关于数字信号处理的问题Acontinuous-timesignalxa(t)iscomposedofalinearcombinationofsinusoidalsignalsoffrequencies250Hz,600Hz,1.1kHz,2.4kHz,and3.8kHz.Thesignalxa(t)issampledata2.0-kHzrate,andthesampledsequence

Question

关于数字信号处理的问题
A continuous-time signal xa(t) is composed of a linear combination of sinusoidal signals of frequencies 250 Hz,600 Hz,1.1 kHz,2.4 kHz,and 3.8 kHz.The signal xa(t) is sampled at a 2.0-kHz rate,and the sampled sequence is passed through an ideal lowpass filter with a cutoff frequency of 900 Hz,generating a continuous time signal ya(t).What are the fre-quency components present in the reconstructed signal ya(t)?

Answer 1

采样定理,采样后的频率应在(0,fs)的区间上
所以
f1=250mod(fs)=250hz
f2=600mod(fs)=600hz
f3=1.1kmod(fs)=1.1hz
f4=2.4kmod(fs)=400hz
f5=3.8kmod(fs)= 1.8khz
截止频率为900hz
所以大于900hz的正弦信号删去
重组的采样后的信号所含频率为250hz,600hz,400hz