计法的特点是什么？？
Starting directly from the frequency domain, the ideal frequency response is sampled to determine the value of Hd(k), so that the designed system function H(z) can be approximated to the ideal system function Hd(z). Both can have the same frequency response, at least at the sampling point frequency. However, the cut-off frequency can only be an integer multiple of 2π/N, and it cannot take any value freely.
如何改进频率取样设计法的阻带技术指标？ ？
Add transition points near discontinuities