Convolution

kernel_intuition

convolution_intuition_kernel_mean_value()

Effect of the kernel mean_value

1. Kernel mean value is positive

2. Kernel mean value is equal0

3. Kernel mean value is negative

convolution_intuition_kernel_size()

Effect of the kernel size

1. Large gaussian width

2. Narrow gaussian width

plank_taper

plank_taper_example()

create a plank taper kernel as passband filter

smoothing_filter_with_convolution

smoothing_filter_convolution_example()

Smoothing filter and convolution theorem

A convolution in the time domain in equal to a multiplication in the frequency domain

Time_domain :

$$\text{fsignal} = \text{convolution}(\text{signal},\text{kernel})$$

Frequency domain:

$$\text{fsignal} = \text{ifft}(\text{fft}(\text{signal})*\text{fft}(\text{kernel}))$$