Consider the following 1-D function ‘f’ and filter ‘w’ CO 2, CO 3 (BL- 1,2,4,5)f: 0 0 1 0 1 0 0 0w: 1 4 2 2 8Illustrate the 1-D convolution of ‘w’ with ‘f’

Convolution is a mathematical operation that combines two functions to produce a third function. In the context of signal processing, it's often used to apply a filter to a signal. Here's how you can compute the 1-D convolution of 'w' with 'f':

1. First, flip the filter 'w' around. This gives us the flipped filter: 8 2 2 4 1.

2. Then, slide the flipped filter over the function 'f' from left to right, one step at a time. At each step, multiply the corresponding elements of 'f' and the flipped filter, and sum the results. This sum is the output of the convolution at that step.

3. Repeat step 2 until the flipped filter has slid all the way to the right end of 'f'.

Here's the step-by-step calculation:

• Step 1: (08) + (02) + (12) + (04) + (1*1) = 0 + 0 + 2 + 0 + 1 = 3
• Step 2: (08) + (12) + (02) + (14) + (0*1) = 0 + 2 + 0 + 4 + 0 = 6
• Step 3: (18) + (02) + (12) + (04) + (0*1) = 8 + 0 + 2 + 0 + 0 = 10
• Step 4: (08) + (12) + (02) + (04) + (0*1) = 0 + 2 + 0 + 0 + 0 = 2
• Step 5: (18) + (02) + (02) + (04) + (0*1) = 8 + 0 + 0 + 0 + 0 = 8
• Step 6: (08) + (02) + (02) + (04) + (1*1) = 0 + 0 + 0 + 0 + 1 = 1
• Step 7: (08) + (02) + (02) + (14) + (0*1) = 0 + 0 + 0 + 4 + 0 = 4
• Step 8: (08) + (02) + (12) + (04) + (0*1) = 0 + 0 + 2 + 0 + 0 = 2

So, the 1-D convolution of 'w' with 'f' is: 3 6 10 2 8 1 4 2.