Problems on LPF 1.1

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A 1kHz signal is sampled at the rate of 1.8kHz and the samples are applied to an ideal rectangular LPF with a cut-off frequency of 1.1kHz, then the output of the filter contains

(a) only 800 Hz component

(b) 800 Hz and 900 Hz components

(c) 800 Hz and 100 Hz components

(d) 800 Hz, 900Hz and 100 Hz components

Answer is ( a )

Concept

Explanation

The frequency at which the aliased signal will be present is given by f_m±kf_s ;where f_m and f_s represent message and sampling frequencies respectively with k being an integer. In this example,

frequency at 1kHz will get aliased at -0.8(=1+1.8)kHz and 2.8(=1+1.8)kHz. 

Similarly the signal at -1kHz will get aliased at 0.8(=-1+1.8)kHz and -2.8(=-1-1.8)kHz.

After passing through an ideal rectangular LPF with cutoff frequency 1.1kHz, only the component of 0.8kHz remains.