More often than not, individuals have bother dealing with the Fourier rework of a sign due to its complicated type. Apart from very particular circumstances, the Fourier rework of a time sequence is more often than not a complex-numbered sequence — and complicated numbers should not at all times easy to understand, particularly if you end up not used to dealing with these sorts of numbers.
On this publish, I wish to present just a few methods to visualise the Fourier rework of a 1D sequence of actual numbers, which is what you deal with 99% of the time, particularly in knowledge evaluation and time sequence.
All photos by creator.
This publish is the third of my Fourier-transform for time-series. Take a look at the earlier posts right here:
- Assessment how the convolution relate to the Fourier rework and how briskly it’s:
- Deepen your understanding of convolution utilizing picture examples:
Earlier than diving into the precise computing and plotting of 1D Fourier transforms, we’ll overview just a few primary ideas of complicated numbers which can be essential to what’s subsequent. As you’ll see, complicated numbers are literally fairly easy: simply take into account them as a vector of two numbers.
The top purpose of this publish is to make you extra comfy with the precise numbers behind your Fourier transforms.
Any complicated quantity might be represented with its canonical type, utilizing 2 actual values, a and b, respectively referred to as their “actual” and “imaginary” elements:
the place i is the unit complicated quantity with the well-known property that for those who sq. it…