Question

For an analog signal E(t) = 4 + 2 sin 47t + 3 sin 16t V which sampled at a sample rate of 32 Hz. What are the criteria to properly construct its discrete time series. Discuss the results when using fs = 16 Hz and at fs = 45 Hz.

Answer 1

given data: E(H = het a sih hint t3 Sin lott. Solutions The man. frequency in signal is 8h. Nyquist Rate = 16 H2 - 2x sman fs=32 Hz Elts) = hetasin fin (h =htasin na - Is= 1/2 +3 Sin Conn 32 132 +3Sin na 8 2 Conditions , fs Nyquist Rate 3) Signal is Proper ifs = Nyquist Rate =) Critical sampling Is a Nyquist Rate » Improper/reader sampling. fs= 32 Hz de Elsa Let's say, & Hz 8 Hz Now sampling = {hts) = (t + la 1 1 28g -fs o The spectrum will be Is Its Namideal BPF 0 Femmes fs > &mex x2 7 Signal can be reconstructed a Band Pass filter If fs <a sman A lasing Oscars. using

Aro need a filter But @ fs = 16 62 We'll need We cannot use a proper deconstructing helhed, fj fsa Qfm we will with sharp cutoff frequencies. Ideal filter Required For 32 Hz & 45 62 sampling rate, there's No problem - an ideal filter