Discrete-time Processing of Continuous-time Signals

Overview

1. Sample the continuous signal
2. Process the sampled signal to produce a discrete-time output
3. Reconstruct discrete-time output to create a continuous-time output

More In-depth

• Signal must be pre-filtered to make it bandlimited so that it can be sampled without aliasing
  • The pre-filter is an analog filter with a cutoff frequency less than the Nyquist rate
  • The system response is only defined for the Nyquist interval
• The analog to digital converter samples and quantizes the filtered signal
• The sampled signal is processed using a discrete-time system, typically a difference equation (FIR or IIR filter)
• The digital to analog converter reconstructs a continuous-time signal from the discrete-time output of the discrete-time system
• There may be analog post filtering done on the reconstructed signal

Effective Frequency Response

• The equivalent continuous-time frequency response corresponding to the effect of processing a continuous-time signal within a discrete-time signal
  • A mapping between discrete-time frequency response and continuous-time frequencies
  • Replace $\hat{\omega}$ with $\omega / f_s$

Example

References