Design a bandstop filter such that the center frequency is F

Design a band-stop filter such that the center frequency is FO=8 kHz and bandwidth is BW = 4 kHz for Figure 10.4. Find the values for the capacitor, inductor, and resistor. Compute the theoretical values of Vout (both magnitude and angle) and |AV = Vout / Vi | of the designed filter inTable 10.4-A.

A band-stop filter is a circuit that passes the voltages with frequencies outside of the specified bandwidth around the center frequency, and blocks the frequencies within the bandwidth around the center frequency. The circuit shown below in Figure 10.4 is considered to be a band-stop filter. R Vout Figure 10.4

Solution

A)

Typically, parametric equalizers are designed as second-order IIR filters. These filters have the drawback that because of their low order, they can present relatively large ripple or transition regions and may overlap with each other when several of them are connected in cascade. The DSP System Toolbox™ provides the capability to design high-order IIR parametric equalizers. Such high-order designs provide much more control over the shape of each filter. In addition, the designs special-case to traditional second-order parametric equalizers if the order of the filter is set to two.

This example discusses two separate approaches to parametric equalizer design. The first is using \'designParamEQ\' and the second is using \'fdesign.parameq\'. \'designParamEQ\' should serve most needs. It is simpler and provides the ability for most common designs. It also supports C code generation which is needed if there is a desire to tune the filter at run-time with generated code. \'fdesign.parameq\' provides many advanced design options for ultimate control of the resulting filter. Not all design options are explored in this example.

Some Basic Designs

Consider the following two designs of parametric equalizers. The design specifications are the same except for the filter order. The first design is a typical second-order parametric equalizer that boosts the signal around 10 kHz by 5 dB. The second design does the same with a sixth-order filter. Notice how the sixth-order filter is closer to an ideal brickwall filter when compared to the second-order design. Obviously the approximation can be improved by increasing the filter order even further. The price to pay for such improved approximation is increased implementation cost as more multipliers are required.

Designs Based on Quality Factor

Another common design parameter is the quality factor, Q. The Q of the filter is defined as Wo/BW (center frequency/bandwidth). It provides a measure of the sharpness of the filter, i.e., how sharply the filter transitions between the reference value (0 dB) and the gain G. Consider two designs with same G and Wo, but different Q values.

Although a higher Q factor corresponds to a sharper filter, it must also be noted that for a given bandwidth, the Q factor increases simply by increasing the center frequency. This might seem unintuitive. For example, the following two filters have the same Q factor, but one clearly occupies a larger bandwidth than the other.

Low Shelf and High Shelf Filters

The filter\'s bandwidth BW is only perfectly centered around the center frequency Wo when such frequency is set to 0.5*pi (half the Nyquist rate). When Wo is closer to 0 or to pi, there is a warping effect that makes a larger portion of the bandwidth to occur at one side of the center frequency. In the edge cases, if the center frequency is set to 0 (pi), the entire bandwidth of the filter occurs to the right (left) of the center frequency. The result is a so-called shelving low (high) filter.

A Parametric Equalizer That Cuts

All previous designs are examples of a parametric equalizer that boosts the signal over a certain frequency band. You can also design equalizers that cut (attenuate) the signal in a given region.