[經(jīng)濟學(xué)]lecture5fourierseries_frequencydomainrepresentationofltisystem_slingandre-wenkub
2022-10-31 22:09:42 本頁面
【正文】 ( jweX )()()( jwjwjw eXeHeY ?Condition: 1. Absolutely summable sequence 2. LTI system The DiscreteTime Fourier Analysis Frequency response function from difference equations When an LTI system is represented by the difference equation, then to evaluate its frequency response , we would need the impulse response h(n). We know that when , then y(n) must be ? ?? ? ???? Nl Mm ml mnxblnyany 1 0 )()()(njenx ??)( njj eeH ?? )(???????? NlljlMmmjmjeaebeH101)(???The DiscreteTime Fourier Analysis Sampling and reconstruction of analog signals Analog signals can be converted into discrete signals using sampling and quantization operations: analogytodigital conversion, or ADC Digital signals can be converted into analog signals using a reconstruction operation: digitaltoanalogy conversion, or DAC Using Fourier analysis, we can describe the sampling operation from the frequencydomain viewpoint, analyze its effects and then address the reconstruction operation. We will also assume that the number of quantization levels is sufficiently large that the effect of quantization on discrete signals is negligible. The DiscreteTime Fourier Analysis Sampling(采樣 ) Continuoustime Fourier transform and inverse CTFT ??????????????????dejXtxdtetxjXtjaatjaa)(21)()()(?1. Absolutely integrable 2. Omega is an analogy frequency in radians/sec The DiscreteTime Fourier Analysis The DiscreteTime Fourier Analysis Sampling Sample xa(t) at sampling interval Ts sec apart to obtain the discretetime signal x(n) ????????????????????????l ssasjsalTTjXTeXnTxnx??? 21)()()(1. relationship between analog signals and sampling signals in frequencydomain. 2. The above relation is known as the aliasing formula The DiscreteTime Fourier Analysis The analog and digital frequencies TFTs1????Fs: the sampling frequency, sam/sec –Amplitude scaled factor: 1/T。 ~(1 / ) ( )N X k~(1 / )
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