Sampling and DSP Instructor: Dr. Mike Turi Department of Computer Science & Computer Engineering Pacific Lutheran University

Outline Sampling ▫More details in a Signals and Systems course A/D or ADC D/A or DAC ▫More details in a DSP course

Sampling Why sample data? Turn continuous-time signal into a discrete-time signal x[n] = x(t)| t=nT = x(nT) ▫x(t) = continuous-time signal ▫T = Sampling interval T ▫X[n] = discrete-time signal

Periodic Signals x(t) = A cos(ωt + θ) for -∞ < t < ∞ ▫A = amplitude ▫ω = angular frequency (radians/sec)  Frequency f = ω/2π ▫θ = phase (radians)

Nyquist Rate Need to sample at twice the maximum frequency of the data ▫Bandwidth = maximum frequency ▫ω = 2B Sampling Theorem ▫Can use a low-pass filter with cutoff frequency B to completely reconstruct original signal

Analog-to-Digital Conversion Sampler ▫Converts continuous-time signal to discrete-time Quantizer ▫Converts discrete-time signal to a discrete-value signal ▫Introduces a quantization error Coding ▫Converts discrete-value to a binary sequence

Digital-to-Analog Conversion Suboptimum interpolator filter ▫DFT: Discrete Fourier Transform ▫FFT: Fast Fourier Transform Sample and hold (S/H) circuit Postfilter (or smoothing filter)

Oversampling Can oversample to reduce resolution requirements of the quantizer