APS审核—数字信号处理Digital_Signal_Processing

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1、SignalSignal is any variable that carries or contains some kind of information that can be recorder，conveyed，displayed，or manipulatedExample： speech ，sound， music， image ，rader and sonar signalDSPDSP is concerned with：The digital representation of signalThe analysis，modification and extraction of in

2、formation from these signalsThe purpose of DSPRemove interference and noise（filtering）from signalObtain and analyze the spectrum of a signalTransform the signal into more suitable formatDigital Signal Processing (DSP) is concerned with the representation, transformation and manipulation of signals o

3、n a computer. Digital Signal Processing begins with a discussion of the analysis and representation of discrete-time signal systems, including discrete-time convolution, difference equations, the z-transform, and the discrete-time Fourier transform. Emphasis is placed on the similarities and distinc

4、tions between discrete-time. The course proceeds to cover digital network and non-recursive (finite impulse response) digital filters. Digital Signal Processing concludes with digital filter design and a discussion of the fast Fourier transform algorithm for computation of the discrete Fourier trans

5、form.1.1 Discrete-Time Signals：Time-Domain RepresentationThe arrow is placed under the sample at time index n = 0 1.2 Sampling: A discrete-time sequence xn may be generated by periodically sampling a continuous-time signal at uniform intervals of time.The spacing T between two consecutive samples is

6、 called the sampling period. Reciprocal of sampling interval T, denoted as FT, is called the sampling frequency (UNIT: HZ)Sampling theorem (Shannon): X a(t)can be represented uniquely by its sampled version xn if the sampling frequency is chosen to be greater than 2 times the highest frequency conta

7、ined in X a(t)1.3 Classification of Sequences1.3.1 xn is a real sequence, if the n-th sample xn is real for all values of n. Otherwise, xn is a complex sequenceExample ：is a real sequence; is a complex sequence1.3.2 A single-input, single-output (SISO) discrete-time system operates on a sequence, ca

8、lled the input sequence, according some prescribed rules and develops another sequence, called the output sequence, with more desirable properties。1.3.4 Basic Operations：AdditionMultiplicationTime-shiftingExample:1.3.4Total energy of a sequence xn is defined byThe average power of an aperiodic seque

9、nce is defined by1.4 Discrete-Time Systems: 1.4.1 Classification Linear Systems Shift-Invariant Systems Causal Systems Stable Systems Passive and Lossless Systems1.4.2 Impulse and Step Responses The response of a discrete-time LTI system to a unit sample sequence dn is called the unit sample respons

10、e or, simply, the impulse response, and is denoted by hn The response of a discrete-time LTI system to a unit step sequence mn is called the unit step response or, simply, the step response, and is denoted by snExample - The impulse response of the systemis obtained by setting xn = dn resulting inEx

11、ample - The impulse response of the discrete-time accumulatoris obtained by setting xn = dn resulting in1.4.3 Input-Output Relationship A consequence of the linear, time-invariance property is that a discrete-time LTI system is completely characterized by its impulse responseExample: Compute its out

12、put yn for the input: As the system is linear, we can compute its outputs for each member of the input separately and add the individual outputs to determine yn.Since the system is time-invariantBecause of the linearity property we getHence, the response yn to an inputwill be Convolution Sum1.4.4 FI

13、R and IIRIf the impulse response hn is of finite length, i.e.,then it is known as a finite impulse response (FIR) discrete-time system.If the impulse response is of infinite length, then it is known as an infinite impulse response (IIR) discrete-time systemExample - The discrete-time accumulator def

14、ined byis an IIR system Nonrecursive System - Here the output can be calculated sequentially, knowing only the present and past input samples Recursive System - Here the output computation involves past output samples in addition to the present and past input samples1.5 Discrete-time Fourier Transfo

15、rm (DTFT)The discrete-time Fourier transform (DTFT) of a sequence xn is given by and are called the magnitude and phase spectra 1.6 Discrete Fourier Transform Using the notation the DFT is usually expressed as: The inverse discrete Fourier transform (IDFT) is given by1.7 Z-Transform1.8 Filter Design