Lec 6: Design Considerations

Question 1

The phase and magnitude of a frequency response?

Answer 1

Question 2

Filter phase linearity key information?

Answer 2

In this example, the phase response is said to be linear, because it is a linear function of frequency.

Not all filters have linear phase.

Question 3

Checking that the filter response is linear?

Answer 3

Question 4

Consider breaking down a square wave into individual frequency components, each component is then scaled and shifted (by the filter magnitude and phase response) and then summed back together.

Linear Phase

Answer 4

Question 5

Consider breaking down a square wave into individual frequency components, each component is then scaled and shifted (by the filter magnitude and phase response) and then summed back together.

Non-linear phase?

Answer 5

Question 6

Identifying linearity in a signal with a greater number of cisoid terms?

Answer 6

Black - Linear phase means that all frequencies are delayed equally, and so the waveform morphology is minimally distorted.

Red - Non-linear phase means that some frequencies are delayed more than others, leading to greater distortion of the signal morphology.

Question 7

The four types of Linear Phase FIR filters

Answer 7

Question 8

The symmetry and anti-symmetry of an impulse response?

Answer 8

Question 9

The impulse response of type 1 Linear phase FIR filter?

Answer 9

Question 10

The impulse response of type 2 Linear phase FIR filter?

Answer 10

Question 11

The impulse response of type 3 Linear phase FIR filter?

Answer 11

Question 12

The impulse response of type 4 Linear phase FIR filter?

Answer 12

Question 13

The all pass filter?

Answer 13

Question 14

All pass filter example

Answer 14

Question 15

What is Zero phase filtering?

Answer 15

Sometimes we want to ensure that we have no effect on the phase at all (i.e we do not want any shift in any frequency component).

This is called zero phase filtering and is actually quite easy to do, but only offline once a signal has already been captured.

Question 16

How is zero phase filtering conducted?

Answer 16

Question 17

Where is zero phase filtering used?

Answer 17

Zero phase filtering can be very important in applications where the timing information needs to be preserved (for example in a communications system, or in the analysis of biomedical signals).

Question 18

casual/non-casual zero phase filtering?

Answer 18

non-casual

Question 19

zero phase filtering MATLAB

Answer 19

Question 20

Differences in FIR IIR stability?

Answer 20

FIR filters (realised non-recursively) are unconditionally stable (all poles are at 0).

Question 21

FIR IIR linearity differences?

Answer 21

FIR filters can have an exactly linear phase response, this is an important requirement in many applications such as digital audio processing.

Question 22

The effect of finite precision in FIR and IIR?

Answer 22

Question 23

FIR IIR differences number of coefficients?

Answer 23

FIR filters require more coefficients (higher order) for sharp cutoff characteristics than IIR filter. Thus equivalent FIR filters tend to be much larger and slower than IIR filters.

Question 24

FIR and IIR differneces Analogue filters ?

Answer 24

Analogue filters may be readily transformed into equivalent IIR digital filters (due to the feedback terms). This is not possible with FIR digital filters as they have no analogue counterpart.

Question 25

FIR and IIR differences ease of design?

Answer 25

In general, FIR filters are more difficult to design, unless CAD support is available.

Question 26

When to use IIR filtering?

Answer 26

Use IIR when the only important requirements are sharp cutoff and high throughput (low order).

Question 27

When to use FIR filtering?

Answer 27