What effect does a first-difference filter have on a signal in digital singal pr

Question

What effect does a first-difference filter have on a signal in digital singal processing? So I ran a signal through a first-difference filter. The results are below. So what exactly would a first-difference filter do to signal or an image? Is it downscaling? What is it filtering example? I just need an explanation of what it does exactly and why the output signal looks how it does. Thanks!

Input: x2 =255*(rem(1:159,30)>19;

first-difference: f=[1 -1]

Figure 1 File Edit View Insert Tools Desktop Window Help Input Signal 300 200 S 100 100 120 140 160 20 40 60 80 Sample Number Output After First Difference Filter 400 ET 200 O-200 -400 20 80 100 120 140 160 40 60 Sample Number

Explanation / Answer

the derivatives in discrete domain is equivalent to differences

first derivative of F(x),

F'(x)=F(x-1)-F(x)

For first derivative

1-must be zero in the region of constant value.

2-must be non zero for the change in the value.

Differentiation is equivalent to low pass filtering if you apply differenttiation on image the you get the edges and edges in the Image is a high frequency component.

In the given example the derivative is zero where the values are constant but we get non zero values where the values are changing. for every change in step in the X[n] we get non zero value and that value is equal to the change in setp.

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