數(shù)字信號處理教學課件：3-6 Digital Processing of Continuous-Time Signals

1、3 .8 Digital Processing of Continuous-Time Signals3 Discrete-Time Signals in the Frequency DomainIn the Time-Domain3.8.1 Effect of Sampling in the Frequency-Domain3 Discrete-Time Signals in the Frequency Domaingn = ga(nT), - n m Then ga(t) is uniquely determined by its samples ga(nT) , -n if T 2 mwh

2、ere T=2/T.The condition T 2 m is often referred to as the Nyquist conditionSampling theorem3 Discrete-Time Signals in the Frequency DomainThe frequency T/2 is usually called the folding frequency orNyquist frequency .Since the minimum sampling frequency T =2m, must be used to fully recover ga(t) fro

3、m its sampled version,the frequency 2m is called the Nyquist rate.3 Discrete-Time Signals in the Frequency DomainIf T2 m , ga(t) can be recovered exactly from gp(t) by passing it through an ideal lowpass filter Hr(j) with a gain T and a cutoff frequency c greater than m and less than T - m as shown

4、below3 Discrete-Time Signals in the Frequency DomainThe spectra of the filter and pertinent signals are shown below3 Discrete-Time Signals in the Frequency DomainOversampling - The sampling frequency is higher than the Nyquist rateUndersampling - The sampling frequency is lower than the Nyquist rate

5、Critical sampling - The sampling frequency is equal to the Nyquist rate3 Discrete-Time Signals in the Frequency DomainFor critical sampling, the continuous signal should not contain an impulse function at m.Example: ga(t) = sin(m t)3 Discrete-Time Signals in the Frequency Domain(3.74a)(3.74b)or(3.63

6、)(3.66)we get:Comparing (3.63) and (3.66),The relation between Ga(j) and G(ej)3 Discrete-Time Signals in the Frequency DomainFrom (3.74) and (3.70),we get: (3.75a)(3.75b)(3.76)3 Discrete-Time Signals in the Frequency DomainRelationship between CTFT and DTFT3 Discrete-Time Signals in the Frequency Do

7、mainExample 3.19 Sampling of a continuous-time signals at two different rate.3 Discrete-Time Signals in the Frequency DomainFig. 3.19 Sampling at 2 HzFig. 3.20 Sampling at 2/3 Hz3 Discrete-Time Signals in the Frequency DomainEffect of aliasing in frequency domainSpeech with aliasingOriginal SpeechOriginal musicMusic with aliasing3 Discrete-Time Signals in the Frequency DomainOrig