What is the difference between Filters and Windowing?

Question

I'm finding some difficulties to understand the difference between Filters, and Windowing.

accoriding to my understanding both filters and window functions will make changes to the input signal parameters, according to wiki,

Filter:

a filter is a device or process that removes from a signal some unwanted component or feature

Windowing:

a window function (also known as an apodization function or tapering function[1]) is a mathematical function that is zero-valued outside of some chosen interval.

---

What I'm trying to understand is this,

1. Where do we use these windowing functions & Filters in practical world?
2. Do I need to use both for better signal quality, if so which one come first(Filters => Window or Window => Filters)?

Answer 1

Filters and windows complement each other, in a way. This is due to the convolutional lemma of the fourier transform.

Let me expand on that. A filter would be a convolution of a signal with another. In a technical sense, a window has a fixed (supposedly short) size and is seen as "cutting out" a short part of the signal. Often, a DFT would follow.

In the fourier domain, convolution and point-wise multiplication trade places, so a convolution in the time domain is a pw. multiplication in the fourier domain and vice-versa.

A filter scales the spectrum with a known frequency response. A window will filter the spectrum instead.

Filters and window functions often (but not always) have different design goals. For example, in a filter you would have rather large bandwidths. Windows percieved as useful have a small bandwidth (often, just a few samples). You can talk about both kinds in the same terms, you just have to remember that both are used in different contexts.