Filter Design Toolbox

Getting Started with the Toolbox

This section provides an example to get you started using Filter Design Toolbox. You can run the code in this example from the Help browser (select the code, right-click the selection, and choose Evaluate Selection from the context menu) or you can enter the code on the command line. This exercise also introduces Filter Design and Analysis Tool (FDATool). You use it to design and analyze filters, and to quantize filters.

As you follow the example, you are introduced to some of the basic tasks of designing a filter and using FDATool. You will engage some of the quantization capabilities of the toolbox, and a few of the filter design architectures provided as well.

Before you begin this example, start MATLAB and verify that you have installed Signal Processing and Filter Design Toolboxes (type ver at the command prompt). You should see Filter Design Toolbox, version 2.0 and Signal Processing Toolbox, version 5.0, among others, in the list of installed products.

Example - Creating a Quantized IIR Filter

Example Background.   Wireless communications technologies, such as cellular telephones, need to account for the receiver's motion relative to the transmitter and for path changes between the stations. To model the channel fading and frequency shifting that occurs when the receiver is moving, wireless communications models apply a lowpass filter to the transmitted signal. With a narrow passband of 0 to 40Hz that modifies the transmitted signal, the lowpass filter simulates the Doppler shift caused by the motion between the transmitter and receiver. As the lowpass filter requires a rather peculiar rising shape across the passband and an extremely sharp transition region, designing and quantizing the filter presents an interesting study in filter design. In Figure 1-2, you see the frequency response curve for the RFC filter. Notice the narrow passband with the rising shape and the sharp cutoff transition. Also note that the y-axis is a linear scale that dramatizes the shape of the passband.

Figure 1-2: Frequency Response of the Filter Used to Simulate the Rayleigh Fading Channel Phenomenon

To create a filter with the passband shape in the figure, we define four vectors that describe the shape.

Vector	Definition
Frequency vector	Specifies frequency points along the frequency response curve. frequency can be in Hz or normalized. In our example, we are using normalized entries.
Edge vector	Specifies the edges, in Hz or in normalized values, of the passband and stopband for the filter. In our example, we are using normalized entries.
Magnitude vector	Specifies the filter response magnitude at each frequency specified in the frequency vector. These values produce the distinctive passband we require.
Weight vector	Specifies the weighting for each frequency in the frequency vector.

Most filter designs do not require you to define four vectors to specify the filter response. Because the passband of the filter we want is not standard, we are going to use the Arbitrary Magnitude filter type in FDATool when we design our filter. This type requires four input vectors to specify the filter. You can also design filters with more normal passband specifications directly in FDATool. You can enter the four vectors in FDATool, but long vectors are easier to enter at the command line. If the vectors exist as files, you can use MATLAB commands to import the vectors into your MATLAB workspace.

Comparison to the Signal Processing Toolbox

Designing the IIR Filter