> anishgoyal █

Notes › ENGR 2341: Signals and Systems Lecture 6

Discrete Time System Response

calendar_today January 21, 2025 article 104 words access_time 1 min replay Modified January 21, 2025

Table of Contents

Discrete-time Convolution

Exact same properties as integral convolution for continuous-time systems

$$y[n] = h[n] * x[n] = \sum_{k=-\infty}^\infty h[k] \cdot x[n-k]$$

System Response

Just like in continuous-time systems, you can use the properties of LTI systems to determine the output if the responses for the inputs are known

FIR and IIR System Response

The difference equation is more straightforward to evaluate than convolution sum for IIRs
- Sum the products of the filter coefficients and the corresponding input/output samples
Causal FIR (this is practically the same as convolution sum)

$$y[n] = \sum_{k=0}^M b_{k}x[n-k]$$

Causal IIR

$$y[n] = \sum_{\ell=1}^M a_{\ell}y[n-\ell]+\sum_{k=0}^M b_{k}x[n-k]$$

References

Discrete-time system response (course handout)

Sources

Discrete-time system response

Graph

mindmap ↗