Ch. 4 Digital Filtering

1. Ch. 4 Digital Filtering DSP-LabVIEW

2. 4.1 Digital Filtering • Finite Impulse Response (FIR) Filters • y[n] = b0 x[n] +b1 x[n-1] + …+ bN x[n-N] • N is the filter order (number of zeros in the system function, H(z)). • b’s are the filter coefficients, and for the FIR filter, the impulse response, h[n]. • x[n] is the input to the filter and y[n] is the output.

3. 4.1 Digital Filtering (p.2) • Design Algorithms for FIR Filters • Remez Exchange Algorithm—equal ripple; this means that the deviation from the desired frequency response is evenly distributed across the passband and stopband. • Kaiser Window • Dolph-Chebyshev Window • Figure 4.1 illustrates the responses of different designs for the same requirements.

4. 4.1 Digital Filters • Infinite Impulse Response (IIR) Filters • y[n] = b0 x[n] +b1 x[n-1] + …+ bN x[n-N] + a1 y[n-1] + …+ aM y[n-M] • The system function, H(z), has N zeros and M poles. • The a coefficients represent the “feedback” portion of the difference equation. • From a system theory view, IIR systems are often compared to continuous time filters.

5. 4.1 Digital Filters (p.4) • Design Algorithms for IIR Filters (Table 4-1)

6. 4.1.2 Stability and Structure • In general, FIR filters require less precision and are computationally more stable than IIR filters. • FIR systems have linear phase.

7. 4.1.2 Stability and Structure (p.2) • Filter Attribute Comparison (Table 4.2)

8. 4.1.2 Stability and Structure (p.3) • The difference equation for a digital filter can be implemented directly, or the computation can be revised to provide different structures. • In the case of IIR filters, a higher order system function can be implemented as a cascade of 2nd (and first) order systems—see Fig. 4-3—to improve stability. • Fig. 4-4 shows a second order Direct-Form II structure.

9. 4.2 LabVIEW Digital Filter Design Toolkit • The DFD Toolkit has tools that can be used to design, analyze, and simulate floating point and fixed point implementations of digital filters. • DFD Classical Filter Design Express VI—used to design and analyze digital filters. • DFD Pole-Zero Placement Express VI—used to alter the poles and zeros in the complex plane. • And more!

10. Lab 4: FIR/IIR Filtering System Design • L4.1FIR Filtering System • L4.1.1 Design FIR Filter with DFD Toolkit • Low Pass Filter • Passband response: .1 dB • Passband frequency: 1200 Hz • Stopband attenuation: 30 dB • Stopband frequency: 2200 Hz • Sampling frequency: 8000 Hz • L4.1.2 Create a Filtering System VI

11. L4.2 IIR Filtering System • L4.2.1 IIR Filter Design • Bandpass filter • Passband response: .5 dB • Passband frequency: 1333 to 2666 Hz • Stopband attenuation: 20 dB • Stoband frequency: 0-1,000; 3,000-4,000 Hz • Sampling frequency: 8,000 Hz. • L4.2.2 IIR Filtering System

12. L4.3 Building a Filtering System Using the Filter Coefficients • Assume that you have obtained the filter coefficients by hand or using some other tool, besides the DFD toolkit. • The coefficients could be entered into a LabVIEW system as an array of numeric constants. • DFD Build Filter from TF.VI —uses direct-form coefficients. • DFD Build Filter from Cascaded Coef.VI —used to build IIR filters as a cascaded of 2nd order sections. • The above can be wired to the DFD Filtering. VI.

13. L4.4 Filter Design Without Using DFD Toolkit • The examples can be implemented with the DFD Toolkit. • Digital FIR Filter VI –configured based on filter specifications. • Digital IIR Filter VI