Lec5: The IIR filter Flashcards
what is the IIR filter?
Infinite Impulse Responce (IIR)
The General IIR filter equation?
al and bk ?
The set of coefficients that describe the filter,
How is the FIR different to the IIR?
It is similar to the FIR filter (the feedforward term), but now we have introduced a feedback term. I.E the output from the filter is passed back into the system.
The total coefficient count of IIR?
M+N+1. The filter order is governed by N
The assumptions of the IIR filter?
For the IIR filter, we make the assumption of initial rest.
Formally: x[n] = 0 for n < n0 and y[n] = 0 for n < n0. Where n0 is our start time.
This is sufficient to result in the IIR filter being both linear and time-invariant.
Why are the initial filter assumptions required?
This is sufficient to result in the IIR filter being both linear and time invariant.
The principle of superposition also holds, because the difference equation involves only linear combinations of the inputs and outputs.
How to demonstrate a basic IIR filter?
We can demonstrate the basic IIR filter by considering the impulse response ℎ[n] for a 1st order filter:
Find the impulse response?
Impulse response graph for a first-order IIR with b0=1 and a1 = 0.8
The z transform of both the feedforward and feedback parts?
Finding the IIR system function?
The numerator and denominator polynomials?
The coefficients of the numerator polynomial B(z) correspond to the feed-forward terms.
Those of the denominator polynomial A(z) for z-l where l>0 correspond to the feed- back terms.
Finding the poles and zeros of the system function H(z)?
Calculating the poles and the zeros?
IIR filter, how to examine the frequency response?
Filter details
Highpass
Note: At DC, the ratio is not quite 0 but 0.55
How to conduct frequency response on a filter?
Filter type?
Bandpass
How can IIR be unstable?
Due to the feedback path (and the infinite impulse response), we have the potential for instability in IIR filters. If the feedback is self sustaining.
The stability of causal IIR systems?
Causal IIR systems, initially at rest, are stable if all poles lie inside the unit circle.
The stability of causal FIR systems?
Causal FIR systems, which have no poles (other than at zero) are unconditionally stable.
How can the stability of a 1st order IIR be investigated?
