Digital Signal Processing Questions & Answers

Digital Signal Processing Questions & Answers 'half-band' FIR - CORRECT ANSWER - for fc = fs/4 then impulse response of FIR is hi=0 for all even values of i - requires only 1/2 number of multiplications during convolution - can use when sampling rate needs to be halved as an anti-aliasing filter anti-aliasing filter - CORRECT ANSWER - limits bandwidth of input signal to some frequency (given by Nyquist Limit) Band-pass signal sampling - CORRECT ANSWER - can reconstruct sampled signals if spectral components lie entirely within interval: nfs / 2 < |f| < (n+1) fs / 2 for n in N - aliasing copies interleave (not overlap) h(t) = (n+1)fs sinc(πt(n+1)fs) - nfs sinc(πtnfs) where sinc(x) = sinx/x (for rect: sinc(x) = sin(πx)/(πx) choosing sampling frequency in practice - CORRECT ANSWER - due to: 1. causality (sinc stretches in both directions) 2. economic constraints can only approximate ideal low-pass filter: instead of a sharp transition between pass-band and stop band, feature a transition band: signal attenuation gradually increases - so choose somewhat higher than twice highest frequency of interest in continuous signal (e.g. 4x) - higher sampling frequency: higher: 1. CPU, 2. power 3. memory tradeoff between: signal quality, analog filter cost and digital subsystem expenses Deconvolution - CORRECT ANSWER - s = u * h F(s) = F(u) • F(h) u = F-1{F(s)/F(h)} Deconvolution: noise - CORRECT ANSWER - But may get noise: c(t) = s(t) + n(t)