How to update my C# WPF binding?

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C#

WPF

Hi I am new in WPF.
As you see in this picture:
http://api.ning.com/files/3FX8CRo2Q3IZ...
I have a textbox that filters items of listbox.
This is my WPF code:

<Grid>
    <TextBlock Height="23" HorizontalAlignment="Left" Margin="28,31,0,0" Name="textBlock1" Text="Filter Tags:" VerticalAlignment="Top" />
    <TextBox Text="{Binding Path=FilterText,Mode=TwoWay}"  Height="23" HorizontalAlignment="Left" Margin="91,28,0,0" Name="textBoxFilterTags" VerticalAlignment="Top" Width="120" TextChanged="textBoxFilterTags_TextChanged" />
    <ListBox ItemsSource="{Binding Path=Filter}"  Height="178" HorizontalAlignment="Left" Margin="12,71,0,0" Name="listBoxTags" VerticalAlignment="Top" Width="254">
        <ListBox.ItemTemplate>
            <DataTemplate>
                <StackPanel Orientation="Horizontal">
                    <CheckBox IsChecked="{Binding Path=Tick,Mode=TwoWay}" Margin="3,1,1,1" />
                    <TextBlock Text="{Binding Path=Name}" Margin="3,1,1,1" />
                </StackPanel>
            </DataTemplate>
        </ListBox.ItemTemplate>
    </ListBox>
</Grid>

my listbox is binded to a property called:

public ObservableCollection<tagtick> Filter
{
    get
    {
       .... // filtering based on filter text
    }
}

Now, my problem is that when I type in the filter text, the listbox should update the filter. I tried using UpdateSourceTrigger but it didnt work. can some one tell me how to trigger the binding update when the text of textbox change?

Thanks in advance.