Lec7: Practical Filters

Question 1

Design criteria of a filter?

Answer 1

Question 2

Filter design flow criteria?

Answer 2

The design process normally follows a flow:

1. Identify key characteristics (lowpass, highpass, etc)
2. Identify cut-off frequency and sampling frequency
3. Make an educated guess at filter type and size (FIR, N = 5)
4. Design filter (either by hand or using CAD)
5. Evaluate filter performance (ripple, phase, etc)
6. Potentially re-design with different filter type or size

Question 3

The most basic method for designing an FIR filter?

Answer 3

Windowing method

Question 4

How to find the time domain representation?

Answer 4

Consider a low pass filter.

We need to calculate the inverse discrete-time Fourier transform

Question 5

How are the coefficients found?

Answer 5

Question 6

Issues with the impulse response,

what is done to make the response casual?

Answer 6

Question 7

The designed filter?

Answer 7

Question 8

The basis of analogue filters?

Answer 8

IIR filters can be based on analogue counterparts, and then the design process can use the traditional techniques (Butterworth, Chebyshev, etc).

Question 9

What must happen after a filter has been designed?

Answer 9

After a filter has been designed, it must be realised by developing a signal flow diagram that describes the filter in terms of operations on the samples.

Question 10

Important factors to consider when designing a filter?

A given transfer function may be realised in many ways, for example:

ax + bx + c = x(a+b) + c

Answer 10

• Here we have computed the same function, but in one of the realisations we have used only one multiplication.
• This can be important in embedded systems, where multiplication is typically slower and more power intensive than simple addition.
• Specifically, some realisations are better for fixed-point arithmetic and other may be better for floating-point arithmetic.

Question 11

FIR Direct Form I

Answer 11

A straightforward approach for FIR filter realisation is Direct Form 1, where the difference equation is evaluated directly.

This form is practical for small filters, but may be inefficient and impractical for complex designs.

Note that z^-1 represents the unit delay

Question 12

IIR Direct Form I

Answer 12

The same approach can also be used to realise an IIR (or FIR) filter using Direct Form I.

In general, this form requires 2” delay elements (for both the feedforward and the feedback terms) for a filter of order “

Question 13

IIR Direct Form II

Answer 13

The alternate Direct Form II only needs N delay units, where N is the order of the filter. This is potentially half as many as Direct Form I.

The disadvantage is that Direct Form II increases the possibility of arithmetic overflow for filters with high Q. This is to do with the order of operations and the way in which floating-point numbers accumulate errors.