I am working on a Digital Down converter (DDC) in xcos. I need to know whether an integrator and a LPF are same.
What is the difference between an Integrator and a Low pass filter?
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There are many different kinds of low-pass filters.
An integrator is one kind of low pass filter. It's a "filter", because it is linear and time-invariant (LTI), and it is "low pass" because its low-frequency response is bigger than its high-frequency response.
But perfect integrators are not typically used by themselves (in DSP) for any tasks that you would call "low-pass filtering". They are unstable at DC, and their response is far from optimal for filtering jobs. Certainly a digital down-converter requires a much better, purpose-designed, low-pass anti-aliasing filter.
But the electronic circuits called "integrators" are imperfect integrators. These kinds of circuits are easy to construct, and with different component values can actually be useful for filtering. They can still be referred to as "integrators" in that case.