Fir versus iir Filters

IIR Filters	FIR Filters
More efficient	Less efficient
Analog equivalent exists	No analog equivalent
May be unstable	Always stable
Non-linear Phase Response	Linear Phase Response
Very sensitive to filter coefficient quantization errors	Low sensitivity to filter coefficient quantization errors
The design methods are not linear in general	The design methods are generally linear

Standard task for laboratory work

1. It is necessary to design and apply simulation of digital filter according to table 1. Build an impulse and step responses of the filter. Sketch a zero-pole map of the filter. Confirm the results of digital filter design via simulation.

Table 1

FILTER SPECIFICATIONS

No.	Filter Type	Magnitude Frequency responce	, Hz	, Hz	, dB	, dB
1.	LPF	Butterworth	0…200	300…	3	50
2.		Chebysev Type I	0…200	300…	1.5	60
3.		Chebyshev Type II	0…200	300…	2	60
4.	HPF	Butterworth	300 …	0…200	3	50
5.		Chebysev Type I	300 …	0…200	1.5	60
6.		Chebyshev Type II	300 …	0…200	2	60
7.	BPF	Butterworth	200…300	0…100, 400…	3	50
8.		Chebysev Type I	200…300	0…100, 400…	1.5	60

Create in a Simulink environment a model of the filter (see Fig. 6). This model comprises the following blocks – two sine waves with appropriate frequencies and . The frequencies are selected in such a way that the first one lies within a pass band range of the filter and the second one lies within a stop band filter range. The model also involves a block for digital filter parameters evaluation basing on the pre-specified performance requirements Digital Filter Design (FDA Tool) from Signal Processing Blockset Library\ Filter Designs\, concatenation matrix block that concatenates the input and output signals and displays the result of concatenation on the vector scope.

Thus, the block-scheme in the Simulink environment takes the following form

Figure 6 Digital Filter Design in Simulink Environment

By double clicking on Digital Filter Design Block set the performance specification of the digital filter and define its coefficients. The block parameter of digital filter has the following form (see Fig.7). On the next step push the button Filter Design.

Figure 7 Digital Filter Block Parameters

In a Matrix concatenation block set concatenation dimension to 1 in order to combine the input and output signals vertically. Specify in a sine wave option: samples per frame to 50.

After evaluating the digital filter coefficients apply simulation within Simulink environment to observe the results of filtering.

2. Analog to Digital Conversion:

a) Transform an analogue low pass filter to digital form via Impulse invariant method. Transfer function of the filter is expressed as follows

.

b) Transform an analogue low pass filter to digital form via Backward difference method.

, T=0.1 s.

c) Transform an analogue low pass filter to digital form via Bilinear method.

.