I find it very helpful to think functions as vectors for understanding Fourier Transform. I learned communication systems and digital image processing but had a hard time to understand FT. Relating FT to a linear map makes me feel less scared of it :)
dtorresr
It is helpful indeed! Seeing it as a type of linear map really helps you understand the basics of the Fourier Transform.
Azure
At this slide around 1:26:40 I think it's Bb3, F4, and Bb4?
shengx
I guess to prove cos(nx) and sin(mx) are orthogonal for any m,n, we can use the fact that the integral from -pi to pi of cos(nx)sin(mx) = 0. This is because cos(nx)sin(mx) is an odd function.
I find it very helpful to think functions as vectors for understanding Fourier Transform. I learned communication systems and digital image processing but had a hard time to understand FT. Relating FT to a linear map makes me feel less scared of it :)
It is helpful indeed! Seeing it as a type of linear map really helps you understand the basics of the Fourier Transform.
At this slide around 1:26:40 I think it's Bb3, F4, and Bb4?
I guess to prove cos(nx) and sin(mx) are orthogonal for any m,n, we can use the fact that the integral from -pi to pi of cos(nx)sin(mx) = 0. This is because cos(nx)sin(mx) is an odd function.
The last comment is very helpful!